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Question: 1. Use direct proof to show that 2n ≤ 2n +2 + 5.
2. Show, by induction, that a polygon formed by n arbitrarily chosen points on a circle has exactly n edges.
3. Go through the inducktive step of the proof for the case n = 5 ducks to see how the subsets of ducks interact.
4. Rewrite this proof for the statement all owls are teal, noting that whereas ducks swim about, owls fly and perch in trees.
Let f and g be the functions given by f(x) = 1 + sin(2x) and g(x) = e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g.
Determine what hunting rate is needed to maintain the current deer population of 30 per square mile. Determine what hunting rate would reduce the population back to the 1700's rate of 10 per square mile.
Give an example of two mutually exclusive events E and F. How can you prove that they are mutually exclusive?
The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle?
If you buy a computer directly from the manufacturer for $2,506 and agree to repay it in 60 equal installments at 1.67% interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?
A random sample of 48 days taken at a large hospital shows that averages of 38 patients were treated in the emergency room per day. The standard deviation for the population is four. Determine the 99% confidence interval of the mean number of patient..
The area A of a rectangular region is the product of the length and width of the rectangle; if we let yrepresent the length, then we have the following. A = yx
If each ton of rock costs $70, each plant is $20, and each tree is $74, what is the maximum number of trees you can buy with a budget of $2,500? Write an inequality that illustrates the problem and solve.
Convert this description into a recurrence for the amount owed after n months.
How many different ways can the letters of the word "BRKIZOVER" be arranged in a row if it is required that the letters IZO remain next to each other in order?
Find the first derivative of f. Find all critical points of f. Identify those intervals where f is increasing and those intervals where f is decreasing. Use the first derivative test to identify local extrema.
Find (partial z)/(partial u)( and ) (partial z)/(partial v) using the chain rule. Assume the variables are restricted to domains on which the functions are defined. Your answers should be in terms of u and v.
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