Question

Captain calculus can leap over tall buildings. when he does so, his height s (in feet) off the ground after t seconds is given by s(t) = t^2+7t+34. for how many seconds is captain calculus more than 40 feet off the ground?

Answer 1

we are given

height function as

`s(t) = t^2+7t+34`

we have to find time at which height is more than 40 feet off the ground

so, we can set up inequality as

`s(t)>40`

`t^2 +7t+34 >40`

now, we can simplify it

`t^2 +7t-6 >0`

Let's assume it is equal to 0

and then we can solve for t

`t^2 +7t-6 =0`

we can use quadratic formula

`t=0.77200`

so,

`t > 0.77200`

so, closest value is 1

so, captain calculus more than 40 feet off the ground after 1 seconds.......Answer