What are the parametric equations for the line parallel to the vector v = (3, 5) and containing the point (6, 10)?
x = 3t + 6
y = 5t + 10
100
What is the explicit formula for the Tower of Hanoi sequence?
T = 2^k - 1
100
If f(x) = 14x^3 - 12x^2 + 16x - 4, what is f''(x)?
f''(x) = 84x - 24
100
Find the measure of x if vectors u = (-1, 2, 5) and v = (4, x , -2) are orthogonal to each other.
x = 7
200
What is z^6 if z = 3 + 5i?
z^6 = 39104 - 3960i
200
What is the measure of the angle between the vectors:
v = (2, -2) and u = (4, 0)?
pi/4
200
Evaluate the series: summation of i = -13 to 16 for
|3i|
681
200
Calculate the integral from -1 to 0 of 1 + x -x^3 dx
3/4
200
In how many ways can you arrange 4 carrots, 3 potatoes, 2 pumpkins, and 2 squashes if the carrots must be kept next to each other and the potatoes must be kept next to each other?
6! 4! 3! = 103680
300
What is the distance from the directrix to the focus at the pole for the conic: r = 42/(2 - 42 sin @)?
k = 6
300
What is the determinant of the matrix:
1 0 2 1,
0 0 3 4,
1 2 5 6,
2 1 2 0
det = -1
300
Given tn = 3n^2 - 7n + 5, what is the recursive formula for the sequence?
t1 = 1
t(n+1) = tn + 6n - 4
300
What is the derivative of f(x) = (1 - x^2)/(4x + 3)
f'(x) = (-4x^2 - 6x - 4)/(4x + 3)^2
300
Given the series: 8 + 2 + ... + 1/2097152. Find the number of terms.
n = 13
400
What is the equation of an ellipse with foci at (0, 6) and (0, 0) and vertices at (0, 8) and (0, -2)?
x^2/16 + y^2/25 = 1
400
What are the 3 row operations allowed in Gaussian Elimination?
Swap any two rows
Multiply a row by a nonzero constant
Add/Subtract any two rows
400
What is the value of the summation of i = 0 to 19 for
5i^3 + i^2 - 2i
222950
400
Suppose we need to enclose a field with a fence. We have 400 feet of fencing and one side of the field is against a wall, so it does not need any fencing. Find the dimensions of the field that would maximize the area enclosed.
100 ft x 200 ft
400
Consider the region bounded by f(x) = x + 5, g(x) = sqrt(x), x = 0, and x = 4. What is the volume of the solid generated by revolving this region around the x-axis?
(604/3)*pi
500
If i is a zero of f(x) = x^4 + 2x^3 + 3x^2 + 2x + 2, what are the remaining zeros (counting multiplicity)?
-i, -1 + i, -1 - i
500
What is x + y for the system?
5x - 8y = 29
2x + 2y = -4
x + y = -2
500
Prove 1+2+3+...+n = n(n+1)/2 using Mathematical Induction.
What is difference between the actual area between the curve y = -x^2 + 10x - 16 and the x-axis and the estimated value based on a Riemann sum using 3 rectangles with the midpoint values?
-2
500
What is a vector parallel to the vector perpendicular to BOTH vectors u = (5, 4, 3) and v = (2, -3, 0)?