Show:
To The Vector Go the Spoils
April Fools and May Tricks
Partial Fractions, or Systems of Equations?
Parametric Paralysis
Kicks and Giggles
100
What distinguishes a vector quantity from a scalar quantity?
Direction
100
What must be true to multiply two matrices of dimensions [A x B] and [C x D]?
The inner dimensions B and C must be equal.
100
Solve the system using substitution: 2x - y = 10 3x + 2y = 1
x = 3 y = 4
100
Identify the parameter in y = -16(t)^2 + 420
The parameter is "t".
100
What, according to The Hitchhiker's Guide to the Galaxy, is the numerical value for the answer to life?
42
200
Multiply the vector [4/5, 2/3] by the scalar value 6. Give your answer in decimal form.
[4.8, 4]
200
Scalar multiplication: Multiply the matrix [ 1 2 -2 0 ] [ 3 -4 0 6 ] [ 6 2 2 -9 ] by the scalar Pi. Give answers to the nearest hundredth.
[ 3.14 6.28 -6.28 0 ] [ 9.42 -12.57 0 18.85 | [ 18.85 6.28 6.28 -28.27 ]
200
Solve using Gaussian elimination: x + z + w = 2 x + y + z = 3 3x + 2y + 3z + w = 8
(-z, -w+2, w+1, z, w)
200
Find an equation for the following parameters: x = 4 - 20t y = 6 - 9t
y = (9/20)x + 4.2
200
Convert (x - 3)^2 + (y - 2)^2 to polar form.
r = 6 cos Θ + 4 sin Θ
300
Let u = [6,9] and v = [3,2]. Find the component form of -3u + 2v.
[-12,-23]
300
Matrix multiplication: [1 4] [3 0 1] [2 6] [0 1 2] [1 7] x
[ 3 4 9 ] [ 6 6 14 ] [ 3 7 15 ]
300
Solve the system using a matrix. x + 2y + z = -1 x - 3y + 2z = 1 2x - 3y + z = 5
x = (9/4), y = (-3/4), z = (-7/4)
300
Find parametric equations for the line through the points A (-5,6) and B (2,-1).
x = 7t - 5 y = 7t + 6 -∞ < t < ∞
300
Find the determinant of: [40 8] [16 13]
392
400
Find the direction angle of the vector [4,20].
78.69 degrees
400
Find the inverse of: [3 -2] [-1 1]
[1 2] [1 3]
400
Decompose (x+2)/(x^2 + 4x + 3).
(1/2)/(x+3) / (1/2)/(x+1)
400
A ball is dropped from a height of 20 meters. Its fall along y is modeled by the parametric equation y = 20 - 4.905(t)^2. Find the time it takes to hit the ground. (Hint: solve for t)
t = 2.02 seconds
400
Find 1 + (i)(sqrt3) using DeMoivre's Theorem
-8
500
Find the angle between the vectors [2,4] and [3,-1].
81.87 degrees
500
Find the determinant of: [6 15] [12 8]
-132
500
Decompose (x+4) / x(x-2).
-2/x + 3/(x-2)
500
A cannonball's trajectory along y is modeled by the parametric equation y = -4.905(t)^2 + 16t. Find the time t between the launch and when it hits the ground.
t = 3.26 seconds
500
Find the work done by a force F of 12 pounds acting in the direction <1,2> in moving an object 4 feet from (0,0) to (4,0)
21.47 foot-pounds