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A chemical reaction combines two chemicals A and B to make a new compound X. The rate at which the compound X is formed is proportional to the amount of A remaining times the amount of B remaining. The system starts with the two chemicals at quantities A(0)=40 grams and B(0) =50 grams. At time t=0, the chemicals are mixed and X is produced at a rate of 2 grams/minute. Write a differential equation that describes the amount of X as a function of time. Include the necessary initial condition.
What similarities and differences do you see between functions and linear equations? Are all linear equations functions? Is there an instance when a linear equation is not a function?
Use the Theorem of Pappus to ?nd the volume of the given solid.
The base of a triangle is 6 cm greater than the height. The area is 56 cm^2. Find the height and the length of the base.
Find all equilibria. Classify as stable, semi-stable, or unstable using phase diagrams for the equation.
Calculate the yield of a wafer with a 15 cm diameter, a cost of 12, contains 84 dies and has a 0.020 defects/cm^2
Suppose that X is not orientable. Prove that X*Y is never orientable, no matter what manifold Y may be. (Hint: First show that X * R^L is not orientable. But every Y has an open subset diffeomorphic to R^L.)
You are designing a rectangular poster to contain 50 in^2 of printing with a 4-in. margin at the top and bottom and a 2-in. margin at each side. What overall dimensions will minimize the amount of paper used?
a building is 48 meters high and casts a shadow 30 meters long. A person casts a shadow 0.8 meters long. How tall is the person?
What is the probability that more than 10 dogs have trait D? B. What is the probability that at most 11 dogs have trait D? Binomial Distribution and Standard Deviation
Find a second independent solution of this equation. write down the wronskian, how you found it, the first order differential equation, satisfied by y2 and say how you solved it
use slope-intercept form to create a graph that shows these earnings and estimate the company's earnings for the next year if the compnay continues to grow at the same rate?
Confirm that (C ([a, b]) , II·II infinity ) where II f II infinity= max I f (x) I a
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