Answer:
0.18
Step-by-step explanation:
The relative frequency of eight graders who want fruit smoothie :
Number of eight graders who want fruit smoothie / total number of students surveyed
= 45 / 250
= 0.18
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.
For this case we have the following equation:
P (t) = P (1 + r / n) ^ (n * t)
Where,
P: initial investment
r: interest
n: periods
t: time
she will take on her 45th birthday:
for t = 25:
P (25) = 1000 * (1 + 0.0165 / 4) ^ (4 * 25)
P (25) = 1509.31 $
Answer:
The future value of this investment when she takes her trip is:
P (25) = 1509.31 $
Answer:
Step-by-step explanation:
Given
Required
Find g(3)
Since g(x) is a linear function, then:
For:
For:
Substitute
So, the function is:
Calculate g(3)
Well you can try rewriting it to this
answer is d 270
first start of by factoring and subtracting the 1 into the right side
sin(x) ( 2 sin (x) + 1) = -1
set each one equal to -1
sin( x) = -1 and 2 sin (x) +1 = -1
2 sin (x) = -2
sin ( x) = -1
so therefore we have our final equation
sin ( x ) = - 1 and sin (x) = -1
so then you look in your unit circle and find what coordinate equals -1 in terms of sin x
