Question

Can someone please help me with these math problems ASAP?! Thanks in advance! ;)

Answer 1

Answer:

11) Here given Function,

$f(x) = \sqrt{2x-11}$

And, $g(x) = -|0.1|x+5$

For f(x) = g(x)

$\sqrt{2x-11}=-|0.1|x+5$

$2x-11=(-|0.1|x+5)^2$

$2x-11=0.01x^2 - 10|0.1|x+25$

$2x=0.01x^2 - 10|0.1|x+25+11$

$2x=0.01x^2 - 10|0.1|x+36$

$0.01x^2 - 10|0.1|x - 2x+36=0$

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,

$f(x) = -16x^2+74x+9$

And, The height gain by the rocket B in x seconds,

$g(x) = -16x^2+82x$

If at x seconds both A and B gain the same height,

That is, f(x) = g(x)

⇒ $-16x^2+74x+9= -16x^2+82x$

⇒$74x + 9 = 82x$

⇒ $82x - 74x = 9$

⇒ $8x = 9$

⇒ x = 1.125 ≈ 1.13

Thus, the required solution is x = 1.13 seconds (approx)