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stiks02 [169]
2 years ago
15

A football is kicked toward the goal. the height of the ball is modeled by the function h(t) = −16t2 64t, where t equals the tim

e in seconds and h(t) represents the height of the ball at time t seconds. what is the axis of symmetry, and how does it relate to the time the ball is in the air?
Mathematics
1 answer:
xenn [34]2 years ago
6 0

Answer:

axis of symmetry : x = 4

Step-by-step explanation:

The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

The vertex of h(t) = -16t^2 + 64x is ( 4 , 0 )

The vertex is the highest point of the graph so it represents that after four seconds the ball is at its highest height when the football is being kicked towards the goal.

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Step-by-step explanation:

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0.25*N=24
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Please help i put a picture below
PSYCHO15rus [73]

Answer:

Step-by-step explanation:

This is not nearly as threatening and scary as I first thought it was.  You must be in the section in Geometry where you are taught that perimeter of similar figures exist in a one-to-one relationship while areas of similar figures exist in a squared-to-squared relationship.  We will use that here.  

The area formula for a regular polygon is

A=\frac{1}{2}ap where a is the apothem and p is the perimeter.  We are first asked for the area of the polygon, but it would make more sense to find the perimeter first, since we need it to find the area.

P = 5(8) so

P = 40

We are given that the area of the triangle inside that polygon is 22.022 units squared.  Knowing that the area formula for a triangle is

A=\frac{1}{2}bh we can sub in what we know and solve to find the height:

22.022=\frac{1}{2}(8)h and

22.022 = 4h so

h = 5.5055 units

It just so happens that the height of that triangle is also the apothem of the polygon, so now we have what we need to find the area of the polygon:

A=\frac{1}{2}(5.5055)(40)

which gives us an area of

A = 110.11 units squared.

Here is where we can use what we know about similar figures and the relationships between perimeters and areas.  We will set up a proportion with the smaller polygon info on top and the larger info on bottom.  We know that the larger is 3 times the smaller, so the ratio of smaller to larger is

\frac{s}{l}:\frac{1}{3}

Since perimeter is one-to-one and we know the perimeter of the smaller, we can create a proportion to solve for the perimeter of the larger:

\frac{s}{l}:\frac{1}{3}=\frac{40}{x}

Cross multiply to get that the perimeter is 120 units.  You could also have done this by knowing that if the larger is 3 times the size of the smaller, then the side measure of the larger is 24, and 24 * 5 = 120.  But we used the way we used because now we have a means to find the area of the larger since we know the area of the smaller.

Area exists in a squared-to-squared relationship of the perimeter which is one-to-one.  If the perimeter ratio is 1:3, then the area relationship is

\frac{s}{l}:\frac{1^2}{3^2} which is, simplified:

\frac{s}{l}:\frac{1}{9}

Since we know the area for the smaller, we can sub it into a proportion and cross multiply to solve for the area of the larger.

\frac{s}{l} :\frac{1}{9} =\frac{110.11}{x}

A of the larger is 990.99 units squared

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What is the square root of 29 rounded to the nearest 10?
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5.40. It would be 5.38 but you round up to 5.40
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