The temperature at a point (x,y,z) is given by T(x,y,z)=1200e-x^{2}-2y^{2}-z^{2} where T is measured in ∘C and x, y, and z in meters. 1. Find the rate of change of the temperature at the point P(2, –2, 2) in the direction toward the point Q(3, –4, 3).Answer: D f(2, –2, 2) =PQ2. In what direction does the temperature increase fastest at P?Answer:3. Find the maximum rate of increase at P.Answer:

Given T(x,y,z)=1200e-x2-2y2-z2 we have to find the rate of change of temperature at point P(2,-2,2)…

Answered: 1. Find the rate of change of the…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter2: Functions And Graphs

Section2.6: Proportion And Variation

Problem 22E: Find the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and...

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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?

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1. Find the rate of change of the temperature at the point P(2, -2, 2) in the direction toward the point Q(3, -4, 3) Answer: D f(2, –2, 2) = PQ 2. In what direction does the temperature increase fastest at P? Answer: 3. Find the maximum rate of increase at P. Answer: