Answer: y=3x-8, y=5x-8, and y=2x-8
Step-by-step explanation:
These equations are all lines in slope-intercept form (y=mx+b where b is the y-intercept). y=3x-8, y=5x-8, and y=2x-8 all have -8 as the b value. Therefore, these equations have the same y-intercept.
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.
It would be 9/6 which simplifies to 3/2
Answer:
20 cm
Step-by-step explanation:
∵ S is the centroid of ΔNLM
∴ S divides NG at ratio 1 : 2 from the base
∴SQ = 1/2 NS
∴3x - 5 = 1/2 (4x)
∴3x - 5 = 2x
∴3x - 2x = 5
∴x = 5
∴ NS = 4 × 5 = 20 cm
y=5, x=7 because if 3x5=15 then 15-7=8 dont report me if i do get this wrong
