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The problem asks to evaluate \( h(5t^2) \) given that \( h(t) = 11 - 7t \).

### Solution:
We know that \( h(t) = 11 - 7t \). This means that for any input \( t \), we simply substitute \( t \) into this equation to find \( h(t) \).

Now, we need to evaluate \( h(5t^2) \). This means we substitute \( 5t^2 \) in place of \( t \) in the equation for \( h(t) \):

\[
h(5t^2) = 11 - 7(5t^2)
\]

Simplifying:

\[
h(5t^2) = 11 - 35t^2
\]

Thus, the final answer is:

\[
h(5t^2) = 11 - 35t^2
\]

Would you like more details on this solution, or do you have any other questions?

Here are five related questions to expand your understanding:
1. What happens if you need to evaluate \( h(3t^2) \) instead?
2. How would the solution change if \( h(t) \) was a different linear function, like \( h(t) = 5 - 2t \)?
3. What would be the effect of plugging in specific values for \( t \) after solving for \( h(5t^2) \)?
4. How can this method be applied if \( h(t) \) was a quadratic function instead of linear?
5. How do transformations like \( h(5t^2) \) affect the graph of \( h(t) \)?

**Tip:** When working with function evaluations, carefully track substitutions to avoid errors in the final expression!

Evaluate h(5t^2) given that h(t) = 11 - 7t.

Learn how to evaluate h(5t^2) given the function h(t) = 11 - 7t by substituting 5t^2 for t. Follow the step-by-step simplification process to get the final result, h(5t^2) = 11 - 35t^2. Suitable for high school students learning function evaluation.

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