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3 years ago

If h(x) = -5x -10 find (h-2)

Mathematics

1 answer:

gizmo_the_mogwai [7]3 years ago

8 0

H(x) = -5x - 10
h(-2) = -5(-2) - 10
h(-2) = 10 - 10
h(-2) = 0

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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

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

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

$= 422$

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3 years ago

An hourly salary of $45 is equivalent to what annual salary? Assume a 35-hour work week.

KonstantinChe [14]

Answer:

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Step-by-step explanation:

45 money per hour times 35 that ir hours on a week equal 1575 times 52.1429 that is amount of weeks on a year equal 82,125.0675

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Answer:

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Step-by-step explanation:

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Fantom [35]

The correct answer among all is D. I'm in K12 8th grade by the way so nice to meet you :)

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bearhunter [10]

Answer:

x < 1

Step-by-step explanation:

x - 4 < - 3

<u> + 4 +4</u> Do inverse operations by adding 4 on both sides

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<------------------------------o------------------>

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