Question

use unit multipliers to convert:
(41) 6. 87 ft² to square inches
(41) 7. 61 yd² to square inches
(41) 8. 32 mi³ to cubic inches
(40) 9. find p: \\(\frac{x}{p} - \frac{k}{m} = c\\)
(40) 10. find p: \\(\frac{xy}{p} - \frac{k}{c} = m\\)
(40) 11. find c: \\(\frac{4p}{x} - \frac{xk}{c} = \frac{y}{m}\\)

Explanation:

Problem 6

Step1: Recall ft to in conversion

1 ft = 12 in, so $1\ \text{ft}^2 = (12)^2\ \text{in}^2 = 144\ \text{in}^2$

Step2: Multiply by conversion factor

$87\ \text{ft}^2 \times 144\ \frac{\text{in}^2}{\text{ft}^2}$

Step3: Calculate the product

$87 \times 144 = 12528$

Step1: Recall yd to in conversion

1 yd = 36 in, so $1\ \text{yd}^2 = (36)^2\ \text{in}^2 = 1296\ \text{in}^2$

Step2: Multiply by conversion factor

$61\ \text{yd}^2 \times 1296\ \frac{\text{in}^2}{\text{yd}^2}$

Step3: Calculate the product

$61 \times 1296 = 79056$

Step1: Recall mi to in conversion

1 mi = 5280 ft = 63360 in, so $1\ \text{mi}^3 = (63360)^3\ \text{in}^3$

Step2: Compute $(63360)^3$

$63360^3 = 63360 \times 63360 \times 63360 = 254358061056000$

Step3: Multiply by 32

$32 \times 254358061056000 = 8139457953792000$

Answer:

$12528\ \text{square inches}$

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Problem 7