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:
The side C equals to 10. hence the answer is letter A
Step-by-step explanation:
To solve this, we need to use trigonometric functions.
we know that sin (α) = Lo / H for a triangle. Being Lo : Length of the opposite side and H: Length of the hypotenuse.
Given α= 45º and Lo= 5√2 and replacing in the equation:
sin (45º) = 5√2 / C (1)
Using trigonometric identities we know that sin(45º) =(√2)/2. Replacing in equation (1):
sin (45º) = (√2)/2 = 5√2 / C ⇒ C = 2 *5 *√2 / (√2) ⇒ C=10
Answer:
2
Step-by-step explanation:
M+m+z/3=3m
m+m+z=9m
2m+z=9m
z=7m
m+m+7m/3=3m
9m=9m
m=1
1+1+z/3=3
2+z=9
z=7
idk but i think that one person gets paid 7 dollars and the other ppl get paid 1 dollar----- this is probably veryyyyy wrong
Answer:
2x-14
Step-by-step explanation:
2(x-7)
distribute
2x-14
