Math

CalculusQ&A LibrarySolution to 7. Separation of variablesbecome dr ue integral evaluate to: In 3y +2 = + cApply e to get: 3y + 2 ca. Some algebra yields the general solution: yimplies c4 = 26 So the particular solution is: | y 26e3a--dr. Use 1-substitution with u 3y+2 and - dy. The integrals13y + 2l duApply some algebra to get: In 3y +2 = 3x + c22c4e3Use IC to find C4 : 8-y(0)Exponential Growth and Mixing problems homework to be handed in. Just two problems:Problem 1. (Exponential growth) Suppose a small colony of 1,000 bacteria, at t 0 minutes is in a large bottle of waterwith lots of food and no predators (so there are no predation or density dependent issues to worryminutes there are 2,500 bacteria in the colony. Let y(t) = the number oin a largeabout). Suppose after 45f bacteria in the colony at time t, t measured in minutesWrite the ODE IVP for the above scenario and find the solution to the IVP. Use the solution to estimate how many bacteriain the bottle at t90 minutes. Circle your answer (the number of bacteria after 90 minutes).werelem 2. (Mixing) We start with 2,000 liters of seawater in a tank. In seawater there are 35 g of salt per liter. Supposewe continually pour fresh water (0.5 g salt/liter) into the top of the tank at the rate of 10 liters/minute and at the bottom ofthe tank, we continually drain off 10 liters/minute. So the amount of water in the tank is always 2,000 liters. Assume that thewater in the tank is being stirred so that the saltwater and the freshwater mix immediately. How long until the concentofrationsalt in the tank is 6 g/liter? Circle your final answer (how many minutes until the salt concentration is 6 g/L)Instructions. On page 1, immediately after your name, write:(1) Number of bacteria after 90 min = your answer(2) Minutes until the salt concentration is 6 g/LyoThen, underneath and on the following pages show all work. Don't skip steps. Show the integration. Use a pencil (so youcan erase your mistakes). Be neat so that I can follow your work. Circle final answers. STAPLE with stapler the pages. Nopaper clips, etc.Question

Asked Feb 14, 2019

24 views

Question 2

Step 1

We have given,

Step 2

Solution...

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: Determine the radius of convergence of the following power series. Then test the endpoints to determ...

A: The power series is given as

Q: 13. The cost of producing x ounces of gold from a new gold mine is C= f(x) dollars. (a) What is the ...

A: Given cost function is:Cost of producing x ounces.

Q: Part d and e

A: (D) When the enclosed region revolve about x=2 line then the radius is on the line joining (2,0) and...

Q: 3. Given the function g(x) 8x defined on [-1, 1], determine if the function satisfies the Mean Value...

A: Given,

Q: Calculate the area, in square units, bounded by g(x)=4x−2 and f(x)=5x−15 over the interval [−11,4]. ...

A: Area of region between g(x) and f(x) over the interval [–11,4] is computed as follows.

Q: For each of the following integrals, indicate whether integration by substitution or integration by ...

A: Known fact:Integration by parts:When an integral contains the product of two functions, then integra...

Q: Find the point on the surface x2 − 2xy + y2 − x + y = 0 closest to the point (3, 4, −5).

A: Consider the provided surface

Q: Differentiate y = (s - sqrt(s) ) / s^2 I don't understand what happens on step 3 of the screenshot...

A: Here use quotient rule of differentiation which is,

Q: curves. Find the volume of the solid generated when R is revolved about the x-axis Let R be the regi...

A: Use disk method to find the volume of the solid generated when R is revolved about the x-axis is cal...