Question 1195454


{{{y=-4(x-10)^2 +400}}}......eq.1 

{{{y= -2(x-20)^2+300}}}.....eq.2
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to find at what time and height should the second missile reach and explode the first missile, find intersection point of the system above

{{{-4(x-10)^2 +400= -2(x-20)^2+300}}}}......solve for {{{x}}}

{{{-4x^2 + 80x -400 +400= -2x^2 + 80x -800+300}}}}

{{{-4x^2 + 80x = -2x^2 + 80x -500}}}}....simplify

{{{-4x^2 = -2x^2 -500}}}}

{{{500 = 4x^2-2x^2 }}}}

{{{500 = 2x^2 }}}}

{{{250 = x^2 }}}}

{{{x=sqrt(250)}}}

{{{x = 5sqrt(10)}}}->exact solution

{{{x=15.8}}}->approximately

find {{{y}}}


{{{y=-4(5sqrt(10)-10)^2 +400}}}......eq.1 

{{{y=200(2sqrt(10) - 5)}}} -> exact solution

{{{y=264.9}}} ->approximately

At time {{{15.8}}} seconds and height {{{264.9}}} meters the second missile should reach and explode the first missile