pls answer all duin terms of w.Let u = ln t, t =16.and r = √√w. Find and simplify2rdwdy in terms of x.17. Let y = 4t² + 3, t = 6es and s = 1 + In x. Finddxdy18. Given y = 5t (3 t), t = In p and p = ex. Find and simplifydx

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Answered: 16. Let u = ln t, t = 2r and r = √w.…

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter58: Achievement Review—section Five

Section: Chapter Questions

Problem 24AR: a. Given: x=360 inches and y=5.10 inches. Compute Dia A to 2 decimal places. b. Given: Dia A=8.76...

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By expanding (xh)2+(yk)2=r2, we obtain x22hx+h22ky+k2r2=0. When we compare this result to the form x2+y2+Dx+Ey+F=0, we see that D=2h,E=2k, and F=h2+k2r2. Therefore, the center and the length of a radius of a circle can be found by using h=D2,k=E2 and r=h2+k2F. Use these relationship to find the center and the length of the radius of each of the following circles. x2+y2+4x14y+49=0
a. Given: x=360 inches and y=5.10 inches. Compute Dia A to 2 decimal places. b. Given: Dia A=8.76 inches and x=10.52 inches. Compute t to 2 decimal places.
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?
Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and z=27,y=12, find y if x=5 and z=8.

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16. Let u = ln t, t = 2r and r = √w. Find and simplify du dw in terms of w.