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Question: 1. Prove that if f'(x) = g'(x) for all x in (a, b), then there is a constant C such that f(x) = g(x) + C on (a, b). [Hint: Apply the Constant Function Theorem to h(x) = f(x) - g(x).]
2. Suppose that f'(x) = f(x) for all x. Prove that f(x) = Cex for some constant C. [Hint: Consider f(x)/ex.]
How high are you off the ground after 5 minutes?
7) The formula A = 2πrh tells us the lateral surface area A of a cylinder with radius r and height h.
The probability of being dealt two pairs in a five card poker hand is 0.0475. What are the odds of being dealt two pairs? Three fair coins are flipped. Outcomes in the sample space are represented by strings such as HHT, HTH, and TTT.
The subspace S of vectors in R5 of the form (x1, x2, x3, x4, x5) with x1 = x2 = 2x3.
Formulate a linear programming model that can be used to determine the number of training programs on team building and the number of training programs on problem solving that should be offered in order to minimize total cost.
Generate appropriate histograms or box plots. Find appropriate statistics that will help to understand the data set. Are there any notable features? Are there any outliers? Describe the key elements of center, variation, distribution, and outliers..
Could you give me one of your concise explanations with examples as to how to use them? I am struggling with the abstract aspects of this concept.
The sleepers of a railway track which is turning round a bend of radius 60m are banked so that a train traveling at 40 km/hr exerts no lateral force on the rails. Find the lateral force exerted on the rails by an engine of mass 10^5 kg when travel..
Let A be the set of points different from the origin in the Euclidean plane. For p, q ? A, define p ~ q if p = q or the line through the distinct points p and q passes through the origin.
With the definition that pi is the area of the unit circle, explain why pi equals 8 times the integral from 0 to 1/sqrt(2) of (sqrt(1 - x^2) - x) dx. use the Romberg algorithm to approximate the integral.
Perform a break even analysis showing an algebraic statement of:
In a standard normal distribution, what z value (s) corresponds to 17% of the data between the mean and the z value?
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