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1. Sketch the curve represented by the vector-valued function and give the orientation of the curve r(t) = 2sin ti + tj + 3cos tk.
2. For the vector-valued function r(t) = (sin t - t cos t)i + (cos t + t sin t)j + (t)k, find
i. r' (t)ii. r'' (t)iii. r' (t) · r'' (t).
3. For the vector-valued function r(t) = (ln t)i + (2 sin t cos t)j + (4/t3) k find
i. r' (t)
ii. ∫ r(t)dt
Suppose that you want to purchase a home for $450,000 with a 30 year mortgage at 6% interest. Suppose that you can put 40% down. Assume that the monthly cost to finance $1,000 is $6.00. What are the monthly payments.
Describe fractional partsso that a child can understand it. What are the two distinct requirements of fractional parts? Explain how children's concepts of partitioning need to be refined to produce a concept of fractional parts.
one card is selected at random from a standard deck of 52 playing cards, what is the probability that the card is an even-numbered card.
if the number of minutes it takes a service station attendant to balance a tire is a random variable having an
Car A and Car B leave the origin at noon. Car A travels north at 33 mph and car B travels east at 56 mph.
Chuck travels 260 miles in the same time that Dana travels 230 miles.If Chuck's rate of travel is 6 mph more than Dana's and they travel the same length of time, at what speed does Chuck travel?
A consumer is trying to decide between two long-distance calling plans. The first charges a flat rate of 10¢ ($0.10) per minute,
Let V be a ?nite-dimensional inner product space over F, and let U be a subspace of V. Prove that the orthogonal complement U⊥ of Uwith respect to the inner product ?⋅,⋅? on V satis?es dim(U⊥)=dim(V)-dim(U).
Find the equation for the plane tangent to the paraboloid z = 2x2 + 3y2 that is also parallel to the plane 4x - 3y - z = 10
Using the shell method to find the volume of a solid revolving about line x = 2 by the region bounded by y=x^3 +x +1, y=1 and x=1.
Mean and Variance of a Probability distribution, A bank keeps tracks of customers coming into the bank between 12 Noon and1 PM on Monday.
Joe believes that the relation {(2,1),(3,-2),(4,5),(5,-2)} is not a function because two values in the domain have the same range value. What is the student's error?
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