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sweet-ann [11.9K]

2 years ago

5

SIERENCE

1 answer:

Svetllana [295]2 years ago

8 0

B for sure because yes

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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

2 years ago

Suppose that A is nonsingular. Prove that its inverse A-1 is unique. [Hint: Show that if there exists two matrices, B and C, suc

Bogdan [553]

Answer with Step-by-step explanation:

Let A is non-singular

$\mid A\mid\neq 0$

We have to prove that $A^{-1}$ is unique.

Suppose B and C are inverse of A such that

$BA=I$ and AC=I

By using property $AA^{-1}=A^{-1}A=I$

$C=C$

$(BA)C=B(AC)$

$I\cdot C=B\cdot I$

$C=B$

Hence, the inverse of A is unique.

4 0

2 years ago

What is the capital of Ethiopia

tester [92]

Addis Ababa is the capital of Ethiopa.

6 0

2 years ago

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Given the system of equations presented here:

Bumek [7]

ANSWER

The correct answer is option B

EXPLANATION

The equations are

$3x+5y=29---(1)$

and

$x+4y=16---(2)$

When we multiply the second equation by $-3$ , we obtain;

$-3x-12y=-48---(3)$

When we combine this new equation with equation (1).

$-7y=-19$

We can see that $x$ has been eliminated from the equation.

We can then, solve for $y$ and then substitute the result in to any of the equations to find $x$ .

Hence the correct answer is option B

8 0

2 years ago

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What is 7x-4y+2x+8y in distributive form? I will give brainliest and 100 points. Thank you.

alexgriva [62]

Answer:

4(2 1/4x + y)

Step-by-step explanation:

Just factor

In this cae no GCF

So just divide By 4 becuase its easy

If you solve it

You’d get 9x+4y

WHich is the combined term of the expression given

5 0

2 years ago

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