Ask question

Ask question

All categories

3 years ago

5

Answer to this question

2 answers:

horrorfan [7]3 years ago

4 0

1,5 is the answer to 8

Alona [7]3 years ago

3 0

-0.6875 is the answer to number 5

You might be interested in

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

What is the answer to −3 − (−1)?

vladimir1956 [14]

Answer:

-2

Step-by-step explanation:

Subtracting a negative number is adding the positive number of that

-3 + 1 += -2

4 0

3 years ago

ANSWER NEEDED QUICKLY‼️ BRAINLIEST TO RIGHT ANSWER

liq [111]

I’m pretty sure the answer is B
(Hope this helps!!) Can I pls have brainliest??

6 0

3 years ago

A missing fraction on a number line is located exactly halfway between 3/6 and 5/6

Dominik [7]

The missing fraction would be $\frac{4}{6}$ since it is exactly in the halfway between $\frac{3}{6} and \frac{5}{6}$

8 0

3 years ago

Jessica had two hundred six dollars to spend on eight books. AFter buying them she ha fourteen dollars. How much did each book c

frutty [35]

Each book costs $24.

206-14=192
192/8=24

8 0

3 years ago