z varies directly as x^2. If z=36 when x=3,find zwhen x=4.

z varies directly as x^2 -----> z = kx^2 , where k is a constant

if z=36, x = 3
336 = k(9)
k = 4

so y = 4x^2
when x=4 , y = 4(16) = 64

or , by ratio ....

z1/z2 = x1^2/x2^2

z1/36 = 4^2/3^2
z1 = 36(16/9) = 64

To find the value of z when x=4, we can use the concept of direct variation.

The statement "z varies directly as x^2" can be represented by the equation: z = k*x^2, where k is the constant of variation.

To find the value of k, we can use the given information that z=36 when x=3.

Substituting these values into the equation, we get: 36 = k*3^2

Simplifying further: 36 = 9k

Dividing both sides of the equation by 9, we find: k = 4

Now we have the value of k, we can substitute it into the equation to find z when x=4.

Using the equation z = k*x^2, we have: z = 4*4^2

Simplifying further: z = 4*16 = 64

Therefore, when x=4, z equals 64.

To find the value of z when x=4, we can use the concept of direct variation.

In a direct variation, when one variable (z in this case) is directly proportional to another variable (x^2 in this case), we can write it as an equation:

z = k * x^2

where k is the constant of variation.

To find the value of k, we can use the given information that z=36 when x=3. Substituting these values into the equation, we get:

36 = k * 3^2
36 = k * 9

Now we can solve for k:

k = 36 / 9
k = 4

So, the equation becomes:

z = 4 * x^2

To find the value of z when x=4, we substitute x=4 into the equation:

z = 4 * 4^2
z = 4 * 16
z = 64

Therefore, when x=4, the value of z is 64.