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Suppose a railroad rail is 6 kilometers and it expands on a hot day by 20 centimeters in length. Approximately how many meters w

sukhopar [10]

Answer:

Step-by-step explanation:

Given that the railroad rail is 6 kilometers before expansion.

When the railroad expands, it makes an isosceles triangle at the center of the rail.

The base of the triangle is 6 kilometers while each leg of the triangle is given by (6 + 10/100,000) / 2 = 6.0001 / 2 = 3.00005 kilometers.

[recall that 100,000 centimeters gives 1 kilometers, thus 10 centimetres gives 10/100,000 kilometers]

Taking one half of the isoceles triangle, we have a right triangle with one of the leg as 6 / 2 = 3 kilometers and the hypothenus = 3.00005 kilometers.

Thus, using the Pythagoras theorem, we find the other leg (height) of the right triangle as follows.

Let the other leg of the right triangle be h, then

Thus, the center of the rail will rise 0.01732058 kilometers above the ground.

But, there are 1,000 meters in 1 kilometers, therefore, the center of the rail will rise 0.01732058 x 1,000 = 17.32 meters above the ground.

5 0

4 years ago

Which expressions are equivalent to 6.6.6.6.6? Choose 2 answers

Margarita [4]

Answer:b and c

Step-by-step explanation:

8 0

3 years ago

The back of Tom's property is a creek. Tom would like to enclose a rectangular area, using the creek as one side and fencing

Anna71 [15]

9514 1404 393

Answer:

1250 square feet

Step-by-step explanation:

If x is the length of the side perpendicular to the creek, then the third side is (100 -2x) = 2(50 -x). The area is the product of length and width:

A = x(2)(50-x)

We observe that this is a quadratic function with zeros at x=0 and x=50. The vertex (maximum) of a quadratic function is on the line of symmetry, halfway between the zeros. The value of x there is (0 +50)/2 = 25.

Then the maximum area is ...

A = (25)(2)(50 -25) = 1250 . . . . square feet

_____

Additional comment

Note that half the length of the fence is used in one direction (parallel to the creek), and half is used in the other direction (perpendicular to the creek). This 50/50 split is the generic solution to all sorts of rectangular corral problems, with or without a creek, with or without internal partitions.

Half the fence is perpendicular to the other half. (If the costs are different in different directions, then the cost is what is split 50/50.)

8 0

3 years ago

Which scale has a scale factor of 1/18? a. 3 in = 6 ft c. 3 in = 54 ft b. 6 in = 9 ft d. 6 in = 6 ft

mestny [16]

Your Answer Is B. Your Welcome :)

7 0

3 years ago

Read 2 more answers

HURRY!!! Which inequality has –12 in its solution set? A B C D x + 6 less-than negative 8 x + 4 greater-than-or-equal-to negativ

frozen [14]

Answer:

The correct answer is D. x + 5≤ - 4

Step-by-step explanation:

Let's review which inequality has - 12 in its solution set, this way:

A. x + 6 less-than negative 8

-12 + 6 < - 8

-6 < - 8 Not correct

B. x + 4 greater-than-or-equal-to negative 6

- 12 + 4 ≥ - 6

- 8 ≥ - 6 Not correct

C. x minus 3 greater-than negative 10

- 12 - 3 > - 10

- 15 > - 10 Not correct

D. x + 5 less-than-or-equal-to negative 4

- 12 + 5 ≤ - 4

- 7 ≤ - 4 This is correct

The correct answer is D. x + 5≤ - 4

4 0

3 years ago

Read 2 more answers