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2 years ago

Ralph’s classroom measures 12 meters in length. What is the length of the classroom in millimeters?

Mathematics

1 answer:

In-s [12.5K]2 years ago

5 0

Answer:

b. 12 000 mm

Step-by-step explanation:

multiply by 1 000

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F=(2xy +z³)i + x³j + 3xz²k find a scalar potential and work done in moving an object in the field from (1,-2,1) to (3,1,4)

Alex73 [517]

Step-by-step explanation:

Given:

$\textbf{F} = (2xy + z^3)\hat{\textbf{i}} + x^3\hat{\textbf{j}} + 3xz^2\hat{\textbf{k}}$

This field will have a scalar potential $\varphi$ if it satisfies the condition $\nabla \times \textbf{F}=0$ . While the first x- and y- components of $\nabla \times \textbf{F}$ are satisfied, the z-component doesn't.

$(\nabla \times \textbf{F})_z = \left(\dfrac{\partial F_y}{\partial x} - \dfrac{\partial F_x}{\partial y} \right)$

$\:\:\:\:\:\:\:\:\: = 3x^2 - 2x \ne 0$

Therefore the field is nonconservative so it has no scalar potential. We can still calculate the work done by defining the position vector $\vec{\textbf{r}}$ as

$\vec{\textbf{r}} = x \hat{\textbf{i}} + y \hat{\textbf{j}} + z \hat{\textbf{k}}$

and its differential is

$\textbf{d} \vec{\textbf{r}} = dx \hat{\textbf{i}} + dy \hat{\textbf{j}} + dz \hat{\textbf{k}}$

The work done then is given by

$\displaystyle \oint_c \vec{\textbf{F}} • \textbf{d} \vec{\textbf{r}} = \int ((2xy + z^3)\hat{\textbf{i}} + x^3\hat{\textbf{j}} + 3xz^2\hat{\textbf{k}}) • (dx \hat{\textbf{i}} + dy \hat{\textbf{j}} + dz \hat{\textbf{k}})$

$\displaystyle = (x^2y + xz^3) + x^3y + xz^3|_{(1, -2, 1)}^{(3, 1, 4)}$

$= 422$

5 0

2 years ago

What is..Simplify 15.8

ycow [4]

Answer:

simplify of 15.8 is 16

Step-by-step explanation:

please mark me as brainliest

5 0

2 years ago

39.2 is what percent p of 112?

jok3333 [9.3K]

39.2 percent out of 112 that is 35%

3 0

2 years ago

Read 2 more answers

For the following system, if you isolated x in the first equation to use the Substitution Method, what expression would you subs

tatiyna

$-x-2y=-4 \\ 3x+y=12 \\ \\ \hbox{the first equation:} \\ -x-2y=-4 \ \ \ \ \ \ |+2y \\ -x=2y-4 \ \ \ \ \ \ \ \ |\times (-1) \\ x=-2y+4$

The expression you would substitute for x is -2y+4. The answer is d.

4 0

3 years ago

A 19% discount on a watch saved a shopper $76 . find the price of the watch before the discount

Alik [6]

The watch costed $400 before the discount.

76 * 100 = 7,600
7,600 / 19 = 400

3 0

2 years ago