Directions: For questions 1-7, use the following function:f(x,y) = 2x³y + y.1) f(-1,2)2) fr(x, y)3) f„(x,y)4) fxx(x,y)5) fry (x, y)6) fyx(x, y)7) fyy (x,y)

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Answered: Directions: For questions 1-7, use the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 21E

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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?
An insect is moving on the surface of a hot plate, the temperature of which at the point x units to the right of the lower left corner and y units up from the lower left corner is given by T(x,y)=100−x3−3y2. If the insect is at the point (1,3) in what direction should it move in order to maintain its temperature?
Find the relationship between x and y such that point (x,y) is equidistant from the points (7,1) and (3,5)
F(x,y)= 2x - y - e^(-x) g(x,y)=-x+2y-e^(-y)
Find ∇f at the given point. f(x,y,z) = x2 + y3 - 2z2 + zlnx, (1,2,5)
Evaluate fx, fy, fz at the given point: a) f (x, y z) = x³yz² at the point (1, 2, 3) b) f (x, y, z) = x² - 2xy + 3yxz² at the point (3, 1, -2) c) f (x, y, z) = 2xe ^ y - 3ye ^ -x at the point (3, 1, -2)

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Directions: For questions 1-7, use the following function: f(x,y) = 2x³y + y. 1) f(-1,2) 2) f«(x, y) 3) f;(x, y)