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larisa86 [58]
3 years ago
11

Solve (2 - x)^2 < 4/25

Mathematics
2 answers:
uysha [10]3 years ago
6 0

Answer:

x>8/5

Step-by-step explanation:

  1. (2-x)^2<4/25

take the square root of both sides

Semenov [28]3 years ago
5 0

Answer:

8/5 < x< 12/5

Step-by-step explanation:

(2 - x)^2 < 4/25

Take the square root of each side

sqrt((2 - x)^2)  <±sqrt( 4/25)

Make two equations

2-x < 2/5    2-x > -2/5

Subtract 2 from each side

2-x-2 < 2/5 -2          2-x-2  > -2/5-2

-x < 2/5 -  10/5             -x > -2/5  - 10/5

-x < -8/5                         -x > -12/5

Multiply by -1, remembering to flip the inequality

x> 8/5                   x < 12/5

8/5 < x< 12/5

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olga_2 [115]

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Use the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = x
valkas [14]
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Let \mathcal D be the region whose boundary is \mathcal S. Then by the divergence theorem,

\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV

Convert to cylindrical coordinates, setting

x=r\cos\theta
y=r\sin\theta

and keeping z as is. Then the volume element becomes


\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz

and the integral is

\displaystyle\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=0}^{z=r\cos\theta+7}4r\cos\theta\cdot r^2\cdot r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta
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4 0
3 years ago
12) Write the equation of a rational function
aev [14]

Answer:

\frac{4(x - 5)(x + 7)(x - 12)}{(x + 1)(x)(x - 12)}

Step-by-step explanation:

A rational function is

\frac{p(x)}{q(x)}

where q(x) doesn't equal zero.

If p is a asymptote, or hole at that value, then we will use

(x - p)

Step 1: We have asymptote as 0 and -1 so our denomiator will include

(x - 0)(x - ( - 1)

Which is

(x)(x + 1)

So our denomator so far is

\frac{p(x)}{x(x + 1)}

Step 2: Find Holes.

Since 12 is the value of the hole,

(x - 12)

is a the binomial.

This will be both on the numerator and denomator so qe have

\frac{(x - 12)}{x(x + 1)(x - 12)}

Step 3: Put the x intercepts in the numerator.

Since 5 and -7 is the intercepts,

\frac{(x - 12)(x - 5)(x + 7)}{x(x + 1)(x - 12)}

Step 4: Horinzontal Asymptotes,

Multiply the numerator and denomiator out fully,

\frac{  {x}^{3} - 10 {x}^{2}  - 59x + 420 }{ {x}^{3} - 12 {x}^{2}   + x - 12}

Take a L

look at the coefficients,

Notice they have the same degree,3, this means if we divide the leading coefficents, we will get our horinzonral asymptote.

Multiply the numerator by 4.

\frac{4(x - 12)(x - 5)(x - 7)}{x(x + 1)(x - 12)}

Above is the function,

5 0
2 years ago
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