Time Remaining: 319:55 equation t for a line through the otleft parenthesis xtot

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Time Remaining: 319:55 equation t for a line through the otleft parenthesis xtotoo Take a Test-Kaylen Scott Google Chrome https//www.mathxd.com/student/player Test cent erwin yes Fall 2016: MATH 364, Calculus III Section 1 Kaylen Scott Test: Final Examination Fall 2016 Time Remaining This Question: 3 pts 23 of 30 (22 complete v For the following trajectory, find the speed associated with the trajectory and then find the length of the trajectory on the given interval ,6 for o sts4 The speed associated with the trajectory is pe an exact answer, using radicals as needed) The length of the trajectory on the given interval is units Type an exact answer, using radicals as needed.) Enter your answer in each of the answer boxes s: A Systems Approach Temple

Explanation / Answer

given r(t)=<4t3 ,-t3 ,6t3>

r'(t)=<12t2 ,-3t2 ,18t2>

speed =|r'(t)|

speed =[(12t2)2+(-3t2)2+(18t2)2]

speed =t2[(12)2+(-3)2+(18)2]

speed =t2[144+9+324]

speed=t2477

length of trajectory =[0 to 4]t2477 dt

length of trajectory =[0 to 4](1/3)t3477

length of trajectory =(1/3)(43-03)477

length of trajectory =(64/3)477

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2)g(w,x,y,z)=(cos(-7w-6x))(sin(8y+z))

gw=(-sin(-7w-6x))(-7-0)(sin(8y+z))

gw=7(sin(-7w-6x))(sin(8y+z))

gx=(-sin(-7w-6x))(0-6)(sin(8y+z))

gx=6(sin(-7w-6x))(sin(8y+z))

gy=(cos(-7w-6x))(cos(8y+z))(8+0)

gy=8(cos(-7w-6x))(cos(8y+z))

gz=(cos(-7w-6x))(cos(8y+z))(0+1)

gz=(cos(-7w-6x))(cos(8y+z))

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