Math Problem Statement

a/M=4g−h

Solution

The equation aM=4gh\frac{a}{M} = 4g - h can be solved for different variables depending on what you're looking for. Here are some possible steps to rearrange this equation for different variables:

  1. Solve for aa:

Multiply both sides by MM to isolate aa: a=M(4gh)a = M(4g - h)

  1. Solve for MM:

Divide both sides by 4gh4g - h to isolate MM: M=a4ghM = \frac{a}{4g - h}

  1. Solve for gg:

To solve for gg, first add hh to both sides: aM+h=4g\frac{a}{M} + h = 4g Now divide by 4: g=aM+h4g = \frac{\frac{a}{M} + h}{4}

  1. Solve for hh:

To isolate hh, subtract 4g4g from both sides: h=4gaMh = 4g - \frac{a}{M}

Do you want to solve for a specific variable or have any details explained further?


Here are 5 related questions to expand your understanding:

  1. How would the result change if we include units for aa, MM, gg, or hh?
  2. Can you factor the expression M(4gh)M(4g - h) in a different way?
  3. What happens if h=4gh = 4g in this equation?
  4. How do we handle the case when 4gh=04g - h = 0?
  5. Can you graph the relationship between aa and MM?

Tip: When solving equations with multiple variables, always ensure to isolate the variable of interest before performing operations like addition or multiplication.

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Math Problem Analysis

Mathematical Concepts

Algebra
Equation Solving
Linear Equations

Formulas

a = M(4g - h)
M = a / (4g - h)
g = (a/M + h) / 4
h = 4g - a/M

Theorems

Basic properties of equations
Multiplication and division in equations

Suitable Grade Level

Grades 9-12