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sergiy2304 [10]
3 years ago
8

Find the mass of the solid cylinder Dequals​{(r,theta​,z): 0less than or equalsrless than or equals2​, 0less than or equalszless

than or equals10​} with density rho​(r,theta​,z)equals1plusStartFraction z Over 2 EndFraction . Set up the triple integral using cylindrical coordinates that should be used to find the mass of the solid cylinder as efficiently as possible. Use increasing limits of integration. Integral from 0 to nothing Integral from nothing to nothing Integral from nothing to nothing (nothing )font size decreased by 3 dz font size decreased by 3 dr font size decreased by 3 d theta
Physics
1 answer:
anygoal [31]3 years ago
6 0

The mass of the cylinder <em>D</em> is obtained by integrating the density function over <em>D</em>:

\displaystyle\iiint_D\rho(r,\theta\,z)\,\mathrm dV

With \rho(r,\theta,z)=1+\frac z2, and

D=\left\{(r,\theta,z)\mid 0\le r\le2,0\le z\le10\right\}

the mass would be

\displaystyle\int_0^{2\pi}\int_0^2\int_0^{10}1+\frac z2\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=4\pi\int_0^{10}1+\frac z2\,\mathrm dz

4\pi\left(z+\dfrac{z^2}4\right)\bigg|_0^{10}

=4\pi\left(10+\dfrac{100}4\right)=\boxed{140\pi}

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a car dealer sells 4 makes of cars in 5 colors with either standard or automatic transmissions. how many variations does the dea
Anuta_ua [19.1K]

<u>The number of variations the dealership have is 40 cars</u>.

Data given;

  • The number of different product = 4
  • The number of transmission = 2 (standard or automatic)
  • The numbers of colors available = 5

<h3>Dealership variation </h3>

This is the total numbers of cars available in the dealer shop at the moment.

To get that, we simply multiply the numbers of colors available, the number of transmission and the makes of car available.

This is equal to

4*2*5=40

From the above calculation, we can say that <u>the variations the dealership offers is 40</u>

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7 0
3 years ago
What is it that lives if it is fed, and dies if you give it a drink?
Anna71 [15]

Fire is it that lives if it is fed, and dies if you give it a drink.

<h3><u>Explanation:</u></h3>

Fire is very essential part of human life. It is used for cooking food and for other important activities. Without fire we cannot not survive. Something or the other should be heated before consumption and this can be achieved only with fir. It is also used in the darker places for viewing many things around us.

Thus, fire can survive if we give fuel or any wooden pieces and when water is poured on it it will turn off. Hence Fire is the one that survives when it is fed and dies when water is given as a drink to it.

4 0
3 years ago
Find the wavelength of the balmer series spectral line corresponding to n = 15.
Anna71 [15]

Answer:

371.2 mm

Explanation:

The Balmer series of spectral lines is obtained from the formula

1/λ = R(1/2² -1/n²) where λ = wavelength, R = Rydberg's constant = 1.097 × 10⁷ m⁻¹

when n = 15

1/λ = 1.097 × 10⁷ m⁻¹(1/2² -1/15²)

    = 1.097 × 10⁷ m⁻¹(1/4 -1/225)

    = 1.097 × 10⁷ m⁻¹(0.25 - 0.0044)

    = 1.097 × 10⁷ m⁻¹ 0.245556

    = 2.693 10⁶ m⁻¹

So,

λ  = 1/2.693 10⁶ m⁻¹

    = 0.3712 10⁻⁶ m

    = 371.2 mm

7 0
3 years ago
How much time does it take to use 300 W of power to do 1800 J of work? Round your answer to the nearest whole number. The time i
patriot [66]
Energy = power × time
1800 = 300 × time
time = 1800 ÷ 300 = 6 s

Hope it helped!
4 0
3 years ago
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kirill115 [55]

Answer:

False

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