All categories

3 years ago

When the solar system formed the spheres that lost most of their gases became the?

1 answer:

7 0

The spheres that lost most of their gases are the terrestrial planets.

Edit: The terrestrial planets are also known as the inner planets or rocky planets, so if you have multiple choice options or you learnt a different term, pick that instead.

You might be interested in

Find the mass and center of mass of the solid E with the given density function ρ. E lies under the plane z = 3 + x + y and abov

makvit [3.9K]

Answer:

The mass of the solid is 16 units.

The center of mass of the solid lies at (0.6875, 0.3542, 2.021)

Work:

Density function: ρ(x, y, z) = 8

x-bounds: [0, 1], y-bounds: [0, x], z-bounds: [0, x+y+3]

The mass M of the solid is given by:

M = ∫∫∫ρ(dV) = ∫∫∫ρ(dx)(dy)(dz) = ∫∫∫8(dx)(dy)(dz)

First integrate with respect to z:

∫∫8z(dx)(dy), evaluate z from 0 to x+y+3

= ∫∫[8x+8y+24](dx)(dy)

Then integrate with respect to y:

∫[8xy+4y²+24y]dx, evaluate y from 0 to x

= ∫[8x²+4x²+24x]dx

Finally integrate with respect to x:

[8x³/3+4x³/3+12x²], evaluate x from 0 to 1

= 8/3+4/3+12

= 16

The mass of the solid is 16 units.

Now we have to find the center of mass of the solid which requires calculating the center of mass in the x, y, and z dimensions.

The z-coordinate of the center of mass Z is given by:

Z = (1/M)∫∫∫ρz(dV) = (1/16)∫∫∫8z(dx)(dy)(dz)

Calculate the integral then divide the result by 16.

First integrate with respect to z:

∫∫4z²(dx)(dy), evaluate z from 0 to x+y+3

= ∫∫[4(x+y+3)²](dx)(dy)

= ∫∫[4x²+24x+8xy+4y²+24y+36](dx)(dy)

Then integrate with respect to y:

∫[4x²y+24xy+4xy²+4y³/3+12y²+36y]dx, evaluate y from 0 to x

= ∫[28x³/3+36x²+36x]dx

Finally integrate with respect to x:

[7x⁴/3+12x³+18x²], evaluate x from 0 to 1

= 7/3+12+18

Z = (7/3+12+18)/16 = 2.021

The y-coordinate of the center of mass Y is given by:

Y = (1/M)∫∫∫ρy(dV) = (1/16)∫∫∫8y(dx)(dy)(dz)

Calculate the integral then divide the result by 16.

First integrate with respect to z:

∫∫8yz(dx)(dy), evaluate z from 0 to x+y+3

= ∫∫[8xy+8y²+24y](dx)(dy)

Then integrate with respect to y:

∫[4xy²+8y³/3+12y²]dx, evaluate y from 0 to x

= ∫[20x³/3+12x²]dx

Finally integrate with respect to x:

[5x⁴/3+4x³], evaluate x from 0 to 1

= 5/3+4

Y = (5/3+4)/16 = 0.3542

The x-coordinate of the center of mass X is given by:

X = (1/M)∫∫∫ρx(dV) = (1/16)∫∫∫8x(dx)(dy)(dz)

Calculate the integral then divide the result by 16.

First integrate with respect to z:

∫∫8xz(dx)(dy), evaluate z from 0 to x+y+3

= ∫∫[8x²+8xy+24x](dx)(dy)

Then integrate with respect to y:

∫[8x²y+4xy²+24xy]dx, evaluate y from 0 to x

= ∫[12x³+24x²]dx

Finally integrate with respect to x:

[3x⁴+8x³], evaluate x from 0 to 1

= 3+8 = 11

X = 11/16 = 0.6875

The center of mass of the solid lies at (0.6875, 0.3542, 2.021)

4 0

3 years ago

Water is boiled in a pan on a stove at sea level. During 10 min of boiling, it is observed that 200 g of water has evaporated. T

diamong [38]

Answer:

Rate of heat is 45.1 kJ/min

Explanation:

Heat required to evaporate the water is given by

Q = mL

here we know that

$L = 2.25 \times 10^6 J/kg$

now we have

$Q = (0.200)(2.25 \times 10^6 J/kg)$

$Q = 452.1 kJ$

now the power is defined as rate of energy

$P = \frac{Q}{t}$

$P = \frac{452.1 kJ}{10}$

$P = 45.1 kJ/min$

6 0

3 years ago

What is 7.832 rounded to the nearest 10th?

Galina-37 [17]

When rounding you look at the number right after the one you want to round. The tenth place is the one right after the decimal. If the number after it is more than five it goes up by one, it it's less than five it stays the same. So since the number after the 8 is a 3 it stays the same.

The answer is 7.8

3 0

3 years ago

To obtain the same resistance force, a greater force must be exerted in a machine of lower efficiency than in a machine

Sindrei [870]

Answer: True.

Explanation:

A resistance force is also known as friction. And the efficiency of a machine is affected by friction.

A machine of lower efficiency has higher magnitude of friction than a machine of higher efficiency.

Therefore, To obtain the same resistance force, a greater force must be exerted in a machine of lower efficiency than in a machine of higher efficiency. This is true

7 0

3 years ago

You leave on a 450 miles trip in order to attend a meeting that will start 10.8 hours after you begin your trip. Along the way y

konstantin123 [22]

Answer:

c. 2.6 h

Explanation:

The longest time spent over dinner is the time that you have available minus the minimum possible time spent in the trip.

The time of the trip is found using:

t = $\frac{d}{v}$

Where distance is d and velocity is v. The time will be minimum at maximum velocity. Replacing with the data we have:

Ttrip = $\frac{450}{55}$ = 8.1818 h

Tdinner = 10.8h - 8.1818 h = 2.6181h

that aproximates 2.6 h.

4 0

3 years ago