Can you add the picture to the question?
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:
Betty had 45 minutes to take her test in mixed number form it is
Step-by-step explanation:
1 hour
1/4 an hour = 15 minutes
1/2 an hour is 30 minutes
1 hr 15- 30= 45
45= 3/4 of and hour remaining to test
Answer:
(7√6)/2
Step-by-step explanation:
The side ratios in these special triangles are ...
30°-60°-90° triangle: 1 : √3 : 2
45°-45°-90° triangle: 1 : 1 : √2
This tells you the length of the horizontal line is 7√3, and the value of x is ...
(7√3)/√2 = (7√6)/2
_____
<em>Additional comment</em>
Call the length of the horizontal line "y". Then the given ratios tell you ...
7 : y = 1 : √3 ⇒ y/7 = √3/1 ⇒ y = 7√3
and
x : y = 1 : √2 ⇒ x/y = 1/√2 ⇒ x = y/√2
When we rationalize the denominator, we get ...
x = (y√2)/2 = ((7√3)√2)/2 = (7√6)/2
Answer:
(Your answer choices were really confusing, so I just put the plain answer)
Step-by-step explanation:
To find the slope of a line with just two points, we can use the formula 
. In this case, 
. This is 
. This reduces to
