The function h(t)=-4.92t^2+17.69t+575 is used to model an object being tossed from a tall building, where h(t) is the height in
meters and t is the time in seconds. Rounded to the nearest hundredth, what are the domain and range? domain: [0, 12.76] range: [1.8, 590.9] domain: [1.80,1276] range: [1.8, 590.9] domain: [1.80,12.76] range: [0, 590.9] domain: [0, 12.76] range: [0, 590.9]
We have the following equation: <span> h(t)=-4.92t^2+17.69t+575
</span> For the domain we have: <span> </span>We match zero: -4.92t ^ 2 + 17.69t + 575 = 0 We look for the roots: t1 = -9.16 t2 = 12.76 We are left with the positive root, so the domain is: [0, 12.76]
For the range we have: We derive the function: h '(t) = - 9.84t + 17.69 We equal zero and clear t: -9.84t + 17.69 = 0 t = 17.69 / 9.84 t = 1.80 We evaluate the time in which it reaches the maximum height in the function: h (1.80) = - 4.92 * (1.80) ^ 2 + 17.69 * (1.80) +575 h (1.80) = 590.90 Therefore, the range is given by: [0, 590.9]
Answer: the domain and range are: domain: [0, 12.76] range: [0, 590.9]
