Question

Suppose that y varies jointly with w and x and inversely with z and y = 400 when w = 10, x = 25, and z = 5. Write the equation that models the relationship.

Answer 1

Answer:

$y =8 \cdot \frac{wx}{z}$

Step-by-step explanation:

Joint variation says that:

If y varies jointly with x and inversely with z

i.e,

$y \propto x$

$y \propto \frac{1}{z}$

then the equation is in the form of :

$y = k\frac{x}{z}$ where, k is the constant of variation.

As per the statement:

Suppose that y varies jointly with w and x and inversely with z

by definition of joint variation we have;

$y = k\frac{wx}{z}$            ......[1]

It is given that: y = 400 when w = 10 , x = 25 and z = 5

Substitute in [1] we have;

$400 = k \cdot \frac{10 \cdot 25}{5}$

Simplify:

$400 = 50k$

Divide both sides by 50 we have;

8 = k

or

k = 8

⇒$y =8 \cdot \frac{wx}{z}$

Therefore, the equation that models the relationship is, $y =8 \cdot \frac{wx}{z}$

Answer 2

The equation that models the relationship between w, x, y, and z is shown below.

$\rm y = 8 \times \dfrac{xw}{z}$

What are ratio and proportion?

A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.

y varies jointly with w and x and inversely with z

$\rm y \propto wx \\\\y \propto \dfrac{1}{z}$

Then we have

$\rm y = k \ \dfrac{xw}{z}$

y = 400 when w = 10, x = 25, and z = 5. Then we have

$\rm 400 = k \times \dfrac{10*25}{5}\\\\\\k \ \ \ = \dfrac{400*5}{10*25}\\\\\\k \ \ \ = 8$

Then we have

$\rm y = 8 \times \dfrac{xw}{z}$

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762