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.
The equation that models the relationship is:
y = k(w*x/z)
where k is the constant of proportionality. We can find k by substituting the given values into the equation and solving for k:
400 = k(10*25/5)
400 = k(50)
k = 8
Therefore, the equation that models the relationship is:
y = 8(w*x/z)
To write the equation that models the relationship, we need to determine the constant of variation. In this case, y varies jointly with w and x, and inversely with z.
The equation for joint variation is of the form:
y = k * w * x
And the equation for inverse variation is of the form:
y = k / z
To incorporate both joint and inverse variation, we can write the equation as:
y = k * (w * x) / z
Now, we can solve for the constant of variation (k) using the given values: y = 400, w = 10, x = 25, and z = 5.
400 = k * (10 * 25) / 5
To solve for k, we first simplify the equation:
400 = 250k / 5
Next, we multiply both sides of the equation by 5 to eliminate the denominator:
5 * 400 = 250k
2000 = 250k
Finally, we solve for k by dividing both sides of the equation by 250:
k = 2000 / 250
k = 8
Therefore, the equation that models the relationship is:
y = 8 * (w * x) / z