Living in the Matrix
Polar Bears
Paramedic Equations
Veni, Vidi, Vector
I won't be a part of this system!
100
When you multiply a 5x3 matrix with a 3x4 matrix, what dimensions do you get on the resulting matrix?
5x4
100
Polar Bear trivia fact time! What are the Polar Bears only predator?
no solution
100
What mode should your calculator be in order to enter a rose curve?
parametric mode
100
What kind of vector is lul=1? (absolute value of u)
a unit vector
100
Solve this system: 2x + 3y = 10 -x + 2y = 2
x=2 y=2
200
What is the determinant of a two by two matrix that is (reading across the first row then across the second row) 5 2 4 3?
9
200
Give two of the four coordinate conversion equations
x=r cos theta; y= r sin theta
200
eliminate the parameter of the equation x=t^2 -2; y=3t+5
y=3(square root of (x+2))
200
(u1,u2)+(v1,v2)=
(u1+v1,u2+v2)
200
Name the four methods for solving systems of equations.
substitution, elimination, graphing, matrices
300
What is the inverse of the matrix 6 3 2 1
no inverse
300
Find the length of each petal of the polar curve: r = 2 + 4 sin(2 theta)
{6,2,6,2}
300
There is a line through points (-2,5) and (4,2). Find the parametrization of the curve.
x=6t-2 y=-3t+5
300
The vectors are u and v are orthogonal if and only if:
u dot v=0
300
Use Gaussian elimination to solve the system of equations: x – y + z = 0 2x – 3z = -1 -x – y + 2z = -1
x=1, y=2, z=1
400
A: [2 4 -5 1 0 -2 5 0 1] B: [4 2 9 0 1 0 0 3 4] Solve A(T)B
[8 20 30 16 8 36 -20 -9 -41]
400
Convert (x-3)^2 +(y-2)^2 =13 to polar form
r=6 cos theta +4 sin theta
400
Peter is firing an arrow 20 ft from the front edge of a circular target of radius 18 in. on the ground. If peter fires the arrow directly at the target and releases it 3 feet from above the ground with an initial velocity of 30ft/sec at an angle of seventy degrees. Will the dart hit the target?
no
400
the dot product of u=(u1,u2) and v=(v1,v2) is
u1v1+u2v2
400
Solve the system of equations graphically: y = ln(x) y = x^2 – 4x + 2
x = .712 , y = -.340 x = 3.828 , y = 1.342
500
Solve the system using matrices 61=2x-3y-7z+2a+4b-6c; 43=6x+1y-5z-8a+9b+5c; 14=7x-5y-4z+13a+2b+11c; 20=-9x+13y+2z+4a-5b+8c; 11=8x+15y-3a+b+6c; 3=5x+19y+z+15a+6b;
x=-1.9 y=1.5 z=-9.5 a=-.36 b=-.04 c=.55
500
KJ is in a plane with the polar coordinates (4 mi, 12 degrees). James is in a plane with the coordinates (2 mi, 72 degrees). Find the distance between the two planes. Hint—use law of cosines.
3.46 mi
500
If Logan fires a nerf bullet at 12 meters a second at an angle of 14 degrees from the horizontal, from a height of 1.5 meters. How long will it take for the bullet to hit the ground and how far will it travel? (acceleration=9.81 m/s^2 and it will be negative since the bullet will be decelerating)
t=.92 seconds distance--11.04 meters
500
If theta is the angle between non-zero vectors u and v, then cosine theta=
(u(dot)v)/(|u||v|)
500
Determine a, b, and c so that the points (-1, 5), (2,-1), and (3,13) are on the graph of f(x) = ax^2 + bx + c.
a=4, b=-6, c=5
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