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satela [25.4K]
3 years ago
8

A circus performer walks on a tightrope 25 feet above the ground. The tightrope is supported by two beams and two support cables

. If the distance between each beam and the base of its support cable is 15 feet, what is the length of the support cable? Round to the nearest foot.
Mathematics
1 answer:
miv72 [106K]3 years ago
5 0
The length of the support cable is about 29 feet.

If you sketch out the question, you will see that it will form a right triangle with the cable as the hypotenuse.

Just set up and use the Pythagorean Theorem.

15^2 + 25^2 = c^2
850 = c^2
29.15 = c
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the sum of three numbers is 144. the third number is 4 times the first. the second number is 6 more than the first. what are the
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A red balloon starts at 7.3 meters off the ground and rises at 2.6 meters per second. A blue balloon starts at 12.4 meters off t
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This problem is an example of solving equations with variables on both sides. To solve, we must first set up an equation for both the red balloon and the blue balloon. 

Since the red balloon rises at 2.6 meters per second, we can represent this part of the equation as 2.6s. The balloon is already 7.3 meters off of the ground, so we just add the 7.3 to the 2.6s: 

2.6s + 7.3

Since the blue balloon rises at 1.5 meters per second, we can represent this part of the equation as 1.5s. The balloon is already 12.4 meters off of the ground, so we just add the 12.4 to the 1.5:

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2.6s + 7.3 = 1.5s + 12.4

Then, we solve for s. First, the variables must be on the same side of the equation. We can do this by subtracting 1.5s from both sides of the equation: 

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Next, we must get s by itself. We work towards this by subtracting 7.3 from both sides of the equation: 

1.1s = 5.1

Last, we divide both sides by 1.1. So s = 4.63. 

This means that it will take 4.63 seconds for both balloons to reach the same height. If we want to know what height that is, we simply plug the 4.63 back into each equation: 

2.6s + 7.3
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After 4.63 seconds, the balloons will have reached the same height: 19.33 meters.
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