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Leokris [45]
3 years ago
14

Can somebody help me with the problem attached. It is on simplifying rational expressions. Thanks!

Mathematics
1 answer:
liq [111]3 years ago
3 0
The answer is 8 as in eight
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A piano is hauled into space a distance 3 earth radii above the surface of the north pole and is then dropped. About how long wi
nikdorinn [45]

Answer:

The answer to the question is

It would take about 167.021 s  to splash down in the arctic ocean.

Step-by-step explanation:

The gravitational force is given by

F_G = \frac{G*m_1*m_2}{r^2}

Where m₁ mass of the piano and

m₂ = mass of the Earth

r = 3·R where R = radius of the earth

as stated in the question we have varying acceleration due to the inverse square law

Therefore at 3 × Radius of the earth we have

F_G = 109.083 N and the acceleration =1.09083 m/s²

If the body falls from 3·R to 2·R with that acceleration we have

S = u·t +0.5×a·t²  = 0.5×a·t² as u = 0

That is 6371 km = 0.5·1.09083·t²

t₁ = 108.079 s and we have

v₁² = u₁² +2·a₁·s₁ =  2·a₁·s₁ = 117.895 m/s

For the next stage r₂ = 2R

Therefore F = 245.436 N and a₂ = F/m₁ = 2.45436 m/s²

Therefore the time from 2R to R is given by

S₂ =R=u·t+0.5·a₂·t² = v₁·t + 0.5·a₂·t²

or 6371 km = 117.895 m/s × t + 0.5 × 2.45436 × t²

Which gives 1.22718 × t² + 117.895 × t -6371  = 0

Factorizing we have (t+134.631)(t-38.56)×1.22718 = 0

Therefore t = -134.631 s or 38.56 s as we only deal with positive values of time in the present question we have t₂ = 38.56 s and

v₂² = v₁² + 2·a₂·S  = (117.895 m/s)² + 2·2.45436 m/s²×6371 km = 45172.686

v₂ = 212.54 m/s

For final stage we have r = R and

F_{G3} = 981.746 N and a₂ = F/m₁ = 9.81746 m/s²

Therefore the time from R to the arctic ocean  is given by

S₃ =R=v₂·t+0.5·a₂·t² = 212.54·t + 0.5·9.81746·t² = 6371

Which gives

Therefore t₃ = 20.382 s

Therefore, it will take about t₁ + t₂ + t₃ = 108.079 s + 38.56 s + 20.382 s  = 167.021 s  to splash down in the ocean

6 0
3 years ago
Greatest to least decimals :>
blondinia [14]

Answer:if the number has a single digit after the decimal add a 0 next to it

Step-by-step explanation:22: 0.1, 0.5, 23: 0.6. 0.20, 0.29, 0.92

24: 0.56, 1.78, 4.09

6 0
3 years ago
Triangle question find the value
swat32

Answer:

55°

Step-by-step explanation:

total angle of a triangle is 180°

we are given 2 angles

85+40+ x = 180

180-125 = 55° (x)

5 0
3 years ago
Pls help asap What is the number of degrees in the acute angle formed by the hands of a clock at 6:44?
sashaice [31]

Answer:

264 degree angle

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
A man that is 6 feet tall casts a shadow 5 feet long. At the same time, a lamppost beside the man casts a shadow 25 feet long. H
Montano1993 [528]

Answer:

The answer to your question is:  L = 30 ft

Step-by-step explanation:

Data

man = 6 ft

man shadow = 5 ft

lamppost shadow = 25 ft

lamppost height = ? = L

Process

                   \frac{6}{5} = \frac{L}{25}

                    L = \frac{6 x 25}{5}

                    L = \frac{150}{5}

                           L = 30 ft

5 0
3 years ago
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