Find the domain of r(t) and the value of r(to).NOTE: Round your answer to two decimal places when needed.r(t) = cos(πt)i - ln(t)j + √t − 8k; to = 9Domain is: Choose oneNOTE: Enter your answer in terms of i, j, and k.r(9)=

To find : the domain in terms of i,j and k

Answered: Find the domain of r(t) and the value…

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter55: Introduction To Circles

Section: Chapter Questions

Problem 24A: Solve the following exercises based on Principles 11-14, although an exercise may require the...

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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
The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?
Solve the following exercises based on Principles 11-14, although an exercise may require the application of two or more of any of the principles. Round the answers to 3 decimal places where necessary unless otherwise stated. a. If radius x = 7.500" and y = 4.500", find PM. b. If radius x = 8.000" and y = 4.800", find PM.
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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Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when needed. r(t) = cos(πt)i − ln(t)j + √t − 8k; to = 9 Domain is: Choose one NOTE: Enter your ver in terms of i, j, and k. r(9) =