Pick 1 and do it l Boost LTE8:07 AM1 0 97%moodle.mcneese.eduMath 292 – Test 3Name:Directions: YOU MUST SHOW ALL WORK TO RECEIVE CREDIT.Giving a calculator answer with no additional work does not count as showing your work.This test is open book and open notebook. All work must be completed on your own.Discussing any portion of this test with another person is considered cheating on this test.Sign on the line below to certify that you did not discuss this test with anyone and will not discuss the testor share information about the test with anyone else on the test date, 12/2/2020.Name:Signature:Note: If you are working on your own paper you are expected to include the above statement andrequired signature on your paper at the start of the test.Test Problems:1. Give an equation of the tangent plane to the surface z= In(4y – x) at the point (3,1,0).8z2. Use the Chain Rule to find đu for z = (3x + cos 3y)5 with x = 1+ 3u and y = e2tu3. a) Find the directional derivative of f(x, y) = Jxyz at the point (3, 2, 6) in the direction ofv = <-1,-2,2 >.b) Give the maximum rate of change of f(x, y) = Jxyz at the point (3, 2, 6). In what direction doesthis maximum occur?4. a) Find all critical points of the function f(x, y) = e'(y² –x³)b) Use the second derivatives test to determine if the function has a local maximum, local minimum,or saddle point at each of these critical points.5. Calculate the iterated integral: "y sin(xy)dxdy .6. Calculate the volume of the solid that lies under the hyperbolic paraboloid x -3y +z=2 and abovethe rectangle [-1,1]×[1,2].Evaluate (f 2xydA where D is the triangular region with0, 0), (1, 2), and (0, 3).8. Sketch the region of integration and then give an equivalent double integral with the order ofintegration reversed. CIS(x,y)dydx .9. Evaluate the integral || e* dA where D is the region to the left of the y-axis that lies between thecircles x + v? =1 and x+ v² =4.10. Find the mass of a lamina that occupies the region bounded by 1- y and y = 0 if the lamina hasdensity function P(x,y) = kx for some nonzero constant k.

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Description: Pick 1 and do it l Boost LTE8:07 AM1 0 97%moodle.mcneese.eduMath 292 – Test 3Name:Directions: YOU MUST SHOW ALL WORK TO RECEIVE CREDIT.Giving a calculator answer with no additional work does not count as showing your work.This test is open book and o

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Answered: 1. Give an equation of the tangent…

Math

Advanced Math

1. Give an equation of the tangent plane to the surface z= In(4y – x) at the point (3,1,0).

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.2: Power Functions

Problem 17E: Tsunami Waves and BreakwatersThis is a continuation of Exercise 16. Breakwaters affect wave height...

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Tsunami Waves and BreakwatersThis is a continuation of Exercise 16. Breakwaters affect wave height by reducing energy. See Figure 5.30. If a tsunami wave of height H in a channel of width W encounters a breakwater that narrows the channel to a width w, then the height h of the wave beyond the breakwater is given by h=HR0.5, where R is the width ratio R=w/W. a. Suppose a wave of height 8 feet in a channel of width 5000feet encounters a breakwater that narrows the channel to 3000feet. What is the height of the wave beyond the breakwater? b. If a channel width is cut in half by a breakwater, what is the effect on wave height? 16. Height of Tsunami WavesWhen waves generated by tsunamis approach shore, the height of the waves generally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk. Greens law tells how water depth affects the height of a tsunami wave. If a tsunami wave has height H at an ocean depth D, and the wave travels to a location with water depth d, then the new height h of the wave is given by h=HR0.25, where R is the water depth ratio given by R=D/d. a. Calculate the height of a tsunami wave in water 25feet deep if its height is 3feet at its point of origin in water 15,000feet deep. b. If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected?