4. 1 kg because you will have to divide 4100 by 1000. Ps. 1 kg is equal to 1000 grams.
Answer:
Step-by-step explanation:
7 3/4+ (12 - 3 6/11)
31/4 + (12 - 3 6/11)
31/4 + (12 - 39/11)
31/4 + 93/11
= <u>7</u><u>1</u><u>3</u><u>/</u><u>4</u><u>4</u><u> </u><u>=</u><u> </u><u>1</u><u>6</u><u> </u><u>9</u><u>/</u><u>4</u><u>4</u>
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.
In order to use the elimination method, we have to multiply the equation by some number, so that one of the variable has the same coefficient.
For example, multiplying the first equation by 3 and the second by 2 gives the following, equivalent system:
Now, we can subtract the two equations, and we will cancel (eliminate) the x variable:
Now that y is known, plug it into one of the equations: for example, if we use the first one we get
