11/17/13

What is its resulting acceleration?
Two 5 kg masses are attached to opposite ends of a long massless cord which passes tautly over a massless frictionless pulley. The upper mass is initially held at rest on a table 50 cm from the... more
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11/16/13

What's the downward acceleration?
Two masses are connected by a light cord which is looped over a light frictionless pulley. If one mass is 3.0 kg and the second mass is 5.0 kg, what's the downward acceleration of the heavier mass?... more
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11/16/13

What's the tension?
Two masses 5.0 and 7.0 kg are originally at rest on a frictionless surface. The masses are connected by a light cord. A second cord is attached to the 7.0 kg mass and pulled with a horizontal force... more
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11/13/13

Compute A^2 and A^3.
Compute A^2 and A^3. Make a prediction for A^5 and A^n:   A=[1, b, 0, 1] and A=[2, 2, 0, 0].   The first row: 1, b. The second row: 0, 1.   The first row: 2, 2. The second row: 0, 0.    
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11/12/13

What are those matrices?
This 4 by 4 matrix will need elimination matrices E21 and E32 and E43. What are those matrices? A=[2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2].   The first row is 2, -1, 0, 0. The... more
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11/12/13

Find and solve?
The parabola y=a+bx+cx^2 goes through the points (x, y)=(1, 4) and (2, 8) and (3, 14). Find and solve a matrix equation for the unknowns (a, b, c).   a+b+c=4 a+2b+4c=8 a+3b+9c=14   a=2, b=1,... more
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11/10/13

Find the definite integral?
Find ∫ 1/(sqrt(4-x^2)) dx from 1 to 2.   Answer: (1/3)pi
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11/10/13

Find the limit?
Find lim t→∞ (4t2(sin(2/t))2).   Answer: 16
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11/10/13

What is the magnitude?
A 20 kg box remains at rest on a horizontal surface while a person pushes directly to the right on the box with a force of 60 N. The coefficient of kinetic friction between the box and the surface... more
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11/09/13

What's the net force?
A person pushes a block of mass M=6.0 kg with a constant speed of 5.0 m/s straight up a flat surface inclined 30 degrees above the horizontal. The coefficient of kinetic friction between the block... more
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11/09/13

What is the coefficient of kinetic friction?
A 22 kg suitcase is dragged in a straight line at a constant speed of 1.10 m/s across a level airport floor by a student on the way to Mexico. The individual pulls with a 1.0x10^2 N force along a... more
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11/09/13

What is the force?
A spaceman of mass 80 kg is sitting in a spacecraft near the surface of the Earth. The spacecraft is accelerating upward at five times the acceleration due to gravity. What is the force of the... more
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11/09/13

Find the integral?
Find ∫ (sin(6x))2(cos(6x))2 dx.
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11/08/13

Find dy/dt?
  Find dy/dt, given that y=x^2+4x and x=cos(3t).
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11/07/13

Find and solve a matrix equation?
The parabola y=a+bx+cx^2 goes through the points (x, y)=(1, 4) and (2, 8) and (3, 14). Find and solve a matrix equation for the unknowns (a, b, c).
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11/06/13

What 3 by 3 matrix E?
What 3 by 3 matrix E multiplies (x, y, z) to give (x, y, z+x)?
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11/06/13

Find the matrix P?
Find the matrix P that multiplies (x, y, z) to give (y, z, x). Find the matrix Q that multiplies (y, z, x) to bring back (x, y, z).
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10/28/13

Find a combination?
Find a combination x1w1+x2w2+x3w3 that gives the zero vector: w1=[1, 2, 3], w2=[4, 5, 6], w3=[7, 8, 9].   The answer is (1/2)w1-w2+(1/2)w3.    
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10/26/13

Find four perpendicular unit vectors?
Find four perpendicular unit vectors with all components equal to 1/2 or -1/2.
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10/26/13

What is that least?
An overhead view of a 12 kg tire that is to be pulled by three horizontal ropes. One rope's force (F1=50 N) is indicated. The forces from the other ropes are to be oriented such that the tire's... more
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10/25/13

How could you prove?
How could you prove cube root of (xyz)≤(1/3)(x+y+z)(geometric mean≤arithmetic mean)?
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10/25/13

What are the smallest and largest values?
If llvll=5 and llwll=3, what are the smallest and largest values of llv-wll? What are the smallest and largest values of v*w?
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10/24/13

Please help me with math?
Why is abs(cos θ) never greater than 1 in the first place?
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10/22/13

Find two vectors?
Find two vectors v and w that are perpendicular to (1, 0, 1) and to each other.  
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10/22/13

Find the angle?
Find the angle θ (from its cosine) between v=[2, 2, -1] and w=[2, -1, 2].   These are vectors with 2 on top, 2 on middle, -1 on bottom. And w with 2 on top, -1 on middle, 2 on bottom. I got the... more
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