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It takes 3x107 years for a particular star to make one orbit around its galaxy. Assume that this star's orbit in its galaxy is circular with a diameter of 104 light years. A light year is the distance that light travels in one year. There are about 5.859x10¹² miles in 1 light-year. Estimate how many miles this star travels in one year.
The star travels about _____ miles in one year.
How many different 6-letter code words can be formed from the first 8 letters of the alphabet if adjacent letters must be different?
Assume f is continuous on the interval (a,b) that contains x0 and f(x0)>0. Show there is an open interval J that contains x0 and m>0 such that f(x)>=m for each x in J.
A flu epidemic hits a large city. Each resident of the city is either sick, well, or a carrier. The proportion of people in each of these categories by age is given by the matrix:
A small gift shop is trying to determine the number of gift items it can sell to maintain a monthly revenue greater than $10,000. The revenue function for this business is R = -0.10N2 +70N, where R=monthly revenue and N=number of gift items sold p..
Find the value of the integral of g(z) around the circle |z - i| = 2 in the positive section when g(z) = 1/(z^2+4)
A formula is derived for the n-th derivative of a function that is a product of two other functions, f(x)=u(x).v(x). This formula is used to write down the n-th derivative of f(x) = e^x/(1 − x).
You pay $6 to play a game where you will roll a die, with a payoff as follows: $8 for a 6, $7 for a 5, and $4 for any other result. What are your expected winnings? Is the game fair?
Prove that f(x) is continuous at every irrational point and discontinuous at every rational point. Show that f is integrable on [0,1]
Suppose that each member of a set of people has a list of k books which he or she wishes to borrow from a library. SUppose also that each book appears on exactly k lists. Show that it is possible for everyone to borrow one of the books on his or h..
The surface area of the right squre pyramid is given by S=b square rt. b^2 + 4h^2. If the pyramid has height of 10 feet and surface area of 100 square feet, what is the length of a side b of its base?
Differentiable function on the interval.
Find whether the given function is linear function or not - For each of the relationships below, explain whether you think it is best described by a linear function or a non-linear function.
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