Please give a clear and complete solution. Consider the functions f: R² → R² given by f(x, y) = (3y - 5x, x³)and g: R² → R² given by g(v, w)=(-2v², w³+7)Find the following (make sure to include all of your reasoning- I expect a clear, complete, and detailed solution.):• Find Df and Dg• Use the chain rule explained in the course videos to find D(g(f)) at the point (x, y)=(2,1).

Answered: Image /qna-images/answer/5b6757e6-52df-4b8d-af38-22b7a62a2e56.jpg

Answered: Consider the functions f: R² → R² given…

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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A sum of 700 is to be used to give seven cash prizes to students of a collage for their overall acadamic performance .if each prize is Rs 20 less than its perceeding prize.find the value of each prize
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Please give solution in correct and step by step detailed format thanku Don't give solution in image format
You are thinking of making your home more energy efficient by replacing some of the light bulbs with compact fluorescent bulbs and insulating part or all of your exterior walls. Each compact fluorescent light bulb costs $4 and saves you an average of $2 per year in energy costs, and each square foot of wall insulation costs $1 and saves you an average of $0.20 per year in energy costs.† Your home has 60 light fittings and 1,200 square feet of uninsulated exterior wall. You can spend no more than $1,300 and would like to save as much per year in energy costs as possible. How many compact fluorescent light bulbs and how many square feet of insulation should you purchase? Please don't give handwritten answer..thanku
Students at Upscale University are required to take at least 3 humanities and 4 science courses. The maximum allowable number of science courses is 12. Each humanities course carries 4 credits and each science course 5 credits. The total number of credits in science and humanities cannot exceed 88. Quality points for each course are assigned in the usual way: the number of credit hours times 4 for an A grade, times 3 for a B grade, and times 2 for a C grade. Susan Katz expects to get B's in all her science courses. She expects to get C's in half of her humanities courses, B's in one-fourth of them, and A's in the rest. Under these assumptions, how many courses of each kind should she take in order to earn the maximum possible number of quality points? Susan Katz should take science courses and humanities courses in order to maximize her quality points.

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