Question

Please help me solve this!!!!

Answer 1

6.0 seconds

Explanation:

Given the function:

`h(t)=-16t^2 + 130t`

that models the height of a firework t seconds after being shot upward (when t = 0), we can find when it reaches a height of 205 ft by plugging 205 in for h(t) and solving for t at that moment:

`205=-16t^2 + 130t`

↓ adding 16t² to both sides

`16t^2 + 205 = 130t`

↓ subtracting 130t from both sides

`16t^2 - 130t + 205 = 0`

↓ assigning variable values for a quadratic in the form
`ax^2 + bx + c`

• 
  `a = 16`
• 
  `b = -130`
• 
  `c = 205`

↓ plugging these into the quadratic formula:
`x = (-b\pm√(b^2-4ac))/(2a)`

`t = (-(-130)\pm√((-130)^2-4(16)(205)))/(2(16))`

↓ simplifying each operation

`t = (130\pm√(3780))/(32)`

↓ taking the positive answer

`t = (130+√(3780))/(32)`

↓ evaluating as a decimal

`t\approx 5.983803...`

↓ rounding to the nearest tenth

`\boxed{t \approx 6.0}`

The firework will reach a height of 205 ft after 6.0 seconds.