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3 years ago

A. Write an expression to represent the difference between the two points shown on the number line.

Mathematics

2 answers:

Maru [420]3 years ago

8 0

-1.6 - 0.3
I hope this hepled you and that the answer is correct

Amanda [17]3 years ago

6 0

Answer:

-1.6 - 0.3 and we use the same school website lol

Step-by-step explanation:

You might be interested in

Write the equation in logarithmic form 4^7=16,384 please show work

nlexa [21]

If a^ x = b then:

x = log_{a}b

For:

4^{7} = 16384 \\ log _{4}16384 = 7

8 0

3 years ago

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

Diane needs 165 pieces of candy to hand out to guests at a party she is hosting. Each bag of candy contains 20 pieces. She has 2

Debora [2.8K]

20x + 25 = 165

x represents the number of bags. You can solve the equation to make sure the answer is 7.

20x + 25 = 165

Subtract 25 from both sides.

20x = 140

Divide 20 off of both sides.

x = 7

5 0

3 years ago

Which expression is equivalent to 4x2 + 9x – (x – 3)2 + 11?

Zanzabum

4x^2+9x-(x^2-6x+9)+11
4x^2+9x-x^2+6x-9+11
3x^2+15x+2

4 0

3 years ago

Identify the domain and range:

Y_Kistochka [10]

Answer:

Domain: [3, ∞)

Range: [-1, ∞)

Step-by-step explanation:

lmk if you want an explanation

6 0

3 years ago