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irga5000 [103]
3 years ago
8

Identify the restrictions on the domain of f(x) = quantity x minus 1 over quantity x plus 4.

Mathematics
1 answer:
DochEvi [55]3 years ago
7 0

Answer:

x \ne - 4

Step-by-step explanation:

The given function is

f(x) =  \frac{x - 1}{x + 4}

This is not defined when the denominator is zero.

Hence the restriction is on the denominator.

This implies that

x + 4 \ne0

x  \ne - 4

The restriction is that x=-4 is not in the domain of the given function.

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I think you have to choose any numbers in the graph to solve for Rafael and Ava
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4 years ago
Suppose f(x,y,z) = x2 + y2 + z2 and W is the solid cylinder with height 7 and base radius 2 that is centered about the z-axis wi
kipiarov [429]

In cylindrical coordinates, <em>W</em> is the set of points

<em>W</em> = {(<em>r</em>, <em>θ</em>, <em>z</em>) : 0 ≤ <em>r</em> ≤ 2 and 0 ≤ <em>θ</em> ≤ 2<em>π</em> and -2 ≤ <em>z</em> ≤ 5}

(A) Then the integral of <em>f(x, y, z)</em> over <em>W</em> is

\displaystyle\iiint_W(x^2+y^2+z^2)\,\mathrm dV = \int_0^{2\pi}\int_0^2\int_{-2}^5r(r^2+z^2)\,\mathrm dz\,\mathrm dr\,\mathrm d\theta

(B)

\displaystyle \int_0^{2\pi}\int_0^2\int_{-2}^5r(r^2+z^2)\,\mathrm dz\,\mathrm dr\,\mathrm d\theta = 2\pi \int_0^2\int_{-2}^5(r^3+rz^2)\,\mathrm dz\,\mathrm dr \\\\\\= 2\pi \int_0^2\left(zr^3+\frac13rz^3\right)\bigg|_{z=-2}^{z=5}\,\mathrm dr \\\\\\= 2\pi \int_0^2\left(\frac{133}3r+7r^3\right)\,\mathrm dr \\\\\\= 2\pi \left(\frac{133}6r^2+\frac74r^4\right)\bigg|_{r=0}^{r=2} \\\\\\= 2\pi \left(\frac{110}3\right) = \boxed{\frac{220\pi}3}

8 0
3 years ago
<img src="https://tex.z-dn.net/?f=x%20-%204%20%3E%206%20" id="TexFormula1" title="x - 4 &gt; 6 " alt="x - 4 &gt; 6 " align="absm
Arisa [49]

the answer is x > 10

steps:

x - 4 > 6

add 4 to both sides:

x - 4 + 4 > 6 + 4

simplify:

x > 10

Hope it helps!

5 0
3 years ago
PLEASE HELP QUICK!!! 20 POINTS!!
bonufazy [111]

Answer:

I think the answer is B or C but mainly I think it is C

Step-by-step explanation:

Hope this helps?

Please mark my answer as brainliest?

I need it please?

7 0
4 years ago
A farmer has 45 chickens and rabbits. There are 140 legs all together . How many chickens do the farmer has? How many rabbits do
r-ruslan [8.4K]

Answer:

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  • 25 rabbits

Step-by-step explanation:

Let r represent the number of rabbits the farmer has. Then 45-r is the number of chickens. The total number of legs is then ...

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The farmer has 20 chickens, and 25 rabbits.

8 0
3 years ago
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