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Leviafan [203]
2 years ago
10

Suppose a railroad rail is 3 kilometers and it expands on a hot day by 15 centimeters in length. Approximately how many meters w

ould the center of the rail rise above the ground?
Mathematics
1 answer:
earnstyle [38]2 years ago
6 0

Answer:

Answer:  13.4 m

Step-by-step explanation:

For small angles, x, in radians,

tan(x) ≈ sin(x) = x

Use this to create an approximate diagram for the problem as shown in the figure below.

The actual deflected shape is parabolic, but it is approximated by an isosceles triangle with small equal angles.

The extend length is 3 km + 12 cm, which is 

3000 + 0.12 = 3000.12 m

Half of the extended length is 1500.06 m

Let h+  the rise of the center of the rail above ground.

From the Pythagorean theorem, obtain

h² + 1500² = 1500.6²

h² = 1500.06² - 1500² = 180.004

h = 13.4 m, which is about 0.9% of the original length.

Read more on Brainly.com - brainly.com/question/5596356#readmore

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The quotient of a number and three is equal to negative eight
GuDViN [60]
There are multiple answers to this
7 0
3 years ago
50
ozzi

Answer:

90 km, N 46° E

Step-by-step explanation:

<em>A jet flies due North for a distance of 50 km and then on a bearing of N 70° E for a further 60 km. Find the distance and bearing of the jet from its starting point.</em>

Look at the diagram I drew of this scenario. You can see the jet flies North for 50 km, and then turns at a 70° angle to fly another 60 km. We want to find the distance from the starting point, SP, to angle C (labeled).

This will be the jet's distance from its starting point.

In order to find the bearing of the jet from its starting point, we will need to find the angle formed between distances b and c, labeled angle A.

The <u>Law of Cosines</u> will allow us to use two known sides and one known angle to solve for the sides opposite of the known angle.

In this case, the known angle is 110° (angle B) so we will use the <u>Law of Cosines</u> respective to B.

  • b² = a² + c² - 2ac cosB

Substitute the known values into the equation and solve for b, the distance from the starting point (A) to the endpoint (C).

  • b² = (60)² + (50)² - 2(60)(50) cos(110°)
  • b² = 6100 -(-2052.12086)
  • b² = 8152.12086
  • b = 90.28909602
  • b ≈ 90 km

The distance of the jet from its starting point is 90 km. Now we can use this b value in order to calculate angle A, the bearing of the jet.

The <u>Law of Cosines</u> with respect to A:

  • a² = b² + c² - 2bc cosA

Substitute the known values into the equation and solve for A, the bearing from the starting point (clockwise of North).

  • (60)² = (90.28909602)² + (50)² - 2(90.28909602)(50) cosA
  • 3600 = 8152.12086 - 6528.909602 cosA
  • -4552.12086 = -6528.909602 cosA
  • 0.6972252853 = cosA
  • A = cos⁻¹(0.6972252853)
  • A = 45.79519
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The bearing of the jet from its starting point is N 46° E. This means that it is facing northeast at an angle of 46° clockwise from the North.

7 0
2 years ago
An employee earns a gross pay of $1,200.00 per week. The employee's net pay is $850.00. The employee's voluntary 401(k) contribu
Yuliya22 [10]

Answer:

$300 was deducted from tax. The tax rate is 26.1%

Step-by-step explanation:

An employee earns a gross pay of $1,200.00 per week. The employee’s net pay is $850.00. The employee’s voluntary 401(k) contribution is $50.00 per month.

There was blank deducted for taxes. The tax rate is blank

Solution:

Contributions that are made for retirement such as 401(k) contribution plans are made on a pretax basis. This means that they are removed from your taxable income, thereby reducing the tax.

Gross pay = $1200

Taxable income = Gross pay -  401(k) contribution

Taxable income = $1200 - $50 = $1150

Net pay = $850

Tax = Taxable income - Net pay

Tax = $1150 - $850

Tax = $300

Tax rate = (Tax / taxable income) * 100%

Tax rate = ($300 / $1150) * 100% = 26.1%

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2 years ago
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antiseptic1488 [7]
The area of a rectangle is its times its width where "A" represents the area, "L" represents the length and "W" represents the width
5 0
3 years ago
PLZ help solve !!!!!!!
Ivahew [28]
37 I think I’m not sure just saying a random number don’t trust me I just needed the points
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