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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 height of a wooden pole, h, is equal to 20 feet. A taut wire is stretched from a point on the ground to the top of the pole.
kykrilka [37]

ANSWER

D. 25 feet

EXPLANATION

The height of the wall,h, the taut wire and the distance from the base of the pole to the point on the ground, formed a right triangle.

According to the Pythagoras Theorem, the sum of the length of the squares of the two shorter legs equals the square of the hypotenuse.

Let the hypotenuse ( the length of the ) taught wire be,l.

Then

{l}^{2}  =  {h}^{2}  +  {b}^{2}

{l}^{2}  =  {20}^{2}  +  {15}^{2}

{l}^{2}  =  400 + 225

{l}^{2}  =  625

l=  \sqrt{625}  = 25ft

8 0
3 years ago
find the volume of the following figure round your answer to the nearest tenth if necessary and make sure to use pi
Vikki [24]

Answer:

524cm^2

Step-by-step explanation:

Formula for Volume of sphere= 4/3 πr^2

We have,

r=5cm

Now,

Volume(v)=4/3 πr^2 = 4/3π 5^3= 4/3π 125 = 166.666666667π = 523.598775599

Rounding to the nearest tenth,

Volume=524cm^2

4 0
3 years ago
5x – 19 &lt;1<br> OR<br> - 4x + 3 &lt; -6<br> Solve for x
astra-53 [7]

Answer:

x < 4

OR

x > - 2.25

= 4 > x > - 2.25

Step-by-step explanation:

5x - 19 < 1

5x < 1 + 19

5x < 20

x < 20/5

x < 4

OR

- 4x + 3 < - 6

- 4x < - 6 - 3

- 4x < - 9

x > 9/- 4

x > - 2.25

7 0
3 years ago
Divide 6K2 - 15k-5 by 3k​
icang [17]

Answer:

Step-by-step explanation:

6k^2

------- = 2k; and:

 3k

-15k

------- = -5

 3k

-5 cannot be evenly divided by 3k, so there's a remainder instead.

6k^2 - 15k - 5

-------------------- = 2k -5 with remainder -5.

         3k

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3 years ago
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3.f(-4) - 3.(2) =<br> Int<br> GA<br> SS
Doss [256]

Answer:

1.7. 9 () “ -- .3 .3 .4 . .9 F 5 XXX Ammo. Phosphate., 1916. . .8 10 0 “ -- .4 .2 .4 . . .9 Essex Fertilizer Co. E 7 Grain, Grass & Potato Fert. . . . . .8 12 0 Yes Passed .

Step-by-step explanation:

1.7. 9 () “ -- .3 .3 .4 . .9 F 5 XXX Ammo. Phosphate., 1916. . .8 10 0 “ -- .4 .2 .4 . . .9 Essex Fertilizer Co. E 7 Grain, Grass & Potato Fert. . . . . .8 12 0 Yes Passed .

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