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3 years ago

11

18-(8×3)÷4 simplify the numerical expression

2 answers:

DIA [1.3K]3 years ago

6 0

-108 Hope is helpful

BARSIC [14]3 years ago

4 0

The answer to the question is... 12

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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

Write as a numerical expression: “ Six less than twice a number is four “

VladimirAG [237]

Answer:

2x - 6 = 4

Step-by-step explanation:

Firstly, let's assume the number is x

Then, twice the number is 2 times x = 2x

6 less than twice the number is four

2x - 6 = 4

2x - 6 + 6 = 4 + 6

2x = 10

2x/2 = 10/2

x = 5

6 0

3 years ago

Is (2,17) a one solution, no solution, infinite solution,or two solution

WARRIOR [948]

Answer:

one solution

Step-by-step explanation:

because it's a gksbn smksidihdbd jaiaigsvs j

3 0

3 years ago

katen-ka-za [31]

Answer:

34

Step-by-step explanation:

F(x) = 2x^3 - 7x + 1

Let x= 3

F(3) = 2* 3^3 - 7*3 + 1

= 2 * 27 -21+1

= 54 -21 + 1

= 34

8 0

3 years ago

Find the value of this expression if x = -9.<br> x2 + 1<br> x+7

Mamont248 [21]

Answer:

-41

Step-by-step explanation:

You would replace all x's with -9 and solve.

6 0

3 years ago