Answer:
Step-by-step explanation:
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.
I would say it is <span>D- (-4,-5), for counterclockwise you turn towards the right. At 180 degrees it would be (4, -5) if you turn again you would get (-4,-5) hope this helps</span>
Answer:
Constant Term
The term in a simplified algebraic expression or equation which contains no variable(s). If there is no such term, the constant term is 0.
Example: –5 is the constant term in p(x) = 2x3 – 4x2 + 9x – 5
Answer: 54 berry plants
Step-by-step explanation:
From the sample there are:
Lettuce = 12
Tomatoes = 6
Peppers = 3
Berries = 9
The total is: = 12 + 6 + 3 + 9 = 30 plants
Berries comprise of:
= 9/30
= 3/10 of the plants
If they want to plant a total of 180, the number of berrie plants needed is:
= 3/10 * 180
= 54 berry plants
