7) A can of soda with a temperature of 56 degrees Fahrenheit is placed in a refrigerator which is set to the F.D.A. recommended temperature of 35 degrees Fahrenheit. After 15 minutes the temperature of the soda is 48 degrees Fahrenheit. Assuming, that the can cools according to Newton's law of cooling answer the following. a) What is the differential equation that models this problem? b) After how long will the soda be 40 degrees Fahrenheit?

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Q: 4. Use L'Hopital's rule to evaluate sinh(2) lim x+0 sec(x) - 1

A: we have to evaluate  limx→0sinh2xsecx-1=00 It is known that ddxsecx=secx tanxddxsinhx=coshxddxtan…

Q: using Mathematica]

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A: Problem is solved using concept of lyapunov function.

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Q: du dt = 2 824 dx2 Ans u(x₂+) = -200 8 ● @ o u (o₂t) =(4,t) = 0 u (x,0) = 25 X 22 -n²tl8 sin n -200…

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Q: hat is grap

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A: We can solve this using given information

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Q: By direct partial integration, Solve the following PDES 8- X²Z 5 4 dz , z(x,0) = x² +X, Z (2,y)= 3y"…

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Q: 2. Given: region R below bounded by the graphs of y = √x-5, y = 11-x, and y = 0. (9,2) (5,0) (11,0)…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…