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.
Answer:
18.84 feet
Step-by-step explanation:
The circumference of a circle can be found using:
c=π*d
The radius is given, but we have to find diameter. The diameter is twice the radius, or
d=2r
The radius is 3 feet. Substitute 3 in for r.
d=2*3
d=6
The diameter is 6 feet.
Now we have the diameter. We can substitute 6 in for d in the circumference formula. We can also substitute 3.14 in for pi.
c=π*d
c=3.14*6
c=18.84
The circumference is <u>18.84 feet</u>
You add all those number together then divide the number you got by how many numbers there are and that's your answer, 61.1
edit : dont listen to me I didnt see the numbers 64 and 65, im sorry
Hi there! Hopefully this helps!
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Answer: 14.
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First we calculate <u>3 to the power of 2</u> and get 9.
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9 + 9 - 
= 14.
Now we add<u> 9 + 9</u> to get 18.
18 - = 14.
Then, we<u> divide 8 by 2</u> to get 4.
18 - 4 = 14.
Then we subtract<u> 4 from 18</u> to get.....You guessed it,<u> 14</u>!
