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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 solution to the following system of linear equations: Solve the following absolute value inequality: ½ |x - 2|
Claire sells packets of sunflower seeds for $0.95 each and packets of morning glory seeds for $1.43 each. She decides to offer a 16-packet spring-garden combination, combining both types of seeds at $1.10 per packet.
Find an equation of the plane that passes through the line of intersection of the planes x + y - z = 2 and 2x - y + 3z = 1 and passes through the point (-1,2,1).
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.
What proportion of time does Dr. Smith eat a home lunch? d. If Taco Bell costs $3 and a home lunch costs $1 and the Springdale room is free, then how much lunch budget should he allow for his semester, which includes 100 lunches?
On the other hand, give an example of a metric space in which every Cauchy sequence converges; and then prove this metric space is Cauchy sequence and also converges.
Using GEOMETRY ONLY, for an equilateral triangular region, for which points is the sum of the distances to the sides of the triangle minimal? Please show me and do not point to a web site.
Describe objects that have each of the following types of symmetry.
Let f: [a,b] ----> R and suppose f is integrable with respect to alpha. Prove that for any c in the real numbers, cf is integrable with respect to alpha and the integral from a to b of cf d(alpha) = c times integral from a to b of f d(alpha).
One-half serving of soy sauce contains 389 milligrams of sodium. How many grams of sodium from soy sauce are included in an egg-foo-young dish made from 4 serving of soy sauce? Round result to the nearest tenth of a gram.
use a suitable method for generating the number of days needed to repair the copier, when it is out of service, according to the discrete distribution shown and Using simulation estimate the loss of revenue due to copier breakdown for one year
Let X be uniform on the set {1/2,1/3,1/4}, and let the distribution of Y |X = x be geometric with parameter x; that is, P(Y = k|X = x) = (1 - x)kx, for k = 0,1,2,..
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