Matthews Simmons
11/29/2023 · Middle School
2. Consider the information given and answer the following. It is known that M varies directly with N . When \( \mathrm{M}=15 \) and \( \mathrm{N}=72 \). a. Find the constant of variation b. Find the equation of variation. c. Find M when \( \mathrm{N}=2 \) II. Answer the following problems involving inverse variation. It is known that A is inversely proportional to B and \( \mathrm{A}=8 \) when \( \mathrm{B}=3.5 \). a. Give the constant of variation. b. Give the equation of variation. c. Find A when \( \mathrm{B}=1.75 \) d. Find B when \( \mathrm{A}=4 \) e. Is \( \mathrm{A}=14 \) when \( \mathrm{B}=2 \) ? Briefly Explain.
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1. **Direct Variation:**
- a. Constant of variation \( k = \frac{5}{24} \)
- b. Equation of variation \( M = \frac{5}{24}N \)
- c. \( M \) when \( N = 2 \) is \( \frac{5}{12} \)
2. **Inverse Variation:**
- a. Constant of variation \( k = 28 \)
- b. Equation of variation \( A = \frac{28}{B} \)
- c. \( A \) when \( B = 1.75 \) is \( 16 \)
- d. \( B \) when \( A = 4 \) is \( 7 \)
- e. Yes, \( A = 14 \) when \( B = 2 \) is correct.
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