227k views
1 vote
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 =

User Rjs
by
8.0k points

2 Answers

5 votes

Answer:

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}

User Troy DeMonbreun
by
8.1k points
2 votes

Answer:

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

User Squarism
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories