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3 years ago

8

Write a linear function f with the values f (3)= -4 and f (5)= -4 f(x)=

2 answers:

Zielflug [23.3K]3 years ago

4 0

(3,-4) and (5,-4) are points on the horizontal line f(x) = -4.

Artemon [7]3 years ago

3 0

Answer:

Step-by-step explanation:

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Evaluate the integral Integral from (5 comma 2 comma 4 )to (7 comma 9 comma negative 3 )y dx plus x dy plus 3 dz by finding para

padilas [110]

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_{(5,2,4)}^{(7,9,-3)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz$

Parameterize the line segment (call it $C$ ) by

$\vec r(t)=(1-t)(5\,\vec\imath+2\,\vec\jmath+4\,\vec k)+t(7\,\vec\imath+9\,\vec\jmath-3\,\vec k)$

$\vec r(t)=(2t+5)\,\vec\imath+(7t+2)\,\vec\jmath+(4-7t)\,\vec k$

with $0\le t\le1$ . Then

$\vec r'(t)=2\,\vec\imath+7\,\vec\jmath-7\,\vec k$

and the line integral is

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_0^1((7t+2)\,\vec\imath+(2t+5)\,\vec\jmath+3\,\vec k)\cdot\vec r'(t)\,\mathrm dt$

$=\displaystyle\int_0^1((2t+5)+2(7t+2)-21)\,\mathrm dt$

$=\displaystyle\int_0^1(28t+18)\,\mathrm dt=\boxed{32}$

Alternatively, if we can show that $\vec F$ is conservative, then we can apply the fundamental theorem of calculus. We need to find $f$ such that $\nabla f=\vec F$ , which requires

$\dfrac{\partial f}{\partial x}=y$

$\dfrac{\partial f}{\partial y}=x$

$\dfrac{\partial f}{\partial z}=3$

Integrating both sides of the first equation with respect to $x$ gives

$f(x,y,z)=xy+g(y,z)$

Differentiating both sides wrt $y$ gives

$\dfrac{\partial f}{\partial y}=x=x+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)$

Differentiating wrt $z$ gives

$\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}$

$\implies h(z)=3z+C$

So we have

$f(x,y,z)=xy+3z+C$

and $\vec F$ is conservative. By the FTC, we find

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=f(7,9,-3)-f(5,2,4)=\boxed{32}$

5 0

3 years ago

-4(x-5 ) - 25 = -5 x =?*

patriot [66]

Answer:

x=0

Step-by-step explanation:

First distribute -4 to x and -5 and get -4x+20-25=-5

Then you combine like terms and get -4x-5=-5

Then add 5 to both sides and get -4x=0

Then divide both sides by -4 and get x=0

7 0

3 years ago

Help guys important math test thingy

STatiana [176]

Answer:

4/12+5/12

=9/12

=3/4

Hope it helps

<h2> please mark Makaylamgalloway07 as BRAINLIEST</h2>

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3 years ago

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Alborosie

.0625 is the answer. Hope this helped

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A bank gives each new customer a 4-digit code number which allows the new customer to create their own password. The digits are

sladkih [1.3K]

Answer:

firstly it is a four number combo with no repeating numbers so it has to include 5 but if you mean it like you said it 0

Step-by-step explanation:

sry i read it wrong the first time

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2 years ago

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