The rotation rate of a mixing blade, in rotations per second, slows as a liquid is being added to the mixer. The blade rotates at 1,000 rotations per second when the mixer is empty. The rate at which the blade slows is four rotations per second less than three times the square of the height of the liquid. If h is the height of liquid in the mixer, which of the following represents R(h), the rate of rotation?
A. 4 - 9h2
B. 1,000 - (4 - 3h)
C. 1,000 - (9h - 4)
D. 1,000 - (3h2 - 4)
Answer:D
The rotation rate of a mixing blade, in rotations per second, slows as a liquid is being added to the mixer. The blade rotates at 1,000 rotations per second when the mixer is empty. The rate at which the blade slows is four rotations per second less than three times the square of the height of the liquid. If h is the height of liquid in the mixer, which of the following represents R(h), the rate of rotation?
A. 4 - 9h2 B. 1,000 - (4 - 3h) C. 1,000 - (9h - 4) D. 1,000 - (3h2 - 4)
Explanation: D Treat this question as a translation problem. According to the question, R(h) = four rotations per second less than three times the square of the height of the liquid. The height of the liquid is represented by h. Therefore, three times the square of the height of the liquid = 3h2. Four less than this amount is 3h2 - 4. Since the original speed was 1,000, subtract this value from 1,000 to get the current rate of rotation. The correct answer is (D).