4. Find the measure of the angle between u = 6i - 3j andv = 2i + j to the nearest tenth of a degree.5. Find the component form and magnitude of AB with initialpoint A(3, -1) and terminal point B(-1, -2).6. A force F, of 25 newtons pulls at an angle of 20° above due east.A force F₂ of 35 newtons pulls at an angle of 55° below due west.Find the magnitude and direction of the resultant force.2

Answered: Image /qna-images/answer/45d34787-72b2-4894-8b98-da4a633b316e.jpg

Answered: 4. Find the measure of the angle…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 32E

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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?
solve for the coodinates of ther point for (b) and (c) as well
By about how much will h(x, y, z) = cos (paixy) + xz2 change if the point P(x, y, z) moves from P0(-1, -1, -1) a distance of ds = 0.1 unit toward the origin?

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4. Find the measure of the angle between u = 6i - 3j and v = 2i + j to the nearest tenth of a degree.