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2 years ago

What is the mass of one water molecule in grams

Mathematics

1 answer:

Rama09 [41]2 years ago

5 0

Answer:

18.02

Step-by-step explanation:

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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

There are 35 female performers in a dance recital. The ratio of men to women in the recital is 2 : 7 How many men are in the rec

Vsevolod [243]

There are 32 female performers in a dance recital the ratio of men to women is 3/8 How many men are in the dance recital

But we have 32 female performers in the dance recital. Hence there are 3×4=12 men in the dance recital.

3 0

3 years ago

What is the lowest common multiple (LCM) of 3 and 4

Kazeer [188]

Answer:

Step-by-step explanation:

The Least Common Multiple (LCM) of some numbers is the smallest number that the numbers are factors of. Like the LCM of 3 and 4 is 12, because 12 is the smallest number that 3 and 4 are both factors for.

8 0

3 years ago

Read 2 more answers

What is the answer to this? Will give brainiest 5[(6-3)^(2)+4*2]=

mylen [45]

85 is the correct answer.

8 0

2 years ago

HELP <br><br>Solve the formula E = /(R + r) for r.

ahrayia [7]

Answer:

r= RE/I

Step-by-step explanation:

E=I(R+r)

divide both sides by I

E/I = R+r

subtract both sides by R

R(E/I) = r

r = RE/I

4 0

2 years ago