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30 points PLEASE HELP WITH MATH PROBLEM

30 points PLEASE HELP WITH MATH PROBLEM-example-1

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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

User Capdragon
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