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Impatient at Gods skill at matching
By JEANNETTE BATZ
The rooms glowing with camaraderie -- or is it the pain pills? Ive celebrated my 40th birthday by throwing my back out, and now Im high on codeine and even the toasters glowing. Wait -- thats toast for my moms famous deviled ham canapés. I watch her feed one to my friends baby boy, cuddling him close on her lap and stroking the crumbs from his fat cheeks. If only she had a grandbaby of her own, I think ruefully.
Then I realize its a double miss -- my friends parents, never much enamored of even their own children, have barely noticed her firstborn. She hides her disappointment well -- right now shes talking brightly about politics -- but she keeps glancing over at my mom and smiling.
Two other friends have sunk deep into the sofa, their laps burdened with shrimp. Ones a gay man whose partner, Tom, nags him constantly to care more about their house: How can he be such a slob and travel all the time and forget to tell the lawn care people about the underground sprinklers? The other, Jean, has an expatriate husband who just put the Atlantic between them, claiming he could no longer face their cozy suburban life and its incessant home improvement projects.
Shame Toms not straight, I think idly, or he and Jean could do the Martha Stewart thing and set the other two free. My eyes rove around the room, falling next on an intelligent, coolly fastidious woman fresh from an Edith Wharton novel. Her husband, standing with impeccable formal courtesy at her side, longs for kids and a dog and a yard -- all of which represent her idea of hell, or at least a bad sitcom. Theyre being introduced to a new couple that, unbeknownst to them, are their mirror image, with the wife yearning for a baby and the husband unable to even say the word without freezing between syllables.
Impatient at Gods lousy matching skills, I shake my head sharply, and the Vicodin wooze free falls into my stomach. Maybe the Israelis had the right idea with the kibbutz, I think queasily. Maybe you need at least 50 people cooperating before everyones dreams can be fulfilled.
Or did we all sabotage ourselves, gravitating toward the very people who could not complete us?
I take the baby onto my lap, wondering if I would have felt more comfortable with this moist helpless bundle of joy if my mom, who sacrificed huge chunks of her life to raise me, hadnt urged me in a different direction? The babys mom, on the other hand, is determined to create the nurturing home she never quite experienced herself. My gay friend might be tired of being chastised about the housework, but he was drawn to Tom in the first place because living with him meant creating a home. My friend who yearns for a yard and kids yearned even more fiercely for a woman who understood his old-fashioned ways.
Pascal wrote of the God-shaped vacuum in each of us, but he forgot to mention the gaping holes left by all our unmet needs and buried dreams. Surely this is the very stuff of tragedy, the curse of being human?
My husband is watching the baby, his eyes soft. When he glances up I expect a twist of pain at our decision, and instead what flies between us is more tenderness, a shared acceptance of what we have and what well miss. The babys mom is hugging my mom goodbye with extra warmth. My friends on the sofa are engrossed, the shrimp plates teetering as they each labor to explain the baffling behavior of the others absent partner.
Gradually the Vicodin wears off, and my all too human body makes its limits known. The limits might be painful, I decide, but theyre not tragic in the least. Our unmet needs teach and shape and soften us, even more than the dreams we manage to fulfill.
The holes might look random and hollow, but they open a way to the God shape.
Jeannette Batz is a staff writer for The Riverfront Times, an alternative newspaper in St. Louis. Her e-mail address is firstname.lastname@example.com
National Catholic Reporter, April 27, 2001


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Dr. David Sprouse
- Family Medicine
- Kerrville, TX
- Languages supported at his practice: English, Spanish
Dr. Sprouse's Background
David R. Sprouse, MD is a practicing Family Practitioner in Kerrville, TX. Dr. Sprouse graduated from The University of Texas School of Medicine at San Antonio in 1986 and has been in practice for 31 years. He currently practices at Family Practice Associates and is affiliated with Peterson Regional Medical Center. Dr. Sprouse accepts multiple insurance plans including Aetna, Medicare and Humana. In addition to English, Dr. Sprouse's practice supports this language: Spanish.
Hospital Affiliations
- Peterson Regional Medical Center
- Medical School, 1986
- The University of Texas School of Medicine at San Antonio
- San Antonio, TX
Learn More About Family Medicine
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Choosing a Dentist You'll Want to See (Again and Again)Maybe you've recently moved, or your old dentist retired, or you've had a bad dental office experience. Whatever the reason, you're on the hunt for a new dentist. Where should you start? What qualities ...Read More
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When you and a friend or family member both enrol on any one of our courses together, you will each receive a 15% reduction on your course fees. The StudyMate Plan is also ideal for therapists who intend to train to set up a business together.
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If you would like to register on the plan please click on the Plan Enrolment button below:
You are eligible to enrol on our NUS Extra scheme for just £9.99 and claim big discounts. As a registered Stonebridge student, you can use the NUS extra card to get money off:
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We are delighted to present you with this list of current new business executive job vacancies in glasgowClick on a job title to view the job details in full.
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Thousands of top recruiters are currently searching our CV database, so register your CV now and search through thousands of fresh vacancies - www.cv-library.co.uk
Business Development Executive / Field Sales Executive – WEEE / Electrical Recycling IT Sales
Client: Red Kite Waste are working on behalf of one of the biggest names in the Electrical Recycling / ... more about Business Development Executive - IT Sales
dnata Travel, part of the Emirates Group, includes the brands of Gold Medal, Travel 2, Netflights, Travelbag, Travel Republic, Global Travel Group and Sunmaster. These brands are based at offices across the UK including London, Kingston-upon-Thames, Chester, Preston, Halifax and Glasgow.
We are now recruiting for a Product & Commercial Executive – Specialist Product, based in Glasgow. You will ... more about Product & Commercial Executive
Position: Specification Sales Executive (will suit a Business graduate with at least two years of specification sales experience)
Location: Scotland - Home Based with travel
Salary: Competitive, company car, bonus, pension and healthcare
Sector: HVAC / Heating / Plumbing / Engineering products
Our client is a leading international company which operates in the HVAC / plumbing ... more about Specification Sales Executive
Scotstaff are currently recruiting for a Glasgow city centre based client, we are looking to find candidates with experience in B2B sales. In a highly motivated department you will be calling prospective clients and developing leads for the experienced sales team.
We are looking for an ambitious new Business Development Executive to join our established sales operation targeting mid-corporate ... more about Business Development Executive
Topstaff has an exciting opportunity with our client, one of the UK's market-leading suppliers and distributors of housewares and home lifestyle products.
Due to continued success and growth plans for 2017 and beyond, they are looking to recruit an experienced, motivated and driven Telesales Executive to join their B2B telesales team.
You'll be tasked with making outbound telesales calls to ... more about Tele-sales Executive
BUSINESS DEVELOPMENT EXECUTIVE, BASED IN GLASGOW, covering Scotland wide territory (with emphasis on CENTRAL BELT).
This is a Field based role, ideally with 1 day a week based in the Glasgow city centre office and 4 on the road (client facing).
£(Apply online only) plus Car, Mobile, Laptop, Bonus and Benefits
Well established Scottish based organisation (established over 150 years), with its ... more about Business Development Executive (Scotland)
Sales Executive - Legionella Control and Management
FPS are currently recruiting for one of Scotland's largest providers of legionella control and management of water systems. They manage a large portfolio of industrial, commercial, local authority and government owned buildings.
To continue the growth of the company and improve the size and diversity of the business market spread, they are ... more about Trainee Sales Executive – Legionella Control and Management
Commercial Account Executive Opportunity
Up To £45k Basic + Array of Company Benefits + Bonus
Would you like to join a leading, regional Insurance Broker in Glasgow? Would you like an opportunity to build up a portfolio of clients and grow the book organically with new business?
IDEX Consulting are offering candidates the chance to apply for an opportunity to grow within an ... more about Commercial Account Executive
Salary Details: £18000 - £20000
Customer Service Executive- Glasgow- Permanent- Full Time- £18000 - £20000 + Bonus Scheme
Are you looking for a new customer services opportunity, working for an exciting, reputable and growing business?
If so, Interactive Investor are currently recruiting for Customer Service Executives to join their growing Customer Services Team. We are looking for ... more about Customer Service Executive
The Client
The client is a well-established name in the Glasgow area with a worldwide client base. They are looking to recruit a new Telesales Executive to sit within their Sales and Marketing team.
The Role
The role is to ultimately to generate GP and provide business exposure, and so duties will include:
• Get to know company and product range
• Self-generate leads
• Cold call businesses, ... more about Telesales Executive
Role: Graduate Field Sales Executive
Location: Glasgow
Salary: £24,000 (£28K OTE)
Ref: J2160SCOGJGFSE
Industry: Manufacturing
Our award winning client is the leading manufacturing player in their market niche! They`re looking for their next graduate intake in order to enhance the company`s presence further!
Benefits/What you get:
- A very competitive starting salary of £24,000
- Superb Y1 ... more about Graduate Field Sales Executive
Find your perfect business partner.
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At RAC Direct Sales we are changing our business model and very excited about our new proposition.
We are looking to recruit entrepreneurs who want to run their own RAC Direct Sales business.
We welcome you to join our club - to run a business with a proven business model in ... more about RAC Venue Based SALES AGENTS - Great Self Employed Opportuni
We are currently recruiting for a driven business to business sales executive to work at our clients head office in Glasgow city centre. preffereably with a background selling in I.T or similar
previous B2B sales is essential for this role.
The ideal candidate will have a strong sales background and posses the ability to work independently generating new business and growing revenues through ... more about B2B sales (I.T background preferred)
Telesales Executive
Monday – Friday Office Hours
£20 – £25K basic, OTE £45K + industry leading perks
The Client
The client is a well-established name in the Glasgow area with a worldwide client base. They are looking to recruit a new Telesales Executive to sit within their Sales and Marketing team.
The Role
The role is to ultimately to generate GP and provide business ... more about Telesales
We are currently recruiting for a Proposal Manager within our Business Development Group, based in Glasgow, Edinburgh, Birmingham or London. Joining an established Proposals Team and centre of excellence, the successful candidate will report to the Head of Proposals, bringing skills and enthusiasm for supporting the production of high-impact proposals and pitch materials.
Key ... more about Proposal Manager
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Tip Top Job site is an online recruitment service for jobseekers to search jobs and recruiters to advertise job vacancies in the UK and worldwide. Search and find a job today!
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Rate Photo
Jul 25, 2015
"A picture of the Cauliflower Couloir hanging up in the Tsaina Lodge detailing the World Extreme Skiing Championships. The far right green line is the descent that Doug Coombs took to win the tittle that year. Sorry about the picture quality from the glare on the glass frame."


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The Governing Body of Holy Trinity seek to appoint to the following posts
Further information and application forms are available online at www.holytrinitybarnsley.org. All Holy Trinity application forms should be returned to Holy Trinity marked for the attention of Miss Y Taylor, PA.
Relief Catering Staff / Cook 1
£8.46 / hour
Holy Trinity is a 3-16 Catholic and Church of England through school – opened in September 2012 it benefits from excellent facilities both for pupils and staff. It has a 700-place secondary phase and a 470-place primary phase.
o Are you interested in working in busy, productive environment?
o Do you want to work within a dynamic and committed Catering Team at Holy Trinity and be instrumental in providing healthy and nutritional meals to our students?
o We welcome team players who are ready to contribute to the ongoing success of our Catering Team.
The Catering team offer a breakfast service through to lunch for pupils and staff. Relief hours are flexible and support the permanent staff covering for holidays and absences due to illness.


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pear, pistachio, frangipane tart from the "top with cinnamon" cookbook
Parmesan Crusted Chantilly Potatoes - sounds like the perfect steak side dish.
This clever take on beloved thumbprint cookies is sweet and savory. Refrigerated dough keeps for days, and the baked cookies freeze well. Recipe: Cornmeal Thumbprint Cookies with Tomato Jam


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This Multiplication worksheet may be configured for 2, 3, or 4 digit multiplicands being multiplied by multiples of ten. You may vary the numbers of problems on the worksheet from 12 to 20.
This multiplication worksheet is appropriate for Kindergarten, 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, and 5th Grade.
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Mom Blog
Mom Blog
A woman can't stop yapping about this and that. She is loud. Maybe she is angry. She is ok because she let out her negative emotion.
However, when she goes silent, she is not ok. She is upset with negative emotion.
When a man feels unpleasant, he can't keep his mouth shut. He is in the fighting mode, or he may want to beat someone. When he goes silent, he is ok. He is just thinking.
Therefore when your wife goes silent, apologize to her.
When she can't keep her mouth shut, let her talk.
When your husband goes silent, don't force him to talk.
When he can't keep his mouth shut, hug him.
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Mind Your Words
Researchers had proved that 0~6 years old children would absorb all the information into their mind without filtering. What your child heard from you get soaked into his mind like water into the sponge which will result in shaping their blueprints of beliefs in their whole life. If you always say "no" to your child, he or she would imprint subconscious beliefs that:
I'm not worthy.
I'm not good enough,
I'm not smart enough.
It's selfish for me to want more. I should be happy with what I have. I don't deserve it.
I can't get what I want. Even if I try, I will fail.
I've already tried everything and nothing has worked.
Nothing ever works out for me.
I'm going to humiliate, shamed or look ridiculed
Motherhood life is an endless loop of sleepless nights and tons of stress. Your mental strings are pulled tight as a violin. Don't be angry or disruptive to your kids merely because you can be. Words carry weight. Just like the toothpaste, you can't take back the words once the words leave your mouth. Mind your words carefully. What you say and what the child hears may not the same thing. Don't let a single day go by without telling the child (via power of positivity):
I know you can do this
I believe in you
I trust you
You are special
I'm proud of you
You make me happy
I like it when you do such good thing
I'm grateful for you
I love you
When you……., I like it
You are doing great
You are a good child because…..
You're amazing
Oh! When you………., this show you had grown up
Do you know that you can't do that in one year before and now you can?
You do it by yourself! Good job.
1. Coffee. Prolong My Working Hours in a Day
People said that coffee helps to prolong our working hours in a day. Over-drink may have the risk for iron deficiency for women. But when you sip a cup of coffee, relax, it stimulates your energy and brings the feeling that everything is ok. Bad coffee is bitter, sour, burnt, and astringent. Good coffee is sweet, fruity, chocolaty, smooth, and light bodied. I like my coffee like a gorgeous woman ~ hot and good taste. Make the D.I.Y. Flat white with latte art without using an espresso machine is easy.
2. Lemon Ginger Water. Help to Weight Loss
We don't want to consume the artificial beverage too much which is negative to our health. Ever wonder why is lemon juice made with artificial flavor, and dishwashing liquid made with real lemons? Let's make your own natural flavor lemon ginger water.
Ingredients: Lemon, ginger, raw honey
3. Fruits & Green Juice. Natural Flavor Drink
A mom, feminine optimistic style, love to travel. Addict to coffee
November 2017


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Spirit vs Led Zeppelin Stairway to Heaven Plagiarism Lawsuit
One of the most popular songs in music history is being questioned for plagiarism in an upcoming court case. Stairway to Heaven by Led Zeppelin may have ripped off the song Taurus by the band Spirit which was released in 1968. The lawsuit is coming from the estate of the late Randy California who wrote the song for Spirit, and it's no coincidence that this is happening right before of the release of a remastered version of Led Zeppelin IV. Francis Alexander Malofiy, the attorney for Spirit, will attempt to get a songwriting credit for California on the song. Stairway to Heaven, which is worth an estimated $560 million, can be heard on every classic rock station in the world and even was famously denied by Wayne Campbell at the guitar store in the first Wayne's World movie.
Jimmy Page supposedly wrote the song (which he refers to as his baby) using the powers of black magic and candles in 1970. Randy California died in 1997 when he saved his son from drowning in Hawaii. Before his death, he told Listener magazine that he believed that Led Zeppelin ripped him off, and was pretty miffed about it. Both bands were on similar bills in the late 60s, so it's very probable that Jimmy Page heard Taurus during that time. Listen to the audio clip of Taurus via the YouTube video below and you will hear that iconic guitar magic. It would be difficult to nail down who initially came out with this very basic chord progression, probably somebody before 1968, but this could be a giant payday for the Randy California family. Maybe they will sing the got $5000 song like Wayne and Garth did in the movie, but add some zeroes to it.
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Knipfel, Jim
AbeBooks Seller Since December 11, 1999Quantity Available: 1
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About this Item
Bibliographic Details
Title: Slackjaw
Publisher: Tarcher
Publication Date: 1999
Binding: Hardcover
Book Condition:Fine
Dust Jacket Condition: Fine
Edition: First Edition
About this title
A staff writer and columnist with the New York Press describes his battle with retinitis pigmentosa, a rare and untreatable genetic disease that results in blindness, and an inoperable brain lesion, in a memoir that celebrates the triumph of the human spirit and determination. 15,000 first printing.Review:
Who would have thought a memoir about going blind and suffering from severe depression could be so funny? From the opening scene, when an uncle who has the same degenerative eye disease warns 12-year-old Jim, "You better start learning Braille now," Knipfel defies all the conventional responses to adversity. You can't help but laugh when a doctor "who had obviously been playing hooky when they were teaching sensitivity in medical school" tells a wailing woman who has just learned her son is dying, "Please sit down... [he] has a good two or three weeks yet." The hard-edged humor comes naturally to a guy who as a grad student formed a band called the Pain Amplifiers; we're not exactly surprised to learn that his column for an alternative newspaper prompted hate mail as well as fan letters. Knipfel's complete lack of self-pity conveys the particulars of failing vision with blunt immediacy (he wears a wide-brimmed hat so he'll feel impending lampposts before he knocks himself senseless against them). His zest for the world's absurdities makes this book an exhilarating guide to "the weirdness parade I have been marching in my whole life." --Wendy Smith
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The Way to Sell Your House Fast for Money
We can't always plan for the future and sometimes the unexpected can happen. There are lots of reasons why a quick house sale for cash may suit your needs without necessarily having to use ways to sell my property without a realtor therefore selling your real estate as is. Should you want to relocate or emigrate quickly consider, by way of example: a house sale's drawn out process could be impractical or even impossible especially if I buy houses for cash tampa. Or a home buyers with cash can keep your credit rating intact and discharge the stress of debt we buy homes with our own 39, weighing you down if you're having problems paying your mortgage payments. Selling a house is stressful at the best of times especially when you thin on how to sell your house to investor, but with these added considerations it can become both a financial and emotional drain. Using a cash property buyer could be the solution you are looking for as you can be selling your home without paying commissions to legit cash home buyers in tampa since you will get quick house sell solution in Tampa FL. Sell house quickly in Tampa Florida to Rochell cash property solutions and get cash for your house in Tampa.
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This is a set of Perl modules for keeping track of the metadata associated with software packages. The idea is to be able to read and write RPM spec files, the files that control Debian packaging, and the like.
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San Jose firefighter suspected of molesting boy
Updated 4:37 pm, Friday, February 14, 2014
A veteran San Jose firefighter has been arrested on suspicion of molesting a boy, authorities said Friday.
Mario Enrique Cuestas, 53, of San Lorenzo was arrested at work Thursday by a Santa Clara County task force led by the state Department of Justice, said Special Agent Michelle Gregory.
Cuestas allegedly provided methamphetamine to the boy and molested him, Gregory said. A tip prompted the investigation that led to his arrest, she said.
Agents seized a computer from his office, Gregory said, as part of the investigation.
"We do not tolerate any type of behavior that's outside the law," said Capt. Cleo Doss, a spokesman for the Fire Department. "This is very unacceptable."
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According to Cuestas' Facebook page, he has been with the Fire Department since 1994. Since 2012, he has also been a choir singer with the Roman Catholic Diocese of San Jose.
Cuestas was being held without bail at County Jail in San Jose and is to appear in court Tuesday.
Henry K. Lee is a San Francisco Chronicle staff writer. E-mail: firstname.lastname@example.com Twitter: @henryklee


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I received the guitar today. It's even better than I hoped it would be. The Tennessee Waltz brought my wife in smiling from the other room. Thank you for the excellent service.
I picked up a Strat on Saturday, and was helped by Nevin. He was extremely helpful, and knowledgeable about the differences in the models. Once I made my selection, he set it up for me and showed me how to make minor adjustments myself.
Overall, great service and a great shop.
I'm sure I will enjoy it thoroughly. I had also contacted an instructor and will be setting up some lessons in the near future. Grant, your help has been wonderful and you will be getting great word of mouth reviews from this satisfied customer!
Got the guitar yesterday, you guys did an awesome job. If I didn't know there had been an issue I would never be able to tell. Please relay my thanks to the boys, that's serious pro work!
Max, just writing to let you know that this guitar is awesome! Very impressive in every way. I'm keeping it for sure. Thanks!
I had the biggest surprise of my life for my birthday: the guitar of my dream (I tried in Madrid last October). I never thought it would be mine. It is an EXTRAORDINARY FLAMENCO GUITAR; the sound is just amazing.


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Instrut Panel Wiring Diagram
Posted by Brenda Botha in Instrut
Tagged with : #instruct scitraining.#antonyms for instruct.#instructs informally.#crossword instruct.
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Watch Lip Sync Battle - Season 1 (2015)
Director: Casey Patterson Entertainment
Production Co:Casey Patterson Entertainment,Eight Million Plus Productions,Matador Content
Genre: Music
Country: USA
Episode: 19 / 19
Duration: 30 Min
Quality: HD
Release: 02 Apr 2015
View: 4522


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Explore Rome Italy and more!
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"Michael Angelo" painting on the ceiling of the Sistine Chapel, Vatican City, Italy. **I am pinning this because of the way they spelled "Michelangelo!


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Ask Professor Puzzler
Do you have a question you would like to ask Professor Puzzler? Click here to ask your question!
"If the two triangles shown are similar, find the value of d/c. I know the answer is 5/6, but I don't know how to get it." ~Kimberly
Good morning Kimberly. As we look at this question, I'd like to point out that it does violate one of our standard rules of geometry - which is that we never assume the diagrams are drawn to scale. The problem writer clearly intends for you to assume that the lines which appear to be horizontal really are horizontal, and the ones that appear to be vertical really are vertical. If you make that assumption, then you can conclude that the side of length 7.5 corresponds to the side of length d, and the side of length 9 corresponds to the side of length c. So we'll go with that assumption.
Since the triangles are similar, and we "know" which sides are corresponding, we can set up a ratio:
7.5/d = 9/c.
This does not give us what we want (d/c). However, we can rearrange that with just a couple steps to obtain the desired result. First multiply both sides by d, to get it in the numerator:
d(7.5/d) = d(9/c)
7.5 = 9d/c
Now divide both sides by 9:
7.5/9 = d/c
This is the ratio you want, except that it's not in simplest form. Multiply numerator and denominator by 2 in order to get rid of the decimal:
7.5/9 = 15/18 = 5/6.
And there's your answer. But I'm not quite done - I'd like to point out something that might be valuable to you. This problem shows us something very interesting that I often make use of when doing similar triangle problems.
We started with a ratio of corresponding sides, and when we were done, we ended with a very different ratio - the ratio of sides within a triangle.
Your standard rule is: The ratios of corresponding sides in two similar triangles are equal.
Our alternate version (which you can call the Kimberly Rule, if you want) is: The ratio of any two sides in a triangle is equal to the ratio of the corresponding sides in a second, similar triangle.
In other words, you could have started out with d/c = 7.5/9 instead of starting out with 7.5/d = 9/c.
I had a student ask today why Cramer's Rule works. That's the sort of question I love, but we didn't have time in class to work through it, so I thought I'd post the exploration of the question here. We'll consider the case of a system of two equations in two unknowns.
Cramer's Rule says that if you have a system written as follows:
ax + cy = e
bx + dy = f
Then we can find the values of x and y by evaluating the following determinants.
In case you're not familiar with determinants, we find the value of a 2 x 2 determinant by multiplying the numbers along the primary diagonal (top-left to bottom-right) and then subtracting the product of the other diagonal. Thus, this could be rewritten as follows:
So that's the form we're going to consider. Ideally, we'd like to show that given the system we started with, the solutions can be written in the form directly above.
If you were solving a system of equations with numeric coefficients, you might find the least common multiple of the coefficients of x, and then figure out what you need to multiply each equation by in order to get those coefficients to cancel. Unfortunately, we don't have numeric coefficients, but we can still do this process. What is the LCM of a and b? Why, it's the product of a and b! So we'll multiply the first equation by b, and the second equation by -a:
bax + bcy = be -bax - ady = -af
Adding these two equations gives us
bcy - ady = be - af
y(bc - ad) = be - af (factor out y)
y = (be - af)/(bc - ad) (divide both sides by (bc + ad)
Now, that doesn't exacly match the result we expected, but if we multiply the top and the bottom by -1, we get:
y = (af - be)/(ad - bc)
That's only half of the problem, of course; we've shown that the "y" formula works; now we just need to show that the "x" formula works.
And you know what? We'd show it exactly the same way, except we'd start by eliminating y instead of x. I'll leave that to you to work out on your own. And, of course, once you've finished that, you can develop your own proof for systems of three equations in three unknowns!
"I keep hearing about people who are good at math and music. But that seems so strange -- music is so artistic and flowery, while math is so technical and straightforward. How could either have anything in common with the other?" ~ Laura from Maine
Hi Laura, thanks for thre great question. I wish I could give you a solid scientific answer to this question, but the inner workings of the brain definitely are not in my field of study. Instead, I can give you some observations about both math and music, based on my own experiences as a mathematician and a musician.
First, I can confirm that what you said is typical in my experience - it is very common for people who are good at music to also be good at math (and vice-versa). Obviously, that's not a 100% rule (probably not even close!) but it is common enough that my high school math teacher used to refer to his best students as his "M & M students." Not because they liked chocolate in a candy shell, but because they excelled in both Math & Music.
So what's the connection? I'm going to suggest three connections: patterns, precision, and creativity.
Patterns in Music
Music is filled with patterns. That can be seen in the simplest of ways: a couple days ago I sat down with my five-year-old son and taught him a little bit about the piano. I showed him how to find the note C by looking for patterns. There are sets of three black keys, and there are sets of two black keys. C is any white key that comes right before a set of two black keys. From there, he could find any C on the keyboard. I showed him that the note names go from A to G, and then start over at A. From there, he could start at the low end of the keyboard and name every single white key on the piano. Patterns.
Eventually he will discover that there are certain intervals (major thirds, minor thirds, etc) that sound really nice together, and others that don't sound quite as nice. He'll discover that those intervals can be shifted up and down the keyboard by octaves, and then he'll discover that they can be shifted by other amounts, and the sound is just as nice.
Musical compositions are also filled wtih patterns. Just listen to Vivaldi's Four Seasons, and you'll hear the same "figure" repeated throughout a movement. Starting on one note, and then on another note, then with some variations to the pattern, but always with a pattern that your ear catches and hangs on to. Some of the most memorable classical compositions are the ones that have memorable patterns that appear over and over (think of "dum-dum-dum-DUM" in Beethoven's fifth symphony, or the themes of Rossini's "The Barber of Seville" and "William Tell Overture" - and if you're not familiar with those two compositions, think of Bugs Bunny as a barber, or the Lone Ranger).
Patterns crop up in more modern music as well - the pattern of verse-chorus-verse-chorus-bridge-chorus is one that gets repeated over and over again in popular music. Your brain processes those patterns even if you're not consciously aware of them.
As an added bonus: most of the patterns we notice in music have a mathematical reason why they exist. For example, an octave is an interval that sounds good because the frequencies of the notes are in a ratio of 1:2.
Patterns in Math
I'm not sure I even need to say that math is filled with patterns. It seems intuitively obvious. But let's consider just a couple things. First, I remember how fascinated I was when I first discovered the nine-times-table:
9 x 2 = 18
9 x 3 = 27
9 x 4 = 36
9 x 5 = 45...
...and so on. As the tens place increases by one, the ones place decreases by one, and in each case, the sum of the digits is 9. What a fascinating pattern.
Fibonacci was famous for discovering patterns, and exploring how they related to the natural world around us - for more on Fibonacci, you might want to consider this book, reviewed here by Book Scrounger: Blockhead: The Life of Fibonacci.
A couple days ago my son went for his yearly checkup, and his doctor commented that math learning at his age is all about finding patterns.
People who like looking for patterns will naturally be drawn to either math or music, or both.
Precision in Music
If you've ever taken music lessons, you understand this one. I remember, as a violin student, being expected to be very precise about a lot of things: how I hold the bow, how I hold the violin, where I put my fingers, how I draw the bow across the strings. And then I'd do scales over and over again, with my teacher telling me, "That C-sharp isn't sharp enough." or "Your bow is way down on the fingerboard." Getting good at playing a musical instrument requires a fairly stubborn and determined mindset to get it right. For a violin student, "getting it right" is sometimes a matter of a miniscule fraction of an inch one way or the other.
So when you said that "math is technical," my response to that is: so is music! Students who can't master the technical aspects will not excel.
Precision in Math
The same stubborn, determined mindset that makes someone decide they're going to practice a D-major scale until they get it right is necessary for a good math student as well. In elementary school it's memorizing those math facts. Then it turns into more and more complicated processes (arithmetic algorithms, arithmetic operations on fractions), and eventually the student is faced with complex algebraic and even calculus problems. And good math students practice these over and over again (it's why those cruel and nasty math teachers assign homework; doing 20 math problems is like practicing your D-major scale over and over and over again). You don't get that kind of precision any other way.
People who have the determination to keep practicing things are more likely to excel in math or music, or both.
Creativity in Music
Eventually, every violin student who sticks with it long enough gets to the point where their teacher says, "Okay, it's time to learn about vibrato." What is vibrato? Vibrato is, according to one dictionary: "a rapid, slight variation in pitch in singing or playing some musical instruments, producing a stronger or richer tone." In a sense, vibrato is a breaking of the rules, because you've been trying desperately to play in tune, and now your teacher is giving you permission to play out of tune. In fact, your teacher is demanding that you play out of tune. In my mind, it was at that moment that I moved from parroting to interpretation. You are no longer at the mercy of the musical composition; the notes on the page become a vehicle for your own personal expression. And vibrato is just one thing - whatever musical instrument you play, as you advance, you will discover more and more that there are ways to express yourself through creative use of the technical skills you've acquired. You've become creative.
And, do I need to mention? Writing musical compositions is a wonderful task in creativity!
Creativity in Math
Really? Math is "creative"? Sure it is! Math is problem solving! Math is curiosity, and exploring beyond what is known. When I graduated from high school, on Class Night, my math teacher presented me with a our school's highest math award, and at the same time presented me with a notebook which contained every math problem I'd solved during my independent study math course that year. What's the big deal about that (you might ask)? The big deal is that every one of the problems I worked on that year was a problem I made up myself, or decided to challenge myself with. Whether it was proving the quadratic formula, deriving a formula for the inverse of an N x N matrix, developing my own theorems, or just posing mathematical questions to myself and trying to solve them, I spent the entire year being creative. And that creativity is what makes a mathematician. Being a good mathematician doesn't mean being able to multiply 324 x 16.9; that's just the precision practice (like learning a musical scale); being a good mathematician means being able to take those skills you've practiced, and put them to use in new ways to solve problems you haven't solved yet.
When I have students who want to take my math classes as "honors level" classes, I expect problem solving from them; I expect them to take the things they've learned and put them to use in brand new ways that they've never thought of before. I expect them to combine two mathematical ideas that they've never used together before, and use them to develop a solution to a problem they didn't think they could solve. I expect them to get creative.
People who are willing to use the tedium of repeated practice to explore new ideas and new ways of doing things will excel at either math, or music, or both.
"There is geometry in the humming of the strings, there is music in the spacing of the spheres." ~ Pythagoras
"I hate converting degrees to radians and the other way. Degrees seem simpler why can't we just stick to that?"
Good question! Degrees have been around for a long time. There are varying theories about where the unit originated. Some suggest that 360 comes directly from the Babylonians' sexagesimal (base 60) system; 360 = 6 x 60.
Others suggest that 360 was chosen because it is (approximately) the number of days in a year. Thus, a degree is roughly the angle traversed by the earth in a single day.
One thing that is certainly true: in the days before calculators, having units based around highly composite number would have been convenient for division purposes. 360 is highly composite, having 24 factors. Look at it this way. If you wanted to divide a circle in half, thirds, fourths, fifths, sixth, eighths, tenths, twelfths, fifteenths, sixteenths (and many others) you could do so without having any decimals to deal with.
That's great, although having calculators makes that less important to mathematicians than it once was.
So that's where degrees came from. What about radians?
Radians come directly from a unit circle. When we talk about the unit circle, we're talking about a circle with radius 1, centered at the origin of the cartesian plane. If you look at the picture, you can see that the radius of the circle has been marked as 1 unit. Now look at the blue line, starting with the red beginning, and going all the way around the circle to the blue arrow. How long is that curved segment?
The answer to that question comes from the formula C = πd - the circumference is pi times the diameter. What is the diameter? It's twice the radius, or 2 x 1 = 2. Thus, the circumference is 2π. With that in mind, a rotation around the circle could be thought of as an arc-length around a unit circle.
Okay, so that's where radians come from - but it doesn't answer the question of why we use them. It does seem like 30º is easier to deal with than π/6, and 270º is easier to deal with than 3π/2. So why deal with radians at all?
Because, as you move through more advanced topics in mathematics, you'll discover that there are certain relationships that only work if you're using radians instead of degrees. Consider the infinite summation below:
This beauty only works if x is in radians; if it's in degrees, it does not work!
But pretty formulas aren't the only reason radians work better. Especially if you're dealing with rotational motion (a car's tires, for example), writing things in radians keeps it simple. Consider the following examples:
#1: A car's tires have a radius of 12 inches. Its rotational speed is 30 degrees per second. How far does the car go in 1 second?
#2: A car's tires have a radius of 12 inches. Its rotational speed is 0.5326 radians per second. How far does the car go in 1 second?
#1 Solution: To find the distance the car has traveled, we divide 30 by 360 to find out what fraction of the circle we've rotated. Then we multiply that fraction by pi and the diameter of the circle to get the distance traveled: 12 x 2 x 30 x π / 360 = 6.3912 inches.
Now, before we look at problem #2, It's important to notice that in your calculations you've multiplied by 2π, and divided by 360. That's 2π/360, which is the same as π/180. That should look familiar to you; it's the conversion factor to swap from degrees to radians. In other words, even though you didn't realize you were doing it, you converted degress to radians in order to solve the problem! Now let's look at the solution to the second problem (which, by the way, is identical to the first, just using different units).
#2 Solution: To find the distance traveled, multiply the radius by the rotation in radians: 12 x 0.5326 = 6.3912 inches.
Wasn't that solution much simpler? You didn't have to do any conversion factors; you just multiplied the radius times the angle! That's pretty sweet!
So, yes, it's a nuisance to have two different units (just be glad you don't have to throw gradians into the mix!), but in the long run, your mathematical and scientific life will be simplified by making the π/180 switch to radians!
"How do you add 8 cubic yards and 8 cubic feet?" ~Anon.
Since you're asking the question, you're probably deduced that you can't simply add 3 and 3 to get 6. If you did that, you'd then have the question of whether the units in the result are cubic yards or cubic feet. The simple rule is that you can't add two quantities which have different units.
If two units are the same type of unit (for example, they're both distances, or they're both times), then you can rewrite one of them so they have the same unit, and then you can add them.
In this case, both units are volumes, which is an amount of 3-dimensional space something takes up. We want to either convert 3 cubic yards into cubic feet, or we want to convert cubic feet into cubic yards. I'm going to convert cubic yards into cubic feet.
If you have 8 cubic yards, you can picture that as a cube. Conveniently, 8 = 23, so you can picture it as a cube that has a width of 2 yards, a height of 2 yards, and length of 2 yards. Length times width times height = 2 yards x 2 yards x 2 yards = 8 yards3.
But we know how to convert 2 yards into feet; there are 3 feet in a yard. So it turns out that our cube's dimensions are 6 feet by 6 feet by 6 feet. So Length times width times height = 6 x 6 x 6 = 216 feet3.
Now that we have written both units in cubic feet, we can add them: 216 feet3 + 8 feet3 = 224 cubic feet.
That answers your question, but we've really only touched the surface of converting units - you can find a more detailed study unit here: Conversions factors and unit conversions.
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The SEC was once again well represented in the 2015 NFL Draft with an FBS-best 54 players selected. The conference has dominated the draft the past nine consecutive years and shows no signs of slowing down in the near future. With this year's draft in the books, here's a look at the next year's top SEC prospects.
Vernon Hargreaves III, CB, Florida, Junior: Hargreaves was one of the few bright spots on a lackluster Florida team. The sophomore was a first team All-SEC selection after recording three interceptions, despite seeing limited targets by opposing offenses. Hargreaves is heralded by opponents as the conference's top cornerback and has the intangiables to excel at the professional level. The 5-foot-11, 195-pound corner's low 40-yard dash was clocked at 4.38, while his instincts and natural ability have also received praise.
Leonard Floyd, DE/LB, Georgia, Junior: Floyd enters 2015 as one of the conference's best pass rushers. The sophomore led the Bulldogs with six sacks and added 17 quarterback hurries, earning an All-SEC honorable mention in 2014. Floyd, who spent a season in prep school before his past two in Athens, decided to forego the draft and return for his junior season, which should see an increase in production after the departures of Amarlo Herrera and Ramik Wilson.
Robert Nkemdiche, DT, Ole Miss, Junior: Defensive tackle is far from a "sexy pick," but Nkemdiche is too good for any team to pass up. The unanimous No. 1 prospect from the 2013 recruiting class has dominated in his first two seasons at Ole Miss and should continue his success in Year Three. At 6-foot-4, 280-pounds, Nkemdiche has a rare blend of size and speed that will shed his label as a defensive tackle and should rank him as an early first round pick.
D'Haquille Williams, WR, Auburn, Senior: Williams decided to return to Auburn for his senior season despite a high draft projection. The 6-foot-2, 216-pound receiver ranked third in the SEC in receiving yards per game (73.0) behind Biletnikoff winner Amari Cooper and South Carolina's Pharoh Cooper and eighth in receiving yards (730). With teammate Sammie Coates — who edged out Williams by 11 yards — embarking on a pro career, the rising senior will assume the role of Auburn's true No. 1 wide receiver and could be the SEC's top pass catcher.
Laremy Tunsil, OT, Ole Miss, Junior: Tunsil has topped several underclassmen projection lists for next year's draft. The 6-foot-5, 305-pound lineman has "the power to generate push on short-yardage runs and the quickness to seal the edge on perimeter runs" and "the length to take away the edge, the balance to mirror and the strength to anchor," according to ESPN Insider College Football. Like Nkemdiche, Tunsil was a prized prospect in Ole Miss' program changing 2013 class and has the intangibles to make an immediate impact at the pro level.


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Saving the Environment
Written by Andrew Langley
Illustrated by
Part of the Charities in Action Series
Saving the Environment by Andrew LangleyAll around the world there are charities trying to save the environment, from campaigning for government action on climate change, pollution, and energy use, to caring for woodland and beaches. This book looks at the efforts of charity workers and volunteers, with exciting stories and case studies, and gives advice on how readers can get involved.
About the Author
Other Formats
Book Info
64 pages
Andrew Langley
More books by Andrew Langley
Raintree an imprint of Capstone Global Library Ltd
Publication date
18th July 2013
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Find quality office cleaners in Folkestone, Kent and get free quotes fast with Bark. Regardless of the size of your office Bark will find the perfect cleaning services near Folkestone, Kent for you.
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Professional Cleaning Services for Shining Properties Choose the cleaning service you need and get any building professionally cleaned. All cleans are carried out by experienced cleaners, with special equipment and chemicals. ⇒ End of tenancy cleaning Top to bottom deep cleaning of rented buildings. Special discounts for landlords and agencies. ⇒ Carpet cleaning Dirt and stains removal from carpets with professional Prochem equipment and chemicals. All carpet cleaning services are available at a discount when booked together with another service. ⇒ Domestic cleaning Regular home cleaning, catering to individual needs. Weekly and fortnightly rates available. ⇒ Office cleaning Daily, weekly and one-off cleaning of offices and commercial spaces. The entire London areas are covered, M25 included.
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North Star CleaningCertificate of Excellence 2015
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Be Clean (south east) LTDCertificate of Excellence 2015
We are a family business with offices in Broadstairs and Herne Bay Kent We offer CARPET AND UPHOLSTERY CLEANING DOMESTIC AND COMMERCIAL CLEANING END OF TENANCY CLEAN BUILDERS CLEAN DEEP CLEANS HOLIDAY LET CLEANING We are proud members of Checkatrade and are Kent Trading Standards Approved. We are also members of the NCCA - National Carpet Cleaners Association. All our staff are fully insured.
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Domestic Cleaning company covering Gillingham, Sittingbourne, Sheerness, Faversham, Folkestone, Canterbury and Dover Please take a look at our website for further details - Cleanhome Sittingbourne Or Contact me on 0800 061 4396 or 07928 257082 Kindest Regards Gemma Raj, Director Cleanhome Sittingbourne
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Flow gutter clearing
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Cleaning Services
121 Cleaning Services
MBT Cleaning services is a proud family run business offering both domestic cleaning and holiday let managment across Kent and Sussex. We have been in the cleaning industry for a number of years and offer a number of services to suit your needs.
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What type of facility needs cleaning?
How often do you require cleaning services?
Monday, Wednesday, Friday
How big is the area needing cleaning?
Extra Large (e.g. multiple floors or units)
How soon would you like the cleaning to begin?
I'm not sure
How many bathrooms/toilets are there?
Two bathrooms
Will the building be occupied while the cleaning is being carried out?
No, building will be vacant
Any additional details?
Offices on 2 floors, cleaning of the 2 kitchenettes and 2 (multiple cubicle) toilet rooms, emptying of bins, hoovering and general cleaning.
What type of facility needs cleaning?
Carehome Cleaning
How often do you require cleaning services?
Once a week
How big is the area needing cleaning?
I would like to discuss with the Pro
How soon would you like the cleaning to begin?
In the next week
How many bathrooms/toilets are there?
To Discuss
Will the building be occupied while the cleaning is being carried out?
Yes, building will be occupied
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This is a carehome and we need weekly cleaning done for the entire carehome. And we need quotation for the same.
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Community facility e.g. church, village hall
How often do you require cleaning services?
Twice a week
How big is the area needing cleaning?
How soon would you like the cleaning to begin?
How many bathrooms/toilets are there?
Three bathrooms
Will the building be occupied while the cleaning is being carried out?
No, building will be vacant
Any additional details?
approx. 1600 sqft 12 staff clean tidy desk washing up clean mop kitchen and toilets wash tea towel and hand towels and hoover


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12 Results Found
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Limeginger Floral DesignBeautiful contemporary or traditional designs for individual bouquets, weddings, funeral tributes and corporate events.
My Chocolate ExplosionInstead of flowers why not have a bouquet of chocolates or sweets. If you live in Medway, Gravesend or Dartford areas free delivery is available!
Flowers by Joanne Gent
Florist, Flowers, Funeral Flowers, Wedding Flowers, Event Decoration, Gifts, Gift BasketsFreelance florist Level 3 Qualified. Traditional and Contemporary florist serving the Eastleigh, Winchester and Southampton areas of Hampshire. Sunday delivery by prior arrangement
Lavender BlueBased in Basingstoke, Hampshire, Lavender Blue is a small, specialist floral design company which creates individual and unique flowers and bouquets for weddings. We also provide a national service offering amazing bespoke felt wedding bouquets for something really different!
Looby Bloom
Beautiful flowers for all occasionsBeautiful flowers for all occasions, Weddings, Parties, Special Events, Gifts and Funerals
The Bloom Room
Artificial roses and floral gift-ware within an affordable budgetThe Bloom Room offers a range of striking artificial roses and floral gift-ware sure to enhance every occasion within an affordable budget
PINKS BY POST – SimplyPinksPINKS BY POST - SimplyPinks Cornish Flowers Free Delivery


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