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Consider the spiral given parametrically by
x(t) = 9e-0.5t sin (2t)
y(t) = 9e-0.5t cos (2t)
on the interval 0 ≤ t ≤ 8.
Fill in the expression which would complete the integral determining the arc length of this spiral on 0 ≤ t ≤ 8.
Determine the arc length of the given spiral on 0 ≤ t ≤ 8.
Now determine the arc length of the given spiral on [0, ∞).
Two cards are drawn from a standard deck of 52 without replacement. By drawing a tree diagram, find the probability the second card drawn is a king?
Suppose T is a Mobius transformation such that the image of the real axis under T is the real axis. Prove that T may be written in the form T(z) = (az+b)/(cz+d) with a, b, c, and d real.
The length of a rectangular board
A class has 10 business majors and 15 econ majors. If Five students are chosen at random, what is the probability that three are business major and two are econ majors?
Suppose there is a hole in the can of paint and 18 lb of paint leaks steadily out of the can during the man's ascent. How much work is done by the man against gravity in climbing to the top?
One of the key principles of differentiation is information dissemination to stakeholders including students, parents, colleagues, and others involved in the education community.
Determine which coin is the counterfeit coin in as few weightings as possible. Does your method also allow you to state whether the counterfeit coin is heavy or light?
If the radius of the outer ripple increases uniformly at the rate of 2 cm. per sec. determine how rapidly the disturbed area of water is increasing at the end of 10 seconds.
Suppose at a given moment, Han Solo is travelling at 60 imperial units per minute and is 8 units away from the intersection and Darth Vader is traveling at 30 imperial units per minute and is 6 units away from the intersection. Calculate how fast ..
A consumer is trying to decide between two long-distance calling plans. The first charges a flat rate of 10¢ ($0.10) per minute,
A group of friends decided to rent a vacation home for a week. They each paid $70 towards the rent. If three more friends had joined them, the cost per person would have been reduced by $14. How many friends went on the trip?
Assuming exponential population growth, predict the populations of China and the U.S. in the years 2100 and 2200. Assuming exponential population growth, approximately when will China's population double?
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