How do you solve this equation?

Question

y varies directly as the square of x. When y is 36, x is 2. Find y when x is 3.

Someone please explain

Answer 1

If y varies directly as the square of x, then the equation is:

y =kx^2 where k is the constant of variation
step 1, solve for k

y=kx^2
36=k2^2
36=4k
k=9

step 2 to solve for y, substitute the calculated value of k and the given value of x to y=kx^2

y=9(3^2)
y =9(9) = 81

A direct variation describes a relation between two variables, say x and y, which are directly proportional. As y varies with x, there exists a constant of variation designated as k.
In the case of the given problem, y increases as x increases in such way that y is determined by a certain factor, 9, that is multiplied to the square of any value of x

Answer 2

Y varies with X^2
then
Y = K(X^2) where K is a constant

Find K

36 = K(2^2)
36 = 4K
K= 36/4=9
K=9

so Y = 9 (X^2)
when x=3
Y=9 * (3^2)
Y=9 * 9
Y=81

Answer 3

Just ask yourself, what times 2 squared (4) = 36? Of course that is 9. So, 9 times 3 squared (9) = 81

Answer 4

use algebra

y varies directly ...meaning .. if x goes up.. y goes up

expressed as y = kx where k is some unknown value (so far)

now... y varies directly as the square of x...
expressed as y = kx^2

now... plug in your given values... (2,36)
36=k*2^2 and solve for k

36 = 4k
9 = k
now put the value of k back into the general equation
y = 9x^2
now put in 3 for x and solve for y
y = 9*(3^2)
y = 9*9
y = 81

Answer 5

y∝x² → y=Kx²
36=K(2)² → K=9
y=9x² → y=9(3²) → y=81

Answer 6

y is directly proportional to x^2

=> y=k(x^2) ---------- (i) where k is any constant

when y=36, x=2
putting in eqn (i)
=> 36 = k * (2^2)
=> k = 9

now put x = 3 and k = 9 in eqn (i)

y = 9 * (3^2)
=> y = 9 * 9
=> y = 81

Answer 7

some possible solutions depending on the interpretion of
" y varies directly as the square of x "

y = (4+x)^2 => y=49
y = (8-x)^2 => y=25

y = a9 + 3b + c
where a,b satisfies eq : 18 = 2a + b, c anything.

Answer 8

y = kx^2

36 = k * (2)^2
36 = 4k
k = 9

y = 9 * 3^2
y = 9 * 9
y = 81

ANS : 81