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.