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Mathematics 21 Online
OpenStudy (anonymous):

Can someone please explain how to answer this problem to me? A sprinkler can eject water at angle of 35, 60, and 75 degrees with the ground. For these settings the paths of the water can be modeled by the equations below where the x and y are measured in feet. 35: y=-0.06x^2+0.7x+0.5 60: y=-0.16x^2+1.73x+0.5 75: y=-0.6x^2+3.73x+0.5 a. Find the maximum height of the water for each setting b. Find out how far from the sprinkler reaches for each setting.

OpenStudy (anonymous):

c. CRITICAL THINKING: Do you think there is an angle setting for the sprinkler to reach father than any of the settings above? How do the angle and the reach represented by the graph of y=-0.08x^2+x+.5 compare with the others? What angle setting would reach the least distance?

OpenStudy (anonymous):

Because it's an inverted parabola, all maxima for the height y is the vertex of them. Remember the vertex formula and all maximum heights are easy. Then, remember the symmetry of the parabola: multiply the x value for the vertex (for the first one it's somewhere near x = 5.8) by 2 to get the maximum distance traveled.

OpenStudy (anonymous):

Reach farther it would be on a pi/4 angles, or 45 degrees. The procedure to find the reach is similar to the above, i.e., find the x coordinate for the vertex and multiply by 2. The angle is a bit trickier, but I think it's a 45 degrees.

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