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:
 h(t)=-4.92t^2+17.69t+575

 For the domain we have:
 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]

 
 the domain and range are:
 domain: [0, 12.76] range: [0, 590.9]

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