Question

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

Answer 1

11) Here given Function,

`f(x) = √(2x-11)`

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

For f(x) = g(x)

`√(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)