Question

PLEASE HELP

Answer 1

Answer:

1).  The constant of variation is 7

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

Step-by-step 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

Answer 2

Answer:

1)  k = 7

2)  w = 6

Step-by-step 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:

$\begin{aligned}y&=kxw\\\implies -42&=k \cdot 2 \cdot -3\\-42&=-6k\\k&=\dfrac{-42}{-6}\\k&=7\end{aligned}$

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:

$\begin{aligned}y&=7xw\\\implies 3&=7 \cdot \dfrac{1}{14} \cdot w\\3&=\dfrac{7}{14} \cdot w\\42&=7w\\w&=6\end{aligned}$