Please don't provide handwritten solution ..... A tank having a capacity of 100 gallons is initially full of water. Pure water is allowed to run into the tank at therate of 1 gallon per minute. At the same time, brine (a mixture of salt and water) containing 1/4 pound of salt pergallon flows into the tank at the rate of 1 gallon per minute. (Assume that there is perfect mixing.) The mixtureflows out at the rate of 2 gallons per minute. Find the amount of salt in the tank after t minutes.

Inflow = pure water at the rate of 1 gallon per minute and brine water at the rate of 1 gallon per…

Answered: A tank having a capacity of 100 gallons…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(c) Find the rotation matrix of a linear transformation T: R² R², which first rotates points 3 clockwise and then reflects points through the z-axis. -
An organic juice company would like to increase its production of juice. The company’s plan for the next five months is to increase the num- ber of gallons of juice it produces each month by 400 gal. For the five-month period, the company wants to produce at least 8500 gal of juice. What is the minimum number of gallons of juice the company can produce in the first month if it is to achieve its goal?
You have been named the Good Reader in your town’s reading club. You’re invited to give a 15-minute speech at the annual reception. You want to spend the speech talking about three themes; (1) how you came to love books, (2) the camaraderie you feel in the club, and (3) your long-term goals for encouraging reading in the town. You would like to spend at least 2 minutes talking about each theme. How many ways can you segment your time so that you talk enough about each theme? Note that you should assume the number of minutes you spend talking about each theme is a natural number. One example of a valid breakdown is 3 minutes on theme 1, 5 minutes on them 2, and 7 minutes on theme 3. Describe how you arrived at your solution.
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In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a new doll called The Dougie that teaches children how to dance. The fixed cost to produce the doll is $100,000. The variable cost, which includes material, labor, and shipping costs, is $32 per doll. During the holiday selling season, FTC will sell the dolls for $40 each. If FTC overproduces the dolls, the excess dolls will be sold in January through a distributor who has agreed to pay FTC $10 per doll. Demand for new toys during the holiday selling season is extremely uncertain. Forecasts are for expected sales of 60,000 dolls with a standard deviation of 15,000. The normal probability distribution is assumed to be a good description of the demand. FTC has tentatively decided to produce 60,000 units (the same as average demand), but it wants to conduct an analysis regarding this production quantity before finalizing the decision. (a) Determine the equation for computing FTC's profit for given values of the…
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Q) Newlyweds Nick and Dana each work two part-time jobs in order to make ends meet as they finish college. Nick’s college schedule allows him to work a total of 30 hours per week both for a department store that pays him $9.50 per hour and for a fast food restaurant that pays him $8.50 per hour. Dana’s college schedule allows her to work a total of 25 hours per week for a grocery store that pays her $10.00 per hour and for a novelty shop that pays her $8.00 per hour. The couple must earn $500 per week in order to eat and pay bills. Question 1: Solve the system by writing its augmented matrix in reduced row echelon form.
Write a complete solution including all necessary calculations, formulas, and a listing of all variables and their values Compare by % age boys test scores in Canada to boys test scores in Japan. Compare by %age girls test scores in South Korea to girls test scores in Russia
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