https://file.aiquickdraw.com/mathbot/file/1726161607655syqglff2.jpg

We are given that \( y \) is directly proportional to \( x^2 \), so we can express the relationship as:

\[
y = kx^2
\]

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

From the given information, when \( x = 5 \), \( y = 112.5 \). We can substitute these values into the equation to find \( k \):

\[
112.5 = k(5^2)
\]
\[
112.5 = k(25)
\]
\[
k = \frac{112.5}{25} = 4.5
\]

Now that we have \( k = 4.5 \), we can find the value of \( y \) when \( x = 8 \) by substituting \( x = 8 \) into the equation:

\[
y = 4.5(8^2)
\]
\[
y = 4.5(64) = 288
\]

Thus, the value of \( y \) when \( x = 8 \) is \( 288 \).

Would you like more details or have any questions?

Here are some related questions you might find helpful:

1. How does direct proportionality differ from inverse proportionality?
2. What would happen to \( y \) if \( x \) were doubled in a direct proportion to \( x^2 \)?
3. How do you determine the constant of proportionality in other types of relationships, such as linear ones?
4. If \( y \) were inversely proportional to \( x^2 \), how would the equation change?
5. How do you use proportionality to model real-world situations?

**Tip:** Always substitute known values into the equation early to simplify and solve for unknown constants.

y is directly proportional to x^2. Given that y = 112.5 when x = 5, work out the value of y when x = 8. If your answer is a decimal, then round it to 1 d.p.

Learn how to solve a direct proportionality problem where y is proportional to x^2. Given y = 112.5 when x = 5, we find the value of y when x = 8. Follow along with step-by-step instructions using algebraic formulas. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation