Can someone please help me with this question:
Write an equation that describes the following variation statement, and then find the constant of proportionality k . z is inversely proportional to x and directly proportional to y ; z = -10 when x = 5 and y = 50.
Hmmm. Still having trouble with direct/inverse proportionality?
z = ky/x
-10 = k(5)(50)
k = -1/25
oops -10 = k(50)/5
k = -1
To write an equation that describes the given variation statement, we know that z is inversely proportional to x and directly proportional to y.
This can be written as the equation:
z = k * (y/x)
Now, we need to find the constant of proportionality, k.
To find the value of k, we can substitute the given values for z, x, and y into the equation and solve for k.
Given: z = -10 when x = 5 and y = 50
-10 = k * (50/5)
Simplifying the equation:
-10 = k * 10
To solve for k, we divide both sides of the equation by 10:
-10/10 = k * 10/10
-1 = k
Therefore, the constant of proportionality, k, is -1.
The equation that describes the given variation statement is:
z = -1 * (y/x)