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The vector r(t) = ln (t2 + 1)i + t j + tan-1 t k, -∞ < t < ∞. is the position vector of a particle moving in space.
(a) Find the particle's speed at time t=1.
(b) Find the angle between the velocity and acceleration vectors at time t=1.
(c) At what time(s), if any, are the particle's velocity and acceleration orthogonal?
There are $560 available to build a fence around a rectangular garden. One side must be reinforced and will cost $10 per foot. The other three sides can be built for $4 per foot. Find the dimensions of the largest possible garden which can be buil..
find the dimensions of the poster with the smallest area. Note: The answer to this problem requires that you enter the correct units.
Compute all unit vectors normal to the plane which contains the points (0, 1, 1), (1, -1, 0), and (1, 0, 2) and compute an equation of the plane - Compute an equation for the plane tangent to the surface given by the equation
After this process completes ( 1 full minute passes) how many balls are left in the barrel?
the duration of telephone calls directed by a local telephone company sigma4.2 minutes n500 97 confidence. use the
During the first part of a trip, a canoeist travels 91 miles at a certain speed. The canoeist travels 14 miles on the second part of the trip at a speed 5mph slower. The total time for the trip is 4 hrs. What was the speed on each part of the trip..
Determine the asymptotic stability of the system x' = Ax where. More specifically, what stability conclusion(s) can be drawn?
An electronics manufacturer has two brands that they wish to release into the market, the Xtreme Sound Radio and the You-Play CD System. Suppose that the quantities of each brand produced by the manufacture are labelled x and y respectively, and the ..
A sphere was measured and its radius was found to be 45 centimeters with a possible error of no more that 0.01 centimeters. What is the maximum possible error in the volume if we use this value of the radius?
When you try to find the average of your grade by the end of the year do you add up all four quarter grades then divide by four? If so then what does that number have to be after you are done dividing?
Car Insurance . Use the histogram below to answer the following questions: How many students were surveyed? What are the lower and upper class limits of the first and second classes?
The probability density function for the lifetime of a bulb is f(t) =(1/6) e^{-t/6}, t is less than 0. What is the probability that both of the bulbs will fail within 4 hours?
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