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Bingel [31]
3 years ago
9

The Smiths are moving across the country. Mr. Smith leaves 4 hours before Mrs. Smith. If he averages 60mph and she averages 80mp

h, how many hours will it take Mrs. Smith to catch up to Mr. Smith?
Mathematics
1 answer:
Ronch [10]3 years ago
4 0

60 miles per hour x 4 hours = 240 miles

Mr smith was 240 miles ahead of Mrs/ smith

The difference in speeds was 80 - 60 = 20 miles per hour

240 miles / 20 miles per hour = 12 hours.

It takes 12 hours to catch up.

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Marsha sees an airplane flying overhead. The spot on the ground that is directly under the plane is 3,600 feet from Marsha's hou
Rudiy27

The elevation of the plane is 3600 ft

Let

  • h = elevation of plane,
  • d = distance from Marsha's house to spot on ground below plane = 3600 feet and
  • Ф = angle of elevation of plane = 45°

From the triangle, we have the trigonometric ratio

tanФ = h/D

<h3>Elevation of the plane</h3>

Making h subject of the formula, we have

h = DtanФ

substituting the values of the variables into the equation, we have

h = DtanФ

h = 3600 ft × tan45°

h = 3600 ft × 1

h = 3600 ft

So, the elevation of the plane is 3600 ft

Learn more about elevation of the plane here:

brainly.com/question/26380084

7 0
2 years ago
Mr. Ratchett, an elderly American, was found murdered in his train compartment on the Orient Express at 7 AM. When his body was
nasty-shy [4]

Answer: Mr. Ratchett died approximately at 2AM.

Step-by-step explanation: <u>Newton's</u> <u>Law</u> <u>of</u> <u>Cooling</u> shows the cooling rate between a body and the environment, by stating that the rate is proportional to the difference in temperatures between them.

Mathematically, it is represented as:

\frac{dQ}{dt}=\alpha.A.(T_{s}-T)

This differential equation solved, gives the solution:

T(t)=T_{s}+(T_{0}-T_{s})e^{-kt}

where

T_{s} is temperature of the environment

T_{0} is the initial temperature of the body

k is a parameter dependent of heat transfer coefficient, heat capacity and area of the body

t is time required to change the temperature

For the murder on the Orient Express, first determine parameter k.

In 1 hour, Mr. Ratchett's body decrease 1°:

27=22+(28-22)e^{-1k}

5=6e^{-k}

e^{-k}=\frac{5}{6}

ln(e^{-k})=ln(0.834)

k = 0.1823

Using the parameter, find estimate time:

28=22+(37-22)e^{-0.1823t}

6=15e^{-0.1823t}

ln(e^{-0.1823t})=ln(0.4)

0.1823t = 0.9163

t=\frac{0.9163}{0.1823}

t ≈ 5 hours

The body was found at 7AM. So, it took approximately 5 hours to cool down to 28° at that time. Therefore, Mr. Ratchett died at 2AM.

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