Question

PLEASE HELP

The variable y varies jointly with x and w when y = -42, x = 2, and w = -3.


1.) Find the constant of variation.


k =


2.) Find w when y = 3 and x = 1/14


w =

Answer 1

1) k = 7

2) w = 6

Explanation:

Joint variation equation

If y varies jointly with x and w:

`\boxed{y \propto xw \implies y=kxw}`

for some constant k.

Given:

• y = -42
• x = 2
• w = -3

Substitute the given values into the joint variation equation and solve for k:

`\begin{aligned}y&=kxw\\\implies -42&=k \cdot 2 \cdot -3\\-42&=-6k\\k&=(-42)/(-6)\\k&=7\end{aligned}`

Therefore, the equation is:

`\boxed{y=7xw}`

To find w when y = 3 and x = 1/14, substitute these values into the found equation and solve for w:

`\begin{aligned}y&=7xw\\\implies 3&=7 \cdot (1)/(14) \cdot w\\3&=(7)/(14) \cdot w\\42&=7w\\w&=6\end{aligned}`

Answer 2

1). The constant of variation is 7

2). w = 6 for the given values of x and y

Explanation:

"Varies jointly" tells us that y is a direct result of a mathematic operation involving x and w. We will assume y is directly prorportional to x and w, in the sense that we can find a multiplicative relationship of the form y=Kxw, where K is the constant of variation.

We are given one data point: y=-42 where x is 2 and w is -3. Let's put those values into our trrial expression:

y=Kxw

-42=K(2)(-3)

-42 = -6K

K = 7

The expression becames y = 7xw

The constant of variation is 7.

The value of w for y=3 and x=(1/14) would be:

y=7xw

3 = 7*(1/14)*w

3 = (1/2)*w

w = 6