y is directly proportional to x squared given that y=122.5 when x=7 work out the value of y when x=8

Since \( y \) is directly proportional to \( x^2 \), we can express the relationship as:

\[
y = kx^2
\]

where \( k \) is the constant of proportionality.

### Step 1: Find the constant \( k \)

We are given that \( y = 122.5 \) when \( x = 7 \). Substituting these values into the equation:

\[
122.5 = k(7^2)
\]
\[
122.5 = k(49)
\]
\[
k = \frac{122.5}{49} = 2.5
\]

### Step 2: Find \( y \) when \( x = 8 \)

Now that we know \( k = 2.5 \), we can substitute this value into the equation along with \( x = 8 \):

\[
y = 2.5(8^2)
\]
\[
y = 2.5(64)
\]
\[
y = 160
\]

Thus, when \( x = 8 \), \( y = 160 \).

Let me know if you need more details, or if anything is unclear!

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Here are 5 related questions you might consider:
1. What happens to \( y \) if \( x \) is doubled in this proportional relationship?
2. How would you express \( y \) in terms of a different variable that also depends on \( x^2 \)?
3. Can you solve for \( x \) if \( y \) is given and you know the constant \( k \)?
4. What is the effect on \( y \) if \( x \) is halved?
5. How would you generalize this for \( y \) being directly proportional to \( x^n \) for any \( n \)?

**Tip:** Always check that your constant \( k \) remains consistent when applying proportionality to different values.

y is directly proportional to x squared given that y=122.5 when x=7. Work out the value of y when x=8.

Learn how to solve a direct proportionality problem where y is proportional to x squared. Given y=122.5 when x=7, find y when x=8. This problem covers key concepts like proportionality and quadratic relationships, with a step-by-step solution. Ideal for students in Grades 8-10.

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