A 42 ft guy wire reaches from the top of a pole to a point on the ground 15 ft. from the
pole. Find how high up the pole does the guy wire reach?
The time t required to empty a tank varies inversely as the rate R of pumping.If a pump
can empty a tank in 50 min.at a rate of 650 k?L/min, how long will it take the pump to
empty the tank at 500kL/min?
Mira’s boat goes 12 mph in still water. It travels 45 miles upstream and back in a total time of 8
hr. What is the speed of the current?
h^2 + 15^2 = 42^2
t=k/R
So, Rt is constant.
You want t such that 500t = 650*50
since time = distance/speed,
45/(12-x) + 45/(12+x) = 8
To find the height at which the guy wire reaches up the pole, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the guy wire, the pole, and the distance on the ground form a right triangle. The height up the pole is one of the legs of the triangle, the distance on the ground is the other leg, and the guy wire is the hypotenuse.
Let's assign variables to the sides of the triangle:
- Let h represent the height up the pole.
- Let d represent the distance on the ground.
- Let g represent the length of the guy wire.
According to the problem:
- The height up the pole (h) is what we need to find.
- The distance on the ground (d) is given as 15 ft.
- The length of the guy wire (g) is given as 42 ft.
Applying the Pythagorean theorem, we have the equation:
h^2 + d^2 = g^2
Substituting the given values, we have:
h^2 + 15^2 = 42^2
Simplifying the equation:
h^2 + 225 = 1764
Rearranging the equation to isolate h^2:
h^2 = 1764 - 225
h^2 = 1539
Taking the square root of both sides, we find:
h = √1539
Using a calculator, we can find that √1539 is approximately 39.22.
Therefore, the guy wire reaches a height of approximately 39.22 ft up the pole.