Question

The blade of a rotor 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 $R\left(h\right)$, the rate of rotation?

• A. $4-9h^2$
• B. $1,000-(4-3h)$
• C. $1,000-(9h-4)$
• D. $1,000-(3h^2-4)$

Answer 1

The correct option is D $1,000-(3h^2-4)$

According to the question,

$R\left(h\right)=$ 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 $=$ $3h^2$.

Four less than this amount is $3h^2-4$.

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).$1000-(3h^2-4)$.