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2 years ago

5

Jeff is making fruit punch for the school dance. He needs 3 3/4 cups of pineapple juice per batch. If Jeff wants to make 4 1/2 b

atches of punch, how many cups of pineapple juice will he need?

1 answer:

sasho [114]2 years ago

8 0

1 batch = 3 3/4 cups
4 1/2 batches = (4 1/2 x 3 3/4) = 9/2 x 15/4 = 135/8 = 16 7/8

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Answer:

4.35 seconds.

Step-by-step explanation:

Let x represent the time the independent variable and y be dependent variable (height of the ball).

We are told that Duffy figured that the ball left his hand at a height of 5 feet. This means at x equals 0, y was 5 or initial height of ball is 5 feet.

We have been given that Duffy's coach measured that his throw reached a maximum height of 18 feet after 2 seconds. This means that at x equals 2 y was 18.

As point (2,18) represents maximum height of ball, so it will be vertex of parabola.

Since initial height of ball is less than maximum height, so our parabola will be downward opening and leading coefficient will be negative.

We know that vertex form of a downward opening parabola is in form: $y=-a(x-h)^2+k$

$y=-a(x-2)^2+18$

Let us find value of a using point (0,5).

$5=-a(0-2)^2+18$

$5=-a*4+18$

$5-18=-a*4+18-18$

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$\frac{-13}{-4}=\frac{-4a}{-4}$

$\frac{13}{4}=a$

Therefore, the equation $y=-(\frac{13}{4})(x-2)^2+18$ can be used to find the height of ball after x seconds.

To find the time it will take the ball to hit the ground, we will substitute y equals 0 in our equation.

$0=-(\frac{13}{4})(x-2)^2+18$

$0-18=-(\frac{13}{4})(x-2)^2+18-18$

$0-18=-(\frac{13}{4})(x-2)^2$

$-18*(\frac{4}{13})=-(x-2)^2$

$\frac{72}{13}=(x-2)^2$

Taking square root of both sides of our equation we will get,

$\sqrt{\frac{72}{13}}=x-2$

$x-2\pm 2.35339$

$x-2=2.35339\text{ (or) } x-2=2.35339$

$x-2+2=2.35339+2\text{ (or) } x-2+2=-2.35339+2$

$x=4.35339\text{ (or) } x=-0.35339$

$x\approx 4.35\text{ (or) } x\approx -0.35$

Since time can not be negative, therefore, the ball will hit the ground approximately after 4.35 seconds.

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