If z varies jointly as the square of x and y, z = 24 when x = 2 and y = 3, find the
value of z when x = 4 and y = 8.
reading it as it was typed, interpreting "and" as addition
"z varies jointly as the square of x and y"
---> z = k(x+y)^2
when z = 24, x = 2, y = 3
24 = k(2+3)^2
24 = 25k
k = 24/25
z = (24/25)(x+y)
plug in your given values
If z varies jointly as the square of x and y, we can express this relationship as:
z = k * x^2 * y,
where k is a constant.
To find the value of k, we can use the given information when x = 2 and y = 3, and z = 24:
24 = k * 2^2 * 3,
24 = 4k * 3,
8 = 4k,
k = 2.
Now that we have the value of k, we can substitute it into the equation to find the value of z when x = 4 and y = 8:
z = 2 * 4^2 * 8,
z = 2 * 16 * 8,
z = 256.
To find the value of z when x = 4 and y = 8 in the given joint variation equation, we can use the formula for joint variation:
z = k * x^2 * y
where k is the constant of variation.
First, let's substitute the given values from the first scenario into the equation:
24 = k * 2^2 * 3
Simplifying, we get:
24 = 4k * 3
24 = 12k
Dividing both sides by 12:
k = 24 / 12
k = 2
Now that we have the value of k, we can substitute the new values of x and y into the equation:
z = 2 * 4^2 * 8
Simplifying:
z = 2 * 16 * 8
z = 256
Therefore, when x = 4 and y = 8, the value of z is 256.