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Please help with all questions !!

Last question(#5) has one of the answer choices with it. I couldn't post the rest of the answer choices. Find what the points should be graphed on.

Please help with all questions !! Last question(#5) has one of the answer choices-example-1
Please help with all questions !! Last question(#5) has one of the answer choices-example-1
Please help with all questions !! Last question(#5) has one of the answer choices-example-2
Please help with all questions !! Last question(#5) has one of the answer choices-example-3
Please help with all questions !! Last question(#5) has one of the answer choices-example-4
Please help with all questions !! Last question(#5) has one of the answer choices-example-5
User Engelbert
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1 Answer

5 votes

Answer:

See below for answers and explanations

Explanation:

Problem 1

  • The equation for a rose curve in polar form is either
    r=a\:cos(n\theta) if the pole is horizontal or
    r=a\:sin(n\theta) if the pole is vertical.
  • The value
    a represents the length of each petal
  • If
    n is odd, there will be
    n petals
  • If
    n is even, there will be
    2n petals

Looking at the graph, the pole is vertical, which means that our polar curve will take the form of
r=a\:sin(n\theta). We see that there are 12 petals, so this must mean that
n=6. Additionally, the length of each petal is 4 units, so
a=4. This means our equation is
r=4\:sin6\theta, making B the correct answer.

Problem 2

This polar curve is a limaçon:

  • A limaçon is in the form of either
    r=a\pm bsin\theta or
    r=a\pm bcos\theta, depending on the direction of the pole where
    a > 0 and
    b > 0
  • If
    (a)/(b) < 1, the limaçon is an inner loop limaçon
  • If
    (a)/(b)=1, the limaçon is a cardioid
  • If
    1 < (a)/(b) < 2, the limaçon is dimpled with no inner loop
  • If
    (a)/(b)\geq 2, the limaçon will be convex with no dimple and no inner loop

Given that our graph is a cardioid (heart-shaped) and it has a vertical pole, this means that our equation takes the form of
r=a\pm bsin\theta where
(a)/(b)=1. However, none of the answers look correct

Problem 3

Only
r=4+7sin\theta is correct since it takes the form of
r=a\pm bsin\theta

Problem 4

The loop starts at
\theta=(2\pi)/(3) if you look at this on a polar graph and ends at
\theta=\pi, so this means that
(2\pi)/(3)\leq\theta\leq \pi is the correct answer

Problem 5

We could graph all the points, but the more important points to notice are
(0,4),
((\pi)/(2),0), and
(\pi,-4). These show us the petals of the curve, which happens to be the option in the picture. This exact function is
r=4\:cos2\theta

User Amer Sawan
by
7.9k points

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