In this problem, how do you get the limits of integration? Pls provide detailed solutions JJJ (2² +z²) dV, S is the solid bounded by the tetrahedronSformed by the planes 12x + 20y + 15z = 60 and the coordinate planes.Evaluate

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Answered: JJJ (2² + z²) dV, S is the solid…

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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Please help me answer this question. I seem to be doing something wrong when integrating and I cant see where.
Firm's production is represented by z=(10(x^(1/2)))*y^(1/2). z=amount of output. x=amount of labor used. y=amount of capital used. Labor cost= 20 dollars per unit, Capital cost= 80 dollars per unit. Part a) 100 units are currently being made as the output. Labor's cost minimizing quantity=20. Capital's cost minimizing quantity=5. Draw a graph of this with both isocosts and isoquants. Part b) The business wants to make the output increase from 100 units to 140 units. In the short run, capital is fixed. What is the amount of labor needed? Show this in your graph in part a. Calculate the new total cost. Part c) In the graph from part a, draw and label a point that shows capital's and labor's cost minimizing level in the long run if the business wants to make 140 units.
Q(x, y) = 42x1/5,A15 Where Q is the output in millions of units of product.
Make Detailed solution TECHNIQUES OF INTEGRATION
A particle moves back and forth along a straight line. Its position (in meters), relative to the origin, at any time t (in seconds) is given by s(t) = 3t³ - 9t² + 5t - 15. Find: (remember to include units)\ 1) the total distance travelled during the first 10 seconds please solve this question, using simple high school calculus. DO NOT use integration or hopitals rule, and please showcase all your work and full steps
A drone, flying at a constant altitude, is designed to monitor an industrial area for signs ofillegal emissions and toxic leaks. Environmentalists studying the area have determined thatthe concentration of pollution (in parts per million) above an emission site, at the altitudewhere the drone is flying, can be modeled byP(x,y)=e-(x^2+2y^2)/10000where x and y are measured in meters, in a rectangular coordinate system, with the sourceof pollution at the origin. When the drone detects pollution on its patrol, it changes courseand travels in the direction in which the concentration of pollution particles increases mostrapidly.(a) Sketch several level curves of the pollution function, along with a possible path that thedrone will follow to the source.(b) Suppose that the drone is located at the point (a, b) when it detects the presence ofpollution. Find an equation describing the drone’s path to the source.
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JJJ (2² + z²) dV, S is the solid bounded by the tetrahedron S formed by the planes 12x + 20y + 15z = 60 and the coordinate planes. Evaluate