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3 years ago

Find 3√27 +3√64 - 3√125

Mathematics

1 answer:

serg [7]3 years ago

4 0

Answer:

the answer is approximately 6.047

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Tim tradesman had a taxable income of $82,500

maria [59]

What is the question?

6 0

3 years ago

5+5-6+10-100 what is the answer

timama [110]

Answer:

-86

Step-by-step explanation:

5+5=10

10-6=4

4-100=-86

5 0

3 years ago

Find the volume of the solid.

dmitriy555 [2]

In Cartesian coordinates, the region (call it $R$ ) is the set

$R = \left\{(x,y,z) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } 2 \le z \le 4-x^2-y^2\right\}$

In the plane $z=2$ , we have

$2 = 4 - x^2 - y^2 \implies x^2 + y^2 = 2 = \left(\sqrt2\right)^2$

which is a circle with radius $\sqrt2$ . Then we can better describe the solid by

$R = \left\{(x,y,z) ~:~ 0 \le x \le \sqrt2 \text{ and } 0 \le y \le \sqrt{2 - x^2} \text{ and } 2 \le z \le 4 - x^2 - y^2 \right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\sqrt2} \int_0^{\sqrt{2-x^2}} \int_2^{4-x^2-y^2} dz \, dy \, dx$

While doable, it's easier to compute the volume in cylindrical coordinates.

$\begin{cases} x = r \cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \end{cases} \implies \begin{cases}x^2 + y^2 = r^2 \\ dV = r\,dr\,d\theta\,d\zeta\end{cases}$

Then we can describe $R$ in cylindrical coordinates by

$R = \left\{(r,\theta,\zeta) ~:~ 0 \le r \le \sqrt2 \text{ and } 0 \le \theta \le\dfrac\pi2 \text{ and } 2 \le \zeta \le 4 - r^2\right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\pi/2} \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta \, dr \, d\theta \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta\,dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} r((4 - r^2) - 2) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} (2r-r^3) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \left(\left(\sqrt2\right)^2 - \frac{\left(\sqrt2\right)^4}4\right) = \boxed{\frac\pi2}$

3 0

1 year ago

A total of 120 smoothies were sold on the first day of the month from July-December. True or false

melisa1 [442]

Answer:

the answer would basically be 720 smoothies in total from Jul.-Dec.

Step-by-step explanation:

YWW :)

6 0

3 years ago

The perimeter of a rectangular pen is 136 meters. If the length is 5 meters more than twice the width, what are the dimensions o

Sati [7]

Answer: width = 21, length = 47

Step-by-step explanation:

Length (L) = 2w + 5

width (w) = w

Perimeter (P) = 136

P = 2L + 2w

136 = 2(2w + 5) + 2w substituted the given values above

136 = 4w + 10 + 2w distributed 2 on the right side

136 = 6w + 10 added like terms (4w and 2w)

126 = 6w subtracted 10 from both sides

21 = w divided both sides by 6

Length (L) = 2w + 5

= 2(21) + 5

= 42 + 5

= 47

7 0

3 years ago