11. A tank contains 100 gallons (gal) of water and 50 ounces (oz) of salt. Water containing a saltconcentration of (1 + sin t) oz/gal flows into the tank at a rate of 2 gal/min, and the mixtureflows out at the same rate. Write an initial value problem for the amount of salt in the tank at anytime t.

Answered: Image /qna-images/answer/d06c9389-fd56-4754-9ab3-7001768e98dc.jpg

Answered: 11. A tank contains 100 gallons (gal)…

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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2. A.tank initially contains 100 gal of a solution that holds 25 lb of a chemical. Water runs into the tank at the rate of 3 gal/min and the solution runs out at the same rate. How much of the chemical remains in the tank after of the chemical in to reduce the amount 15 min? How long does it take the tank to 1 lb?
1. Miles' neighbor, Andy says his maximum heart rate is 90 BPM at 50% intensity. Use your model to determine how old Andy is. Be prepared to explain HOW you got the answer. V=1.37⋅y+17.8V=1.37⋅y+17.8 V = value of CA wine market in billions y = years since 2000 Q. In what year should the CA wine market be worth $45 billion (assuming this equation applies at that time)?
6. A 50 gallons tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 4 gal/min, while the well-stirred mixture leaves the tank at the rate of 2 gal/min. Find a. the amount of time required for overflow to occur b. the amount of salt in the tank at the moment of overflow
2. Caffeine is eliminated from the body at a continuous rate of approximately 17% per hour. A standard cup of coffee contains 150mg of caffeine. a) Write a formula for the amount of caffeine C in mg as a function of the number t of hours after drinking a cup of coffee. b) Find the number of hours (to the nearest hour) it makes for half of the caffeine from a cup of coffee to be eliminated from the body. c) Find the number of hours (to the nearest hour) it takes for only 1.5mg of the caffeine from a cup of coffee to remain in the body.
Assign variables and restate the following problem in terms of known and unknown derivatives (but do not solve it): How fast is the volume of a cube increasing if its side increases at a rate of 0.5 cm/s?
1. Suppose that a commercial truck has an efficiency of 120 – 2v m(v) miles/gallon going at speed of v miles/hour. The driver's rate is 15 dollars/hr, and gas is $3.50/gal- lon. a. Find the cost C(v) per mile to travel at speed v mph. b. Find the cheapest driving speed.

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