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Drupady [299]
3 years ago
11

Texas University Quarterback, Michael Daniels, is standing on his own 10-yard line. He throws a pass tword the opposite goal lin

e. The football is 2 yards above the ground when the quarterback lets it go. It follows a parabolic path. Reaching its highest point, 30 yards above the ground. It is caught 50 yards downfeild at a point 2 yards above the ground. Let X be the number of yards the football travels horizontally, and let Y be the number of yards the ball is above ground.
Draw the graph of the function

Mathematics
1 answer:
dimulka [17.4K]3 years ago
3 0

Answer: The function is y=-\frac{28}{625}(x-35)^2+30.

Explanation:

It is given that Michael Daniels, is standing on his own 10-yard line. He throws a pass toward the opposite goal line. The football is 2 yards above the ground when the quarterback lets it go.

It follows a parabolic path. Reaching its highest point, 30 yards above the ground. It is caught 50 yards downfield at a point 2 yards above the ground.

So, the initial point is (10,2) and the other point is (60,2).

The height function of a football represents a downward parabola. The maximum point of the function is called vertex. So the vertex is (h,30).

The two point (10,2) and (60,2) have same y-coordinate, therefore the function is maximum at the midpoint of both points.

midpoint=(\frac{10+60}{2}, \frac{2+2}{2})=(35,2)

So, the function is maximum at x=35. Hence the vertex is (35,30)

The standard form of the parabola is,

y=a(x-h)^2+k

Where (h,k) is vertex and a is scale factor.

Since vertex is (35,30).

y=a(x-35)^2+30

The initial point is (10,2).

2=a(10-35)^2+30

-28=625a

a=-\frac{28}{625}

So the function of height is.

y=-\frac{28}{625}(x-35)^2+30

The graph of the function is shown below.

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aivan3 [116]

Answer:

820

Step-by-step explanation:

If you use order of operations, you can find that 3x0 and 1x400x100x456x0 is just 0 so you just have to add 2x2 and 34x24. Which is 820

order of operations is

GEMDAS

Grouping symbols

exponents

multiplication and division (these don't have to be in order)

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3 0
3 years ago
A line through the origin and (10,4) is showin in the standard (x,y) coordinate plane below. The acute angle between the line an
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Answer:

\cos\theta=\frac{10}{\sqrt{116}}

Step-by-step explanation:

To solve this, we can imagine a line drawn directly down from the point (10,4) to the x-axis. This would make a right triangle with length 10 and height 4.

\cos\theta is equal to the length of adjacent leg to the angle divided by the length of the hypotenuse of the triangle. From the picture, we can see the adjacent leg is 10.

We can use Pythagorean's Theorem to find the hypotenuse (let c represent the length of the hypotenuse):

10^2+4^2=c^2

100+16=c^2

116=c^2

c=\sqrt{116}

Thus, we know the adjacent is 10, and the hypotenuse is \sqrt{116}. This means \cos\theta=\frac{10}{\sqrt{116}}.

Hope this helps!

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What number is 1/10 as great as 7962?
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Answer:

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