CALCULUS

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The region R is a rectangle with vertices P(a,lna), Q(a,0), S(3,0), and T(3,lna), where 1<a<3.
I found that the expression for the area of the rectangle is f(a) = (ln(a))(3-a).
The area of the rectangle is maximized for some c beween 1 and 3. Write the expression you would need to solve in order to find c.

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The region R is a rectangle with vertices P(a,lna), Q(a,0), S(3,0), and T(3,lna), where 1<a<3. A.) Write an expression that gives the area of the rectangle as a function of a. B.) The area of the rectangle is maximized for some …
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The text passage contains a mathematical question related to calculus and optimization. It describes a rectangle with given vertices and asks for the expression that needs to be solved to find the value of \(a\) that maximizes the area of the rectangle.
single_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
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CALCULUS

posted by .

The region R is a rectangle with vertices P(a,lna), Q(a,0), S(3,0), and T(3,lna), where 1<a<3.
I found that the expression for the area of the rectangle is f(a) = (ln(a))(3-a).
The area of the rectangle is maximized for some c beween 1 and 3. Write the expression you would need to solve in order to find c.

Similar Questions

1. Math

If the length of a rectangle is (2x-1)cm and its width is (x+3)cm. How do i write an expression in the form ax^2+bx+c for the area of the rectangle?

How do you write the expression for the area of the rectangle If the length of a rectangle is two more than three times it's width,then write an expression for area of the rectangle Find the perimeter of the rectangle in problem 1.

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The region R is a rectangle with vertices P(a,lna), Q(a,0), S(3,0), and T(3,lna), where 1<a<3. A.) Write an expression that gives the area of the rectangle as a function of a. B.) The area of the rectangle is maximized for some …
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The leng of the smaller rectangle is 1 inch less than twice its wide. both the dimensions of the larger rectangle are 2 inches longer than the smaller rectangle. the area of the shaded region is 86 square inches. what is the area of …
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Top of the rectangle is 2x+5 right hand side is 5. Write an expression for the area of the rectangle. Then find the area of the rectangle in square feet if x=3. Then I need to find the value of x if the area of the rectangle is 1y0 …
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A rectangle has dimensions in feet as shown in the figure it is 2x +5 And one side is 8. I need to write an expression for the area of the rectangle. B. Find the area of the rectangle, in sq.ft. if x=3 C. Find the value of x if the …
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Please help with the below question. I think my answer is correct but not sure. The area of a rectangle can be found using the formula A=lw. The length of the rectangle is 14a6^b7^c13^ and the width of the rectangle is (7a9^b-3^c18^)2^ …

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The text passage contains a mathematical question related to calculus and optimization. It describes a rectangle with given vertices and asks for the expression that needs to be solved to find the value of \(a\) that maximizes the area of the rectangle.

TYPE: SINGLE_QUESTION