Answer:
11) Here given Function,
[tex]f(x) = \sqrt{2x-11}[/tex]
And, [tex]g(x) = -|0.1|x+5[/tex]
For f(x) = g(x)
[tex]\sqrt{2x-11}=-|0.1|x+5[/tex]
[tex]2x-11=(-|0.1|x+5)^2[/tex]
[tex]2x-11=0.01x^2 - 10|0.1|x+25[/tex]
[tex]2x=0.01x^2 - 10|0.1|x+25+11[/tex]
[tex]2x=0.01x^2 - 10|0.1|x+36[/tex]
[tex]0.01x^2 - 10|0.1|x - 2x+36=0[/tex]
When we solve this equation,
We found,
x = 12.5227 ≈ 12.53
Thus, the required solution is, x = 12.53
12) Here the height of rocket A in x second,
[tex]f(x) = -16x^2+74x+9[/tex]
And, The height gain by the rocket B in x seconds,
[tex]g(x) = -16x^2+82x[/tex]
If at x seconds both A and B gain the same height,
That is, f(x) = g(x)
⇒ [tex]-16x^2+74x+9= -16x^2+82x[/tex]
⇒[tex]74x + 9 = 82x[/tex]
⇒ [tex]82x - 74x = 9[/tex]
⇒ [tex]8x = 9[/tex]
⇒ x = 1.125 ≈ 1.13
Thus, the required solution is x = 1.13 seconds (approx)
