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ycow [4]
3 years ago
9

Is 500/1000 closer to zero 1 1/2 or one

Mathematics
1 answer:
notka56 [123]3 years ago
7 0
500/1000 = 1/2   Same distance to zero and one
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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
How to expand the number 2,937,082​
denis-greek [22]
2x1,000,000
9x100,000
3x10,000
7x1,000
0x100
8x10
2x1
7 0
2 years ago
Identify the pair of angles shown in the figure.
Katen [24]

Answer:

d

Step-by-step explanation:

i think

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HELP :6 lb 5oz - 4lb 12oz ( there are 16 ounces in one pound) A.2lb 7oz B.1lb 7oz C1lb 9oz.
stiks02 [169]

Answer:

C. 1 lb. 9 oz.

Step-by-step explanation:


5 0
3 years ago
Convert 4/3 to mixed number
elixir [45]
Answer: 1 1/3

All you do is see how many times 3 goes into 4 which is 1 so 1/3 and you add 1 so if added it equals 4 1 1/3

Can I get brainly its okay if no.
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