Given parameters:
y varies directly as w;
This interpreted implies that as y increases, we increases by a certain factor or amount;
So, y ∝ w
y = kw
where k is the constant of proportionality
Now, given that y = 8 and w = 2
Input in the equation to solve for k;
8 = k x 2
Solving k gives, k = 4
Now to the second part,
if v is directly proportional to w;
v = k w
So v = 4w
The equation that relates v to w is v = 4w
Answer:
y = (x/(1-x))√(1-x²)
Step-by-step explanation:
The equation can be translated to rectangular coordinates by using the relationships between polar and rectangular coordinates:
x = r·cos(θ)
y = r·sin(θ)
x² +y² = r²
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r = sec(θ) -2cos(θ)
r·cos(θ) = 1 -2cos(θ)² . . . . . . . . multiply by cos(θ)
r²·r·cos(θ) = r² -2r²·cos(θ)² . . . multiply by r²
(x² +y²)x = x² +y² -2x² . . . . . . . substitute rectangular relations
x²(x +1) = y²(1 -x) . . . . . . . . . . . subtract xy²-x², factor
y² = x²(1 +x)/(1 -x) = x²(1 -x²)/(1 -x)² . . . . multiply by (1-x)/(1-x)
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The attached graph shows the equivalence of the polar and rectangular forms.
Answer:
119j+28
Step-by-step explanation:
7(17j+4) Remove the parentheis
distribute 7 through the parentheis
The expression that is equal to 2022 by adding a set of parentheses is 12 x 12 x 12+ 12 x 12+ 12 x 12 + 12 / (12 /12 + 12 / 12).
<h3>How to solve a long-expression problem?</h3>
In mathematics, parentheses are used to group a set of mathematical terms. In a long-expression, like the one presented, using parenthesis implies:
- The terms in the parentheses are solved separately from those outside the parentheses.
- The terms in the parentheses are solved before solving those outside.
- Moving the parentheses will affect the result of the whole expression.
Based on this, the expression that equals 2022 is:
- 12 x 12 x 12+ 12 x 12+ 12 x 12 + 12 / (12 /12 + 12 / 12)
<h3>Let's solve it to prove this result</h3><h3 />
- 12 x 12 x 12+ 12 x 12+ 12 x 12 + 12 / (12 /12 + 12 / 12)
First, solve the parenthesis first by dividing and then by adding.
- 12 x 12 x 12+ 12 x 12+ 12 x 12 + 12 / (1 + 1)12 x 12 x 12+ 12 x 12+ 12 x 12 + 12 / 2
Now, let's solve this expression, the first step is to solve the multiplications.
Now, solve the division.
Finally, add everything.
- 1728 + 144 + 144 + 6 = 2022
Learn more about mathematics in: brainly.com/question/12083755
Answer:
all are showing that y is a function of x
