Home » Past Questions » Math » A total of 2 questions refer to the following information.a  = 1,052 + 1.08tThe...

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.


More Past Questions:


Discussion