Julian kicked a soccer ball into the air with an initial upward velocity of 40 feet per second. the height h in feet of the ball above the ground can be modeled by h=-16t^2+40t, where t is the time in seconds after julian kicked the ball. find the time it takes the ball to reach 25 feet above the ground

x=5/4

Step-by-step explanation:

Since we're finding the time it takes for the ball to reach 25 feet, this means h is 25

h=-16t%5E2%2B40t Start with the given equation

25=-16t%5E2%2B40t Plug in h=25

16t%5E2-40t%2B25=0 Add 16t%5E2 to both sides. Subtract 40t from both sides.

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve 16%2Ax%5E2-40%2Ax%2B25=0 ( notice a=16, b=-40, and c=25)

x+=+%28--40+%2B-+sqrt%28+%28-40%29%5E2-4%2A16%2A25+%29%29%2F%282%2A16%29 Plug in a=16, b=-40, and c=25

x+=+%2840+%2B-+sqrt%28+%28-40%29%5E2-4%2A16%2A25+%29%29%2F%282%2A16%29 Negate -40 to get 40

x+=+%2840+%2B-+sqrt%28+1600-4%2A16%2A25+%29%29%2F%282%2A16%29 Square -40 to get 1600 (note: remember when you square -40, you must square the negative as well. This is because %28-40%29%5E2=-40%2A-40=1600.)

x+=+%2840+%2B-+sqrt%28+1600%2B-1600+%29%29%2F%282%2A16%29 Multiply -4%2A25%2A16 to get -1600

x+=+%2840+%2B-+sqrt%28+0+%29%29%2F%282%2A16%29 Combine like terms in the radicand (everything under the square root)

x+=+%2840+%2B-+0%29%2F%282%2A16%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

x+=+%2840+%2B-+0%29%2F32 Multiply 2 and 16 to get 32

So now the expression breaks down into two parts

x+=+%2840+%2B+0%29%2F32 or x+=+%2840+-+0%29%2F32

Lets look at the first part:

x=%2840+%2B+0%29%2F32

x=40%2F32 Add the terms in the numerator

x=5%2F4 Divide

So one answer is

x=5%2F4

Now lets look at the second part:

x=%2840+-+0%29%2F32

x=40%2F32 Subtract the terms in the numerator

x=5%2F4 Divide

So another answer is

x=5%2F4

So our only solution is:

x=5%2F4 (which is x=1.25 in decimal form)

So at 1.25 seconds, the ball is 25 feet high.

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