Question
Bacteria in a certain culture increase at a rate proportional to the number present. If the number of
bacteria doubles in three hours, in how many hours will the number of bacteria triple?
(A) \(\frac{3ln 3}{ln 2}\) (B) \(\frac{2ln 3}{ln 2}\) (C)\( \frac{ln 3}{ln 2}\) (D) \(ln\left ( \frac{27}{2} \right )\) (E)\(ln\left ( \frac{27}{2} \right ) \)
Answer/Explanation
Ans:A
Question
What is the area of the largest rectangle that can be inscribed in the ellipse \(4x^{2}+9y^{2}=36\)
(A) \(\sqrt[6]{2}\) (B) 12 (C) 24 (D) \(\sqrt[24]{2}\) (E) 36
Answer/Explanation
Ans:B
Question
The position of an object attached to a spring is given by \(y(t)=\frac{1}{6}cos(5t)-\frac{1}{4}sin(5t) \), where t is time in seconds. In the first 4 seconds, how many times is the velocity of the object equal to 0?
(A) Zero
(B) Three
(C) Five
(D) Six
(E) Seven
Answer/Explanation
Question
Consider all right circular cylinders for which the sum of the height and circumference is 30 centimeters. What is the radius of the one with maximum volume?
(A) 3 cm (B) 10 cm (C) 20 cm (D) \(\frac{30}{π^{2}}cm\) (E) \(\frac{10}{π}cm\)
Answer/Explanation
Ans:E
