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Ivahew [28]
3 years ago
7

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y

-axis.
y = 5x2, y = 30x − 10x2
Engineering
1 answer:
kow [346]3 years ago
3 0

Answer:

40π

Explanation:

First, find the limits (intersections).

5x² = 30x − 10x²

15x² − 30x = 0

x² − 2x = 0

x (x − 2) = 0

x = 0 or 2

Within this interval, 30x − 10x² is greater than 5x².

Dividing the volume into cylindrical shells, the volume of each shell is:

dV = 2π r h t

dV = 2π x (30x − 10x² − 5x²) dx

dV = 2π x (30x − 15x²) dx

dV = 30π (2x² − x³) dx

The total volume is the sum (integral):

V = ∫ dV

V = ∫₀² 30π (2x² − x³) dx

V = 30π ∫₀² (2x² − x³) dx

V = 30π (⅔ x³ − ¼ x⁴)|₀²

V = 30π (⅔ 8 − ¼ 16)

V = 30π (16/3 − 4)

V = 10π (16 − 12)

V = 40π

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<em>Explanation:</em>

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2 years ago
We can process oil into a lot of useful fuels to run our cars, trucks, and even airplanes. Oil is used for making lots of other
Ostrovityanka [42]

Answer:

Explanation:

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4 0
2 years ago
Which crystal system(s) listed below has (have) the following relationship for the unit cell edge lengths?
lianna [129]

Answer:

Both B and G ( Hexagonal and Tetragonal )

Explanation:

The crystals system listed below has the following relationship for the unit cell edge lengths; a = b ≠ c ( hexagonal and Tetragonal )

hexagonal ; represents  a crystal system  which has three equal axes that have an angle of 60⁰ between them while Tetragonal denotes crystals that have  three axes which have only two of its axes equal in length.

5 0
2 years ago
.a. What size vessel holds 2 kg water at 80°C such that 70% is vapor? What are the pressure and internal energy? b. A 1.6 m3 ves
vesna_86 [32]

Answer:

Part a: The volume of vessel is 4.7680m^3 and total internal energy is 3680 kJ.

Part b: The quality of the mixture is 90.3%  or 0.903, temperature is 120 °C and total internal energy is 4660 kJ.

Explanation:

Part a:

As per given data

m=2 kg

T=80 °C =80+273=353 K

Dryness=70% vapour =0.7

<em>From the steam tables at 80 °C</em>

Specific volume of saturated vapours=v_g=3.40527 m^3/kg

Specific volume of saturated liquid=v_f=0.00102 m^3/kg

Now the relation  of total specific volume for a specific dryness value is given as

                                  v=v_f+x(v_g-v_f)

Substituting the values give

v=v_f+x(v_g-v_f)\\v=0.00102+0.7(3.40527-0.00102)\\v_f=2.38399 m^3/kg

Now the volume of vessel is given as

v=\frac{V}{m}\\V=v \times m\\V=2.38399 \times 2\\V=4.7680 m^3

So the volume of vessel is 4.7680m^3.

Similarly for T=80 and dryness ratio of 0.7 from the table of steam

Pressure=P=47.4 kPa

Specific internal energy is given as u=1840 kJ/kg

So the total internal energy is given as

u=\frac{U}{m}\\U=u \times m\\U=1840 \times 2\\U=3680 kJ

The total internal energy is 3680 kJ.

So the volume of vessel is 4.7680m^3 and total internal energy is 3680 kJ.

Part b

Volume of vessel is given as 1.6

mass is given as 2 kg

Pressure is given as 0.2 MPa or 200 kPa

Now the specific volume is given as

v=\frac{V}{m}\\v=\frac{1.6}{2}\\v=0.8 m^3/kg

So from steam tables for Pressure=200 kPa and specific volume as 0.8 gives

Temperature=T=120 °C

Quality=x=0.903 ≈ 90.3%

Specific internal energy =u=2330 kJ/kg

The total internal energy is given as

u=\frac{U}{m}\\U=u \times m\\U=2330 \times 2\\U=4660 kJ

So the quality of the mixture is 90.3%  or 0.903, temperature is 120 °C and total internal energy is 4660 kJ.

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2 years ago
Joe Bruin has a big lawn in front of his house that is 30 meters wide and 20 meters long. Josephine makes him go out and mow the
zysi [14]

<u>Explanation:</u>

5 Horsepower for 30 mins,

(5)(745.7) = 3.7285 KW power delivered

General Efficiency of IC engine = 20%

Power required = \frac{3 \cdot 7285}{0 \cdot 2}=18 \cdot 6425 kw

Energy required per week,

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Lawn area = (30) (20) = 600m^{2}

let sunlight hours be 8 hours

Hence, solar power input on lawn,

=5.62×3600 = 20232 kJ/m^{2}/day

energy input in lawn = (600) (20232) (7)

                                  = 84974.4 mJ/week

Chemical efficiency by photosynthesis = 4%

Chemical content in grass = (84974.4) (0.04)

                                            = 3398.97 mJ

Mass of the clippers  \(=(30)(20)(1 \cdot 096)^{2}(667)\)

                                  \(=478632 \cdot 33\) pounds

Removing water content,

dried grass clippings \(=95726.46\) pound

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Trash cans repaired  

                                     =\frac{11533}{50} =230.66\\=231 cans

By burning the gas, total energy input = 3398.97 MJ × 0.2

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Efficiency of steeling engine  =  20%

Energy output by engine = 679.794 ×0.2

                                          = 135.96 mJ

Energy required by mover = 33.5565 mJ

Hence, Energy (output) ⇒ energy required

5 0
3 years ago
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