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# A total of 2 questions refer to the following information.a  = 1,052 + 1.08tThe...

### Question

A total of 2 questions refer to the following information.

= 1,052 + 1.08t

The speed of a sound wave in air depends on the air temperature. The formula above shows the relationship between a, the speed of a sound wave, in feet per second, and t, the air temperature, in degrees Fahrenheit (°F).

At which of the following air temperatures will the speed of a sound wave be closest to 1,000 feet per second?

### Options

A)
−46°F
B)
−48°F
C)
−49°F
D)
−50°F

The correct answer is B.

### Explanation:

Choice B is correct. The air temperature at which the speed of a sound wave is closest to 1,000 feet per second can be found by substituting 1,000 for $$a$$ and then solving for $$t$$ in the given formula. Substituting 1,000 for $$a$$ in the equation a = 1,052 + 1.08t gives 1,000 = 1,052 + 1.08t. Subtracting 1,052 from both sides of the equation 1,000 = 1,052 + 1.08t and then dividing both sides of the equation by 1.08 yields $$t = \frac{-52}{1.08} \approx -48.15$$. Of the choices given, $$-48^{\circ}F$$ is closest to $$-48.15^{\circ}F$$.
Choices A, C, and D are incorrect and might arise from errors made when substituting 1,000 for $$a$$ or solving for $$t$$ in the equation a = 1,052 + 1.08t or in rounding the result to the nearest integer.