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irga5000 [103]
2 years ago
14

PLEASE HELP!!!! 20 POINTS!!!!

Mathematics
2 answers:
galben [10]2 years ago
6 0
These are two questions and two answers.

Question 1) Which of the following polar equations is equivalent to the parametric equations below? 

<span> x=t²
y=2t</span>

Answer: option <span>A.) r = 4cot(theta)csc(theta)
</span>

Explanation:

1) Polar coordinates ⇒ x = r cosθ and y = r sinθ

2) replace x and y in the parametric equations:

r cosθ = t²
r sinθ = 2t

3) work r sinθ = 2t

r sinθ/2 = t 
(r sinθ / 2)² = t²

4) equal both expressions for t²

r cos θ = (r sin θ / 2 )²

5) simplify

r cos θ = r² (sin θ)² / 4

4 = r (sinθ)² / cos θ

r = 4 cosθ / (sinθ)²

r = 4 cot θ csc θ ↔ which is the option A.


Question 2) Which polar equation is equivalent to the parametric equations below?

<span> x=sin(theta)cos(theta)+cos(theta)
y=sin^2(theta)+sin(theta)</span>

Answer: option B) r = sinθ + 1


Explanation:

1) Polar coordinates ⇒ x = r cosθ, and y = r sinθ

2) replace x and y in the parametric equations:

a) r cosθ = sin(θ)cos(θ)+cos(θ)
<span> b) r sinθ =sin²(θ)+sin(θ)</span>

3) work both equations

a) r cosθ = sin(θ)cos(θ)+cos(θ) ⇒ r cosθ = cosθ [ sin θ + 1]  ⇒ r = sinθ + 1


<span> b) r sinθ =sin²(θ)+sin(θ) ⇒ r sinθ = sinθ [sinθ + 1] ⇒ r = sinθ + 1
</span><span>
</span><span>
</span>Therefore, the answer is r = sinθ + 1 which is the option B.
Zarrin [17]2 years ago
4 0

*In order from the original test*

1. B. x=3cos^2 theta, y=3cos theta sin theta

2. A. r=4cot theta csc theta

3. B. r=sin theta+1

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1 9/10

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6 0
2 years ago
Read 2 more answers
HELP
Semmy [17]

The second and third functions both decrease with a slope of -4, but the second fiction has a y intercept of -3 and the third has a y intercept of +3. The first and fourth functions are both increasing with a slope of positive 4. The first one has a y intercept of -3, but the fourth has a y- intercept of -3. all of the functions are linear.

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8 0
2 years ago
Number two please! Simplify. Also please explain.
marin [14]

Answer:

<u>2x−15</u>

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Step-by-step explanation:

3x squared cancels out then you are left with

<u>6x-45</u>

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then you simplify and get  <u>2x-15</u>

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3 0
2 years ago
(A) Find the slope of the line that passes through the given points.
Mariulka [41]

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Check the picture below.

6 0
2 years ago
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