It cost $68.00 for 16 square feet of flooring. how much does it cost for 12 feet of flooring

Step-by-step explanation:

Question

It cost $68.00 for 16 square feet of flooring. How much does it cost for 12 feet of flooring

These are two questions and two answers.

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

x=t²

y=2t

option A.) r = 4cot(theta)csc(theta)

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?

x=sin(theta)cos(theta)+cos(theta)

y=sin^2(theta)+sin(theta)

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)

b) r sinθ =sin²(θ)+sin(θ)

3) work both equations

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

b) r sinθ =sin²(θ)+sin(θ) ⇒ r sinθ = sinθ [sinθ + 1] ⇒ r = sinθ + 1

Therefore, the answer is r = sinθ + 1 which is the option B.