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V125BC [204]
3 years ago
14

Find the work required to move an object in the force field F = e^x + y (1, 1, z) along the straight line from A(0, 0, 0) to B(-

4, 5, -5). Check to see if the force is conservative. Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) A. The force is not conservative. The work is ___. B. The force is conservative. The work is _____ .
Mathematics
1 answer:
DENIUS [597]3 years ago
8 0

\vec F(x,y,z)=(e^x+y)(1,1,z)

is conservative if we can find a scalar function f such that \nabla f=\vec F. This would require

f_x=e^x+y

f_y=e^x+y

f_z=(e^x+y)z

Integrating both sides of the first equation wrt x gives

f(x,y,z)=e^x+xy+g(y,z)

Differentiating both sides of this wrt y gives

f_y=x+g_y=1\implies g_y=1-x\implies g(y,z)=y-xy+h(z)

but we assumed g was a function of y and z, independent of x. So there is no such f and \vec F is not conservative.

To find the work, first parameterize the path (call it C) by

\vec r(t)=(1-t)(0,0,0)+t(-4,5,-5)=(-4t,5t,-5t)

for 0\le t\le1. Then

\vec r'(t)=(-4,5,-5)

and the work is given by the line integral,

W=\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_0^1(e^{-4t}+5t,e^{-4t}+5t,-(e^{-4t}+5t)5t)\cdot(-4,5,-5)\,\mathrm dt

W=\displaystyle\int_0^1(125t^2+5t+(25t+1)e^{-4t})\,\mathrm dt=\boxed{\frac{2207}{48}-\frac{129}{16e^4}}

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Step-by-step explanation:

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ace bike rentals rents bikes for $28 per day. Renters can keep the bike for 8 hours. Bart's bikes rents bikes for $30 per day. R
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Bart company charges a lower rate. It is lower by rate $ 0.5 per hour

<h3><u>Solution:</u></h3>

Given that Ace bike rentals rents bikes for $28 per day. Renters can keep the bike for 8 hours

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\text {hourly rate }=\frac{\text { Rental price }}{\text { total time in a day }}

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\text {hourly rate }=\frac{28}{8}=3.5

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<em><u>Hourly rate of Bart company:</u></em>

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total time in a day 10 hours

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6 0
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Janelle has $75. She buys jeans that are on sale for half price and then uses an in-store coupon for $10 off. After paying $1.80
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75.00-37.20=37.80-1.80=36.00
so she spent 36.00 with sales tax . then 36.00*2=72.00+10.00=82.00
the jeans original price was 82.00 
 Check:
6 0
3 years ago
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