Question 150685
Parts A and B are correct.


C)



From {{{s(t)=-16t^2+40t+30}}}, we can see that {{{a=-16}}}, {{{b=40}}}, and {{{c=30}}}.


In order to find out when the rock will reach the max height, use this formula: {{{t=(-b)/(2a)}}}.



{{{t=(-b)/(2a)}}} Start with the given formula.



{{{t=(-(40))/(2(-16))}}} Plug in {{{a=-16}}} and {{{b=40}}}.



{{{t=(-40)/(-32)}}} Multiply 2 and {{{-16}}} to get {{{-32}}}.



{{{t=5/4}}} Reduce.


So the rock will reach the max height when {{{t=5/4}}} or {{{t=1.25}}}. So the rock takes 1.25 seconds to reach the peak.


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D)


{{{s(t)=-16t^2+40t+30}}} Start with the given equation.



{{{s(5/4)=-16(5/4)^2+40(5/4)+30}}} Plug in {{{t=5/4}}}.



{{{s(5/4)=-16(25/16)+40(5/4)+30}}} Square {{{5/4}}} to get {{{25/16}}}.



{{{s(5/4)=-25+40(5/4)+30}}} Multiply {{{-16}}} and {{{25/16}}} to get {{{-25}}}.



{{{s(5/4)=-25+50+30}}} Multiply {{{40}}} and {{{5/4}}} to get {{{50}}}.



{{{s(5/4)=55}}} Combine like terms.


So at the peak, the rock is 55 feet high. So the max height is 55 feet.