find H, in the formula 0.066 = (10x5-7.5xH) divided by 6.8x60kg

To solve for \( H \) in the equation:

\[
0.066 = \frac{(10 \times 5 - 7.5 \times H)}{6.8 \times 60}
\]

Let's break it down step by step.

1. First, calculate the denominator:

\[
6.8 \times 60 = 408
\]

So, the equation becomes:

\[
0.066 = \frac{(10 \times 5 - 7.5 \times H)}{408}
\]

2. Multiply both sides by 408 to eliminate the denominator:

\[
0.066 \times 408 = 10 \times 5 - 7.5 \times H
\]

3. Calculate the left side:

\[
0.066 \times 408 = 26.928
\]

Now the equation is:

\[
26.928 = 50 - 7.5 \times H
\]

4. Subtract 50 from both sides:

\[
26.928 - 50 = -7.5 \times H
\]

This simplifies to:

\[
-23.072 = -7.5 \times H
\]

5. Finally, divide both sides by -7.5 to solve for \( H \):

\[
H = \frac{-23.072}{-7.5} \approx 3.076
\]

So, \( H \approx 3.08 \) (rounded to two decimal places).

Would you like any further details or have any questions about this solution? Here are some related questions:

1. How would the solution change if the mass was different?
2. What is the impact on \( H \) if the coefficient 7.5 were changed?
3. How would you isolate \( H \) if there were additional terms in the numerator?
4. How can this equation be represented graphically?
5. How does rounding affect the final result?
6. What happens if the initial value of 0.066 is changed?
7. What would be the result if \( H \) were negative?
8. How would this equation be solved if it were part of a system of equations?

**Tip:** Always double-check calculations by plugging the value back into the original equation to verify accuracy.

Learn how to solve the linear equation 0.066 = (10 * 5 - 7.5 * H) / (6.8 * 60 kg) step-by-step with a detailed solution. This problem involves calculating the value of H using basic algebraic operations. Suitable for students in Grades 9-12.

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