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1. Given a path
r(t) = e(1/4)t sin ((1/2)t)i + e(1/4)t cos ((1/2)t)j + e(1/4)tk.
2. Find the velocity vector, acceleration vector and the speed of the curve
Let the acceleration vector be given by
a(t) = 6ti - 5j + 12t2 k.
Find the velocity vector, and position vector, with the initial conditions r0 = 3i + 4j and v0 = 4j - 5k.
3. Find the arc length of
r(t) = 3 sin (2t)i + 3 cos (2t)j + 8tk.
between t = 0 and t = π
4. Find the curvature of the curve
r(t) = 3 sin (2t)j + 3 cos (2t)j at (0, 3).
Find a linear equation given the total cost of C, of producing X units given that 200 graphing calculators cost $1050 to produce and 525 calculators cost $2350 to produce.
Problem 1: Find the average rate of change of the function over the given interval.
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If the price was $1.50 per gallon one week, and $2.00 the next week, what was your average price per gallon?
Find a matrix A that admits no LU decomposition, even if we only require that L is lower triangular ( not necessarily unit!) and U is upper triangular.
Fenced-In Land. A farmer has 100 yd of fencing. What are the dimensions of the largest rectangular pen that the farmer can enclose?
The sampling distributions of a sample statistic
describe a study you might design that could use the chi square statistic. what are the variables? what are the null
What is the decimal notation for the fraction 1/4? How can you show that 1/4 = 25/100? How can you write 5/16 as a decimal? How would you write 1/9 as a decimal?
An irrigation sprinkler in a field of lettuce sprays water over a distance of 25 feet as it rotates through an angle of 155°. What area of the field receives water? If necessary, round the answer to two decimal places.
a 17-ft ladder is leaning against a wall. If the bottom of the ladder is pulled alone the ground away from the wall at a constant rate of 5ft/sec, how fast will the top of the ladder be moving away
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