I think the answer is <span>x=220</span>
-7(2)+y=60
-14+y=60
y=60+14
Y=74
Answer:
y = -3x + 1
Step-by-step explanation:
Starting with the point (-1, 4) and the slope m = -3, write out the point-slope equation of a straight line: y - k = m(x - h) becomes y - 4 = -3(x + 1), or:
y = -3x - 3 + 4
y = -3x + 1 This is the same as answer choice (b).
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: C. 71,224,900
Based on the power, move the decimal point that many spaces to the right. (e.g., If it's 7.9 × 10^3, then move the decimal three spaces to the right, and you'd get 7900.)
3.14159 × 10^7 = 31415900
9.897752 × 10^6 = 9897752
2.468 × 10^7 = 24680000
Out of all the numbers mentioned in the question, 71,224,900 is the only one that's greater than 3.14159 × 10^7 = 31415900.
