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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 2: Q. 175 (page 144)

Solve the formula $h = 54 t + \frac{1}{2} a t^{2}$ for $a$ .

Short Answer

Expert verified

The solution for $a$ is as $a = \frac{2 (h - 54 t)}{t^{2}}$

Step by step solution

01

Step 1. Given information

The given formula is $h = 54 t + \frac{1}{2} a t^{2}$ .

02

Step 2. Simplifying

Subtract $54 t$ form both sides and simplify as shown below:

$h = 54 t + \frac{1}{2} a t^{2} h - 54 t = 54 t + \frac{1}{2} a t^{2} - 54 t h - 54 t = \frac{1}{2} a t^{2}$

03

Step 3. Simplify further

Multiply by $2$ on both sides and simplify as shown below:

$h - 54 t = \frac{1}{2} a t^{2} 2 (h - 54 t) = (\frac{1}{2} a t^{2}) 脳 2 2 (h - 54 t) = a t^{2}$

04

Step 4. Simplify further

Divide by $t^{2}$ on both sides and simplify as shown below:

$2 (h - 54 t) = a t^{2} \frac{2 (h - 54 t)}{t^{2}} = \frac{a t^{2}}{t^{2}} a = \frac{2 (h - 54 t)}{t^{2}}$

05

Step 5. Final answer

The solution for $a$ is as $a = \frac{2 (h - 54 t)}{t^{2}}$ .

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