Question

30 points PLEASE HELP WITH MATH PROBLEM

Answer 1

10) What is the base of the triangle?

From this triangle we know:

THE AREA:

`A=80cm^2`

THE HEIGHT:

`H=B+12`

We know that the area, height, and base of a triangle are related according to the following formula:

`A=(BH)/(2) \\ \\ Substituting \ H: \\ \\ A=(B(B+12))/(2) \\ \\ Substituting \ A: \\ \\  80=(B(B+12))/(2) \\ \\ 2(80)=B(B+12) \\ \\ 160=B^2+12B \\ \\ B^2+12B-160=0`

Solving B by quadratic formula:

`B_(12)=(-b \pm √(b^2-4ac))/(2a) \\ \\ B_(12)=(-12 \pm √(12^2-4(1)(-160)))/(2(1)) \\ \\ B_(12)=(-12 \pm √(12^2-4(1)(-160)))/(2(1)) \\ \\ B_(1)=8 \ and \ B_(2)=-20`

Since we can’t have a negative value of the base, the correct option is:

`B=8cm`

11) How long will it take the water balloon to hit the ground?

We must use the formula:

`h(t)=-5.2t^2+v_(0)t+h_(0)`

Since James drops the balloon from a height of 45m, then this is the initial height, so
`h_(0)=45m`. Moreover, at the very instant he drops the balloon the initial velocity is zero, so
`v_(0)=0`. When the ballon hit the ground
`h(t)=0`. Therefore:

`0=-5.2t^2+45`

Solving this equation:

`5.2t^2=45 \\ \\ t^2=(45)/(5.2) \\ \\ t^2=8.653 \\ \\ t=√(8.653) \\ \\ t=2.941s`

Rounding to the nearest tenth:

`\boxed{t=2.9s}`

Finally, the water balloon will hit the ground after 2.9 seconds.

12) Height and initial velocity

We have the equation:

`h(t)=-16t^2+32t+12`

But we know that this equation follows the form:

`h(t)=-16t^2+v_(0)t+h_(0)`

According to this:

The height of the platform is
`h_(0)=12ft`

The initial velocity of the ball is
`v_(0)=32ft/s`