List all the steps to solve 27x = 148.5

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=1/x^5, y=0,

igomit [66]

If you wanted to rotate f(x) around the y axis from x=a to x=b then the volume would be
$\pi \int\limits^a_b {(f(x))^2)} \, dx$

that would be

$\pi \int\limits^8_1 {(\frac{1}{x^5})^2} \, dx$
$\pi \int\limits^8_1 {\frac{1}{x^{10}}} \, dx$
1/x^10=x^-10
integrate
-1/(9x^9)
so
$\pi \int\limits^8_1 {\frac{1}{x^{10}}} \, dx$ =
$\pi [\frac{-1}{9x^{9}}]^8_1=\pi (\frac{-1}{9(8^{9})}-\frac{-1}{9(1^{9})})=$
$\pi (\frac{-1}{9(8^{9})}+\frac{1}{9(1^{9})})=\pi (\frac{-1}{9(8^{9})}+\frac{1}{9})=$
$\pi (\frac{-1}{9(8^{9})}+\frac{8^9}{9(8^9)})=\pi (\frac{8^9-1}{9(8^{9})})=$
$(\frac{\pi8^9-\pi}{9(8^{9})})=\frac{134217727 \pi}{1207959552}$
that's the volume of the solid

4 0

4 years ago

A 50-gal tank initially contains 20 gal of pure water. Salt- water solution containing 0.5 lb of salt for each gallon of water b

icang [17]

Answer:

x(15) = 21 lb

Step-by-step explanation:

Rate of change in volume of salt water solution = rate of volume incoming - rate of volume outgoing

dV/dt = 4 - 2 =2gal/min

So, the equation for volume at cetain time t at given conditions and values becomes,

V(t) = 2t + V

V(t) = 2t + 20 gal-------------------euqation (1)

Rate of change in amount of salt = rate of salt in - rate of salt out

dx/dt = {0.5*4} - {[x(t)/V(t)]*2}

dx/dt = 2-2[(x(t))/(2t+20)]

dx/dt = 2-[(x(t))/(v(t))] lb/min

Now, with integrating factor, we get

exp[∫(1/(1+10))dt)] = t+10

the equation becomes

(t + 10)*x' + x = 2*(t+10)

((t+10)*x') = 2*(t+10)

(t+10)*x = t² + 20t + C

As x(0) = 0,

x(t) = (t²+20t)/(t+10)

x(15) = (15²+20*15)/(15+10)

x(15) = 21 lb

4 0

3 years ago

XY is a translation of XY.

seropon [69]

Given:

The graph of a translation. X'Y' is a translation of XY.

To find:

The rule of the translation.

Solution:

Let the rule of the translation be

$(x,y)\to (x+a,y+b)$ ...(i)

So, we need to find the value of a and b.

From the given graph, it is clear that X(-4,-9) and X'(-1,0).

Using (i), the image of X(-4,-9) is

$X(-4,-9)\to X'(-4+a,-9+b)$

We have, X'(-1,0). So,

$X'(-4+a,-9+b)=X'(-1,0)$

On comparing both sides, we get

$-4+a=-1$

$a=-1+4$

$a=3$

And,

$-9+b=0$

$b=9$

So, the missing values in the rule of the translation are 3 and 9 respectively.

Therefore, the rule of translation is $(x,y)\to (x+3,y+9)$ .

3 0

3 years ago

Solve this system

madam [21]

Answer:

Its the first option

Step-by-step explanation:

4 0

3 years ago

Find the circumference of a circle whose area is 24 * pi ft squared

Ahat [919]

Area = 24*Pi ft²

Area = Pi*r²

Pi*r² = 24*Pi

Canceling out Pi

r² = 24

Take square root of both sides

r = √24

r ≈ 4.899

Circumference = 2*pi*r

≈ 2*pi*4.899

≈ 2*3.141*4.899

≈ 30.78

Circumference ≈ 30.78 units.

Hope this explains it.

5 0

3 years ago