4/5 ,8/10, 16/20,
You multiply both numbers with the same number.
For ex. 4×2=8 5×2=10 so we have 8/10
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:
B. No
Step-by-step explanation:
-A right angle triangle has two complimentary acute angles and one right angle.
-
is usually one of the acute angles and is equivalent to 90º minus it's complimentary acute angle.
-Complimentary angles add up to 90º.
#For complimentary angles:
The two acute angles cannot have the same Cosine value.
Hence, she's not correct.
The taylor series for the f(x)=8/x centered at the given value of a=-4 is -2+2(x+4)/1!-24/16 
/2!+...........
Given a function f(x)=9/x,a=-4.
We are required to find the taylor series for the function f(x)=8/x centered at the given value of a and a=-4.
The taylor series of a function f(x)=
Where the terms in f prime 
(a) represent the derivatives of x valued at a.
For the given function.f(x)=8/x and a=-4.
So,f(a)=f(-4)=8/(-4)=-2.
(a)=(-4)=-8/(
=-8/16
=-1/2
The series of f(x) is as under:
f(x)=f(-4)+
=-2+2(x+4)/1!-24/16 /2!+...........
Hence the taylor series for the f(x)=8/x centered at the given value of a=-4 is -2+2(x+4)/1!-24/16 /2!+...........
Learn more about taylor series at brainly.com/question/23334489
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