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2 years ago

Find the GCF of 207c^3 and 108c^2

Mathematics

1 answer:

geniusboy [140]2 years ago

7 0

Answer: 9c²

<u>Step-by-step explanation:</u>

To find the Greatest Common Factor of 207c³ and 108c², first factor them down to their primes and see what they have in common.

207c³ 108c²

∧ ∧ ∧ ∧

9·23 c·c·c 9·12 c·c

∧ ∧ ∧

3·3 3·3 3·4

∧

2·2

207c³: 3·3·23 c·c·c

108c²: 2·2·3·3·3·4 c·c

GCF = 3·3 c·c

= 9c²

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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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2 years ago

Find the slope of <br> -2y-10+2x=0

Anna [14]

The answer to -2y-10+2x=0 is 1

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I’ll mark you if it’s right.

Kamila [148]

Answer:

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2 years ago

What is the difference of (2x+7)-(8x+5)

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Answer:

If you need the equation: 10x - 12

If you need the equation more simplified: x - 1.2

Step-by-step explanation:

(2x + 7) - (8x + 5)

Move the parts of the equation around

(2x + 8x) - (7 + 5)

Add 2x and 8x together

10x - (7 + 5)

Add 7 and 5 together

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If you need it even more simplified, continue

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x - 12/10

Simplify

x - 1.2

I Hope That This Helps! :)

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Answer:

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Step-by-step explanation:

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