Question

Please help, I need input on if I did this correctly and you just substitute.

I have the function h(t) = -16t^2 + 15t + 6.5
t equals 15/32.

If you substitute 15/32 for t, what do you get?

Any help is appreciated, thank you very much!

Answer 1

The value of h(t) when
`t=(15)/(32)` is 10.02.

Solution:

Given function
`h(t)=-16t^2+15t+6.5`

To find the value of h(t) when
`t=(15)/(32)`:

`h(t)=-16t^2+15t+6.5`

Substitute
`t=(15)/(32)` in the given function.

`$h\left((15)/(32) \right)=-16\left((15)/(32) \right)^2+15\left((15)/(32) \right)+6.5`

`$=-16\left((225)/(1024) \right)+15\left((15)/(32) \right)+6.5`

Now multiply the common terms into inside the bracket.

`$=-\left((3600)/(1024) \right)+\left((225)/(32) \right)+6.5`

Now, in the first term, the numerator and denominator both have common factor 16. So reduce the first term into the lowest term.

`$=-\left((225)/(64) \right)+\left((225)/(32) \right)+6.5`

To make the denominator same, take LCM of the denominators.

LCM of 64 and 32 = 64

`$=-\left((225)/(64) \right)+\left((225*2)/(32*2) \right)+6.5*(64)/(64)`

`$=-(225)/(64) +(450)/(64)+(416)/(64)`

`$=(-225+450+416)/(64)`

`$=(641)/(64)`

= 10.02

`$h\left((15)/(32) \right)=10.02`

Hence the value of h(t) when
`t=(15)/(32)` is 10.02.