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3 years ago

14

Simplify 4х+ 2-

1 answer:

exis [7]3 years ago

7 0

Answer:

3x - 2

Step-by-step explanation:

$4x + 2 - \frac{ {x}^{2} + x - 12}{x - 3} \\ \\ = 4x + 2 - \frac{ {x}^{2} + 4x - 3x- 12}{x - 3} \\ \\ = 4x + 2 - \frac{ {x}(x + 4) - 3(x + 4)}{x - 3} \\ \\ = 4x + 2 - \frac{ (x + 4) \cancel{(x- 3)}}{\cancel{(x- 3)}} \\ \\ = 4x + 2 - (x + 4) \\ \\ = 4x + 2 - x - 4 \\ \\ = 4x - x + 2 - 4 \\ \\ = 3x - 2$

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The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z) with position vector r = x, y,

suter [353]

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$\frac{25k}{34}[\frac{1}{4}-\frac{1}{50^{1/2}}] \\$

Step-by-step explanation:

The straight line path between point (a,b,c) and (l,m,n) is parametric by the expression

$r(t)=(1-t)(a,b,c) +t(l,m,n)\\$

since we are giving point (4,0,0) and (4,3,4), the parametric equation is giving below

$r(t)=(1-t)(4,0,0) +t(4,3,4)\\$

using the dot product system of multiplication, we have

$r(t)=(4,3t,4t) \\$

t is between 0,1.

Next we define the line integral for work done which is express as

$\int\limits^a_b {F.} \,dr\\$

First we define the general expression for the force

$f(x,y,z)=\frac{K(x,y,z)}{(x^{2}+y^{2}+z^{2})^{3/2}} \\$

If we substitute our parametric equation we arrive at

$F(r(t))=\frac{K(4,3t,4t)}{(4^{2}+(3t)^{2}+(4t)^{2})^{3/2}}\\F(r(t))=\frac{K(4,3t,4t)}{(16+34t^{2})^{3/2}}\\$

also we need to find the expression for <em>dr</em>

$r(t)=(4,3t,4t)\\dr=(0,3,4)dt\\$

Now we substitute into the integral expression

$\int\limits^1_0 {\frac{k(4,3t,4t)}{(16+34t^{2})^{3/2}}} \, .(0,3,4)dt$

using dot product we arrive at

$\int\limits^1_0 {\frac{25kt}{{(16+34t^{2})^{3/2}} } \,$

let make a simple substitution so we can simplify the integral,

let assume $u=16+34t^{2}\\$

$\frac{du}{dt}=68t\\ dt=\frac{du}{68t} \\$

and changing setting the new upper and lower limit, we have

$\frac{25k}{68} \int\limits^a_b {\frac{1}{u\frac{3}{2} } } \, du\\a=50\\b=16\\$

by simple integral we arrive at

$-\frac{25k}{34}[\frac{1}{u^{1/2}}] ^{50}_{16} \\\frac{25k}{34}[\frac{1}{4}-\frac{1}{50^{1/2}}] \\$

Hence the workdone is

$\frac{25k}{34}[\frac{1}{4}-\frac{1}{50^{1/2}}] \\$

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3 years ago

What is 26633646376+63761876784

Lemur [1.5K]

Answer:63,761,876,784

Step-by-step explanation:

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