X + 5 + 11x = 12x + y
Simplify: 12x + 5 = 12x + y (We are adding x and 11x on the left side)
Subtract 12x from each side makes each zero.
5 = y
So we can plug in and test. I'm picking two random numbers to plug in for x. 10, and 82
x = 10, y = 5
10 + 5 + 11(10) = 12(10) + 5
125 = 125
x = 82, y = 5
82 + 5 + 11(82) = 12(82) + 5
989 = 989
So we verified y = 5
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.
So there are 41 two pointers and three pointers.
there are 21 two pointers and 20 three pointers
I believe the correct answer from the choices listed above is option D. The graph <span>G(x) as compared to the graph of F(x) would be that the </span><span>graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units down. 2 is a stretch factor and -5 is the shift downwards of the graph. Hope this answers the question.</span>
I think it may be 5+3 and carry the one up top to get the sum of 56.
