https://file.aiquickdraw.com/mathbot/file/1725641720554uzy5ikyq.jpg

Let's solve each problem step-by-step from the image you provided:

### 6. Solve for \( h \) from \( A = \frac{a \cdot h}{2} \)
Given the formula for the area of a triangle, where \( A \) is the area, \( a \) is the base, and \( h \) is the height, we can isolate \( h \) as follows:
\[ A = \frac{a \cdot h}{2} \]
To solve for \( h \):
\[ h = \frac{2A}{a} \]

### 7. Solve for \( Q_2 \) from \( \eta = \frac{Q_1 - Q_2}{Q_1} \)
Given the formula related to efficiency or some relative measure, we can solve for \( Q_2 \) (assuming \( Q_1 \) and \( \eta \) are known):
\[ \eta = \frac{Q_1 - Q_2}{Q_1} \]
Multiply both sides by \( Q_1 \):
\[ \eta Q_1 = Q_1 - Q_2 \]
Now, rearrange to solve for \( Q_2 \):
\[ Q_2 = Q_1 - \eta Q_1 \]
\[ Q_2 = Q_1(1 - \eta) \]

### 8. Solve for \( r \) from \( V = \pi r^2 h \)
This formula is for the volume of a cylinder, where \( V \) is volume, \( r \) is the radius, and \( h \) is the height. To find \( r \):
\[ V = \pi r^2 h \]
Divide both sides by \( \pi h \) (assuming \( h \neq 0 \)):
\[ r^2 = \frac{V}{\pi h} \]
Take the square root of both sides:
\[ r = \sqrt{\frac{V}{\pi h}} \]

Let me know if you need any further details on any step or if you have any questions!

**Further Questions:**
1. Would you like to explore examples of applying these formulas in real-life situations?
2. How would you verify the solutions in a practical setting?
3. Are you interested in learning about variations of these formulas in different geometric or physical contexts?
4. Do you need assistance with how to input real values into these equations to solve practical problems?
5. How might errors in measurement affect the outcomes of these formulas in experimental or real-world scenarios?

**Tip:** Always double-check your algebraic manipulations by plugging known values back into the original equations to ensure the results make sense.

Solve the following math problems step by step: 1) Solve for h from A = (a * h) / 2. 2) Solve for Q2 from η = (Q1 - Q2) / Q1. 3) Solve for r from V = πr^2h.

Learn how to solve algebraic and geometric equations with detailed step-by-step solutions. This guide includes solving for height in a triangle, efficiency calculation, and finding the radius in a cylinder. Perfect 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