Answer:
30 dollars a week
Step-by-step explanation:
2100/70 is 30
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>87 less than the quotient of an unknown number and 43 is -75
Converting that to mathematical equation:
87 - (x / 43) = -75
Evaluating the equation, we can the value of x.
87 - (x/43) = -75
-x/43 = -75 - 87
-x/43 = -162
-x = -6966
x = 6966</span>
Answer:
B. 434.89
Step-by-step explanation:
A basketball is a sphere and the volume formula is:
V = 4/3πr³
Given:
d = 9.4
r = 9.4/2
r = 4.7
Work:
V = 4/3πr³
V = 4/3π(4.7)³
V = 4/3π(103.823)
V = 434.89
Answer:
4/20
Step-by-step explanation:
8 socks we don't know
1 sock 19 socks
11 white
1 more sock 7 /20 chance to pick a random sock
