z varies jointly with y and the square of x. If z=256 when
y=−8 and x=−4, find z when x=−3 and y=−4.
"z varies jointly with y and the square of x" ----> z = k(y x^2)
256 = k(-8(16))
k = -2
so you know z = -2yx^2
plug in your given values and find z
To determine the equation representing the joint variation of z with y and the square of x, we can use the formula:
z = k * x^2 * y
where k is the constant of variation.
Given that z = 256 when y = -8 and x = -4, we can substitute these values into the formula to solve for k:
256 = k * (-4)^2 * (-8)
256 = k * 16 * (-8)
256 = -128k
Dividing both sides by -128:
k = -256/128
k = -2
Now that we have the constant of variation, we can substitute x = -3 and y = -4 into the equation and solve for z:
z = (-2) * (-3)^2 * (-4)
z = (-2) * 9 * (-4)
z = 72
Therefore, when x = -3 and y = -4, z is equal to 72.
To solve this problem, we can start by writing the equation that relates z, x, and y. The phrase "z varies jointly with y and the square of x" can be translated into a mathematical equation as follows:
z = k * y * x^2
where k is a constant of proportionality.
Next, we can use the given information to find the value of k. We are told that when y = -8 and x = -4, z = 256. Substituting these values into the equation, we have:
256 = k * (-8) * (-4)^2
256 = k * (-8) * 16
256 = k * (-128)
Now we solve for k:
k = 256 / (-128)
k = -2
Now that we have the value of k, we can find z when x = -3 and y = -4 by substituting these values into the equation:
z = (-2) * (-4) * (-3)^2
z = (-2) * (-4) * 9
z = 72
Therefore, when x = -3 and y = -4, the value of z is 72.