solve math problems

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solve math problems

hw_2.pdf

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MA 343 Homework 3 1. A 1000-gal tank has 400 gal of water with 200 g of salt. The tank has 3 gal/min pouring out while it has 5 gal/min pouring in (with a 2 g/gal salt concentration). What is the amount of salt in the tank at any time (before the tank overflows)? 2. If 5000 dollars is borrowed at eight percent interest (compounded continuously) and is paid off at annual rate k (assumed to be paid continuously), how much total interest is accrued if the loan is paid off in 4 years? Round your answer to two decimal places. 3. For what interval will there exist a unique solution (if any) for the initial √ value problem ty 0 − tan(t) = y, y(3) = 2? 4. Where in the ty-plane (if anywhere) will y 0 = p 9 − t2 − y 2 satisfy the hypotheses of Theorem 2.4.2? 5. Use the method of problem 27 on p. 77 to solve y 0 + 2xy + xy 4 = 0. 1
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