Math 6-1

What is the value of x in Arctan 3x + Arctan 2x = 45 degrees?

• 1

• -1

• 1/6

• -1/6

Find the volume (in cubic units) generated by rotating a circle x^2 +y^2+6x+4y+12=0 about the y-axis.

• 47.23

• 59.22

• 82.11

• 39.48

If i = (-1)^(1/2), find the value of i^39.

• 1

• -i

• -1

• i

Solve the equation cos^2 A=1−cos^2 A.

• 45°, 315°

• 45°, 225°

• 45°, 135°

• 45°, 225°

Find the change in volume of a sphere if you increase the radius from 2 to 2.05 units.

• 2.51

• 1.52

• 1.25

• 2.15

What is the general solution of (D−1)y(t)=0?

• y = C₁e^t + C₂e^t + C₃ \cos t + C₄ \sin t

• y = C₁e^t + C₂e^t + C₃e^t + C₄e^t

• y = C₁e^t + C₂e^(-t)

• y = C₁e^t + C₂te^t

What percentage of the volume of a cone is the maximum right circular cylinder that can be inscribed in it?

• 24 percent

• 34 percent

• 44 percent

• 54 percent

If -3e^x+2 =0, find x.

• ln 2

• ln 4

• ln 3

• no solution

On a certain day, the nurses at a hospital worked the following number of hours: Nurse Howard worked 8 hours, Nurse Pease worked 10 hours, Nurse Campbell worked 9 hours, Nurse Grace worked 8 hours, Nurse McCarthy worked 7 hours, and Nurse Murphy worked 12 hours. What is the average number of hours worked per nurse on this day?

• 8

• 9

• 10

• 7

Joy is 15 percent taller than Joseph and Joseph is 10 percent taller than Tom. How many percent is Joy taller than Tom?

• 18 percent

• 20 percent

• 21 percent

• 23 percent