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16 May, 08:04

A model rocket is launched from the ground with an initial velocity of 60 feet per second. the function g (t) = - 16t^2 + 60t represents the height of the rocket, g (t), t seconds after it was launched ... what is the absoloute max, zeros, domain, and range

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  1. 16 May, 08:10
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    If we use our trusty ti's this will be a breeze

    domain is the numbers we can use

    obviously we can't have negative time so therefor the domain is all positive integers (0,1,2,2.3, 3/2,3, pi ...)

    zeroes is when you set absolute max using ti is

    remember vertex form which is

    max height of something in

    ax^2+bx+c form is - b/2a

    -16t^2+60t+0

    a=-16

    b=60

    -60 / (2 times - 16)

    -60/-32=30/16=15/8=1 and 7/8 so subsitute for t

    g (15/8) = - 16 (15/8) ^2+60 (15/8) = 225/4=56.25=max height

    zeroes is when the equation equals 0

    so set it to zero

    0=-16t^2+60t

    factor

    0 = (-4t) (4x-15)

    set each to zero

    -4x=0

    x=0

    4x-15=0

    add 15

    4x=15

    divid 4

    x=15/4

    so the zeros are t=0 and t=15/4

    domain is all the nuumbers that can be used logically for time

    logically, we cannot have negative time, so all real positive

    [0,∞)

    (that means from 0 to infinity includng 0 so 0 < t<∞))

    range is the output

    output=height

    we find the min height and max height

    min=0

    max=56.25

    so range=0 to 56.25 or

    [0,56.25]

    max height=56.25 ft (15/8 seconds)

    zeroes=0 sec and 15/4 sec

    domain=all real positive numbers including zero or [0, ∞)

    range=[0,56.25]
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