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Rudik [331]
3 years ago
15

a rope is 24 feet long. it is cut into two pieces such that one piece is half the length of the other. find the lengths of the t

wo pieces of rope
Mathematics
2 answers:
marishachu [46]3 years ago
4 0

Answer:

THE STATED SOLUTION IS CORRECT (LENGTHS OF 16 FEET AND 8 FEET)

BASED ON THE WAY THE VARIABLE IF DEFINED THE EQUATION SHOULD BE X+2 X=24 .

THE WAY THE VARIABLE IS DEFINED AND BECAUSE X=16 THE LONGER PIECE OF ROPE WOULD BE 32 FEET, WHICH IS NOT POSSIBLE .  SO A, B, AND D ARE YOUR ANSWERS ON E20 (JUST FINISHED THE QUESTION )

Step-by-step explanation:

Ivahew [28]3 years ago
3 0

Answer:

16 ft and 8 ft

Step-by-step explanation:

x + 1/2 x=24

2/2 x + 1/2 x= 24

3/2 x=24

3 x= 48

x=16

1/2x=16/2=8

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Find the work done by F= (x^2+y)i + (y^2+x)j +(ze^z)k over the following path from (4,0,0) to (4,0,4)
babunello [35]

\vec F(x,y,z)=(x^2+y)\,\vec\imath+(y^2+x)\,\vec\jmath+ze^z\,\vec k

We want to find f(x,y,z) such that \nabla f=\vec F. This means

\dfrac{\partial f}{\partial x}=x^2+y

\dfrac{\partial f}{\partial y}=y^2+x

\dfrac{\partial f}{\partial z}=ze^z

Integrating both sides of the latter equation with respect to z tells us

f(x,y,z)=e^z(z-1)+g(x,y)

and differentiating with respect to x gives

x^2+y=\dfrac{\partial g}{\partial x}

Integrating both sides with respect to x gives

g(x,y)=\dfrac{x^3}3+xy+h(y)

Then

f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+h(y)

and differentiating both sides with respect to y gives

y^2+x=x+\dfrac{\mathrm dh}{\mathrm dy}\implies\dfrac{\mathrm dh}{\mathrm dy}=y^2\implies h(y)=\dfrac{y^3}3+C

So the scalar potential function is

\boxed{f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+\dfrac{y^3}3+C}

By the fundamental theorem of calculus, the work done by \vec F along any path depends only on the endpoints of that path. In particular, the work done over the line segment (call it L) in part (a) is

\displaystyle\int_L\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(4,0,0)=\boxed{1+3e^4}

and \vec F does the same amount of work over both of the other paths.

In part (b), I don't know what is meant by "df/dt for F"...

In part (c), you're asked to find the work over the 2 parts (call them L_1 and L_2) of the given path. Using the fundamental theorem makes this trivial:

\displaystyle\int_{L_1}\vec F\cdot\mathrm d\vec r=f(0,0,0)-f(4,0,0)=-\frac{64}3

\displaystyle\int_{L_2}\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(0,0,0)=\frac{67}3+3e^4

8 0
3 years ago
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likoan [24]
67 percent
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3 years ago
Choices:<br><br> One-sixth cups<br> Five-sixths cups<br> 1 and two-thirds cups<br> 1 and 5 / 6 cups
navik [9.2K]

Answer:

Patel will require more orange juice = \frac{371}{660} cups

Step-by-step explanation:

Patel needs the orange juice for his family = 3 cups

He needs more orange juice = 3 cups - Sum of juice squeezed from different oranges

=3-(\frac{13}{15}+\frac{1}{5}+\frac{9}{20}+\frac{5}{11}+\frac{7}{15})

L.C.M. of the denominators = 660

=3-\frac{572+132+297+300+308}{660}

=3-\frac{1609}{660}

= \frac{1980-1609}{660}

= \frac{371}{660}

Therefore, amount of orange juice required more = \frac{371}{660} cups

3 0
3 years ago
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