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Calculus

# Polar Equations - Area

A cow is tied to one point of a silo of radius 30, with a rope of length $$30 \pi$$ which would allow it to reach the opposite end of the silo.

What is the total area of the grass that the cow can graze on?

Given the graph above of the polar equation $$r=4+3\sin \theta,$$ what is the area of the shaded region?

Find the area enclosed by one loop of the $$4$$-petal flower defined by the parametric equation $$r=5\cos 2\theta.$$

Find the area of the region that lies inside the circle $$r=27\sin \theta$$ and outside the cardioid $$r=9+9\sin \theta.$$

Find the area of the region bounded by the curve defined by $r^2=5\sin 2\theta, r \geq 0, 0 \leq \theta \leq \frac{\pi}{2}.$

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The text passage contains multiple mathematical questions related to finding areas defined by polar equations and parametric equations, with no answers provided.
multiple_questions
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
system
×
Calculus

# Polar Equations - Area

A cow is tied to one point of a silo of radius 30, with a rope of length $$30 \pi$$ which would allow it to reach the opposite end of the silo.

What is the total area of the grass that the cow can graze on?

Given the graph above of the polar equation $$r=4+3\sin \theta,$$ what is the area of the shaded region?

Find the area enclosed by one loop of the $$4$$-petal flower defined by the parametric equation $$r=5\cos 2\theta.$$

Find the area of the region that lies inside the circle $$r=27\sin \theta$$ and outside the cardioid $$r=9+9\sin \theta.$$

Find the area of the region bounded by the curve defined by $r^2=5\sin 2\theta, r \geq 0, 0 \leq \theta \leq \frac{\pi}{2}.$

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user
The text passage contains multiple mathematical questions related to finding areas defined by polar equations and parametric equations, with no answers provided.

TYPE: MULTIPLE_QUESTIONS