A firefighter holds a hose 3 m off the ground and directs a stream of water toward a burning building. The water leaves the hose at an initial speed of 16 m/sec at an angle of 308. The height of the water can be approximated by h ( x ) = − 0.026 x 2 + 0.577 x + 3 , where h ( x ) is the height of the water in meters at a point x meters horizontally from the firefighter to the building. a. Determine the horizontal distance from the firefighter at which the maximum height of the water occurs. Round to 1 decimal place. b. What is the maximum height of the water? Round to 1 decimal place. c. The flow of water hits the house on the downward branch of the parabola at a height of 6 m. How far is the firefighter from the house? Round to the nearest meter.
A firefighter holds a hose 3 m off the ground and directs a stream of water toward a burning building. The water leaves the hose at an initial speed of 16 m/sec at an angle of 308. The height of the water can be approximated by h ( x ) = − 0.026 x 2 + 0.577 x + 3 , where h ( x ) is the height of the water in meters at a point x meters horizontally from the firefighter to the building. a. Determine the horizontal distance from the firefighter at which the maximum height of the water occurs. Round to 1 decimal place. b. What is the maximum height of the water? Round to 1 decimal place. c. The flow of water hits the house on the downward branch of the parabola at a height of 6 m. How far is the firefighter from the house? Round to the nearest meter.
Solution Summary: The author calculates the horizontal distance from the firefighter at which the water will be at its maximum height.
A firefighter holds a hose 3 m off the ground and directs a stream of water toward a burning building. The water leaves the hose at an initial speed of 16 m/sec at an angle of 308. The height of the water can be approximated by
h
(
x
)
=
−
0.026
x
2
+
0.577
x
+
3
, where
h
(
x
)
is the height of the water in meters at a point x meters horizontally from the firefighter to the building.
a. Determine the horizontal distance from the firefighter at which the maximum height of the water occurs. Round to 1 decimal place.
b. What is the maximum height of the water? Round to 1 decimal place.
c. The flow of water hits the house on the downward branch of the parabola at a height of 6 m. How far is the firefighter from the house? Round to the nearest meter.
The cost of fuel consumed by a locomotive is proportional to the square of the speed and is equal to Q1600/h when the speed is 40km/h. Regardless of the speed, the cost per hour increases, for other reasons, by Q3600/h.
a) Calculate the speed at which the locomotive must go so that the cost per kilometer is minimum.
The relationship between the height H of an adult female and the length x of her tibia, in centimeters, is estimated by the linear model H(x) = 2.90x + 61.53. If incomplete skeletal remains of an adult female include a tibia measuring 30.9 centimeters, estimate the height of the female. Round to the nearest tenth.
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