There is one cup of lemonade to four cups of iced tea.
12 oz for 2.68 = .22 per unit
16 oz for 2.49 = .16 per unit
the 16 oz for 2.49 is your better deal
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.
<span><span> x-4/x3-64</span> </span>Final result :<span> x4 - 64x3 - 4
—————————————
x3 </span>
At around 20'000ft. and higher.
