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1. Make up a differential equation that you feel confident possesses only the trivial solution y = 0. Explain your reasoning.
2. Suppose P(x) is continuous on some interval I and a is a number in I. What can be said about the solution of the initial-value problem y' + P(x)y = 0, y(a) = 0?
3. Is the set of functions f1(x) = e^(x + 2) , f2(x) = e^(x - 3) linearly dependent or linearly independent on (- ∞, ∞ )? Discuss.
Find the volume of the solid formed when when the graph of the region bounded by y=e^x, x=0, x=2, and y=0 is revolved about the x-axis.
Find the two mean proportionals between two cubes guaranteed by Proposition VIII-12.
Give examples (either a graph or the system of equations) of the 3 types of solutions to a system of linear equations - one solution, no solution, infinitely many solutions.
An extension ladder adjusts in length from 10 ft to 16 ft. Suppose you've leaned your ladder against your house, so that, at its minimum length, it touches the base of your first floor window, 9 feet above the ground.
The credit remaining on a phone card is a linear function of the total calling time. The function gives a line with a slope of -.32, when graphed.
Determine the distances from A to B and from C to B. Show all work to receive full credit. Round to the nearest hundredths.
Relationship between the variables
Find the solution to the given system for the given initial condition
In the following, we are in the process of determining whether integer n = 1373 is a prime or not, using the Rabin-test. Assume that a random number generator returns a = 5. Use modular exponentiation to evaluate the relevant expressions, and disc..
Show that the mean value theorem applies or does not apply to the following. f(x)=sqrt(25-x^2), [-4,4]. State the conditions clearly, and, if appropriate, find the c guarenteed by the theorem.
A target heart rate T that is half a person's maximum heart rate is given by T=110 - 1/2A where A is a person's age.
Check to be sure that all deposits included in your record book are included and service charges are subtracted and make a list of outstanding checks, with the amounts for which they were written.
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