Tutor profile: Marilyn K.
Subject: SAT II Mathematics Level 2
The radius and height of a cylinder are equal and the volume of the cylinder is 4. What is the height of the cylinder? A. 2.92 B. 3.14 C. 1.46 D. 0.73
The correct answer is A. The volume of a cylinder is V = 1/2(pi•r^2)h. In this scenario h = r and V = 4 so 4 = 1/2 pi h^3 h = cube root(4 • 2 • pi) = 2.93
Carla is paying $70.50 per day to visit Disney World. She is taxed 6.5% for her ticket each day and charged an additional one time untaxed fee of 5 dollars to use the trolley. Which of the following equations shows the cost of Carla visiting Disney World for x days. A. (70.50x + 5)1.065 B. (70.50 + 5)1.065x C. (70.50)1.065x + 5 D. x(1.065•70.50 + 5)
Option C is correct. The total amount that Carla will spend at Disney is the ticket price, the 6.5% tax on the ticket price, and the 5 dollar trolley fee. If Carla visited for x days, then the total ticket price would be 70.50 times the number of days (x) and the tax (6.5%) times the ticket price (70.50) times the total number of days. This can be written as x • 1.065 • 70.50. Finally, we need to add the 5 dollars fee once with no tax, giving us option C
What is the integral of (x^3/sqrt((x^2)+9)) dx
x = 3 tan (theta) dx = 3 sec^2 (theta) d(theta) sqrt(x^2 + 9) = sqrt(9tan^2(theta) + 9) = 3sqrt(tan^2(theta) + 1) = 3sqrt(sec^2(theta)) = 3sec (theta) so the integral of (x^3/sqrt((x^2)+9)) dx = integral of 27tan^3(theta) • 3sec^2(theta) / 3sec(theta) d(theta) = integral of 27tan^3(theta) • 3sec(theta) d(theta) = 27 integral of ((sec^2(theta) - 1) (sec(theta))(tan(theta)) d(theta)) u = sec(theta) du = sec(theta)tan(theta) 27 integral of ((sec^2(theta) - 1) (sec(theta))(tan(theta)) d(theta)) = 27 integral of (u^2 - 1) du =27 (u^3/3 - u) + C = 9u^3 - 27u + C =9sec^3(theta) - 27sec(theta) + C
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