Find X. round to the nearest tenth. Pls help I’m taking a quiz i’ll give brainliest

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

3 .. 4) through: (-2,5), slope 2.

ArbitrLikvidat [17]

Answer:

y - 5 = 2(x + 2)

General Formulas and Concepts:

Point-Slope Form: y - y₁ = m(x - x₁)

x₁ - x coordinate

y₁ - y coordinate

m - slope

Step-by-step explanation:

Step 1: Define

Slope m = 2

Point (-2, 5)

Step 2: Create equation

y - 5 = 2(x + 2)

8 0

3 years ago

What value does the 7 represents in the number 94.087?

Roman55 [17]

0.007, also known as the thousandths place in decimals.

7 0

3 years ago

Read 2 more answers

Use the graph of the function f(x) to complete the statements below.

vovangra [49]

The answer is f12 submit 8765

4 0

2 years ago

Over the last 40 years, the percent decrease in egg consumption in the U.S. is 35%. Forty years ago, the average consumption was

Kisachek [45]

Answer:

260 eggs per person per year.

Step-by-step explanation:

We have been given that over the last 40 years, the percent decrease in egg consumption in the U.S. is 35%. Forty years ago, the average consumption was 400 eggs per person per year.

To find the average consumption of eggs today, we will find 65% (100%-35%) of 400.

$\text{The average consumption of eggs today}=\frac{65}{100}\times 400$

$\text{The average consumption of eggs today}=65\times 4$

$\text{The average consumption of eggs today}=260$

Therefore, the average consumption of eggs today is 260 eggs per person per year.

7 0

3 years ago