If \( y \) varies directly as \( x^2 \) and \( y = 12 \) when \( x = 2 \), find \( y \) when \( x = 5 \).

when x = 5 , y = 75 .
Direct variation means that y is proportional to x 2 . This can be written as:
y = k x 2
where k is the constant of proportionality. To find k , we use the fact that y = 12 when x = 2 :
12 = k ( 2 ) 2
12 = 4 k
k = 4 12 ​
k = 3
Now that we have the constant of proportionality, we can find y when x = 5 :
y = 3 ( 5 ) 2
y = 3 × 25
y = 75 .

Answered by asad00ira | 2024-06-24

When x = 5 , y is 75. We found this by first determining the constant of proportionality k = 3 using the initial conditions given and then applying this to find y at the new value of x . This shows the direct variation relationship between y and x 2 .
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Answered by asad00ira | 2024-12-20