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MArishka [77]
3 years ago
8

using the equation representing the height of the firework (h = -16t^2 + v↓0 + h↓0), algebraically determine the extreme value o

f f(t) by completing the square and finding the vertex. Interpret what the value represents in this situation.

Mathematics
1 answer:
Hitman42 [59]3 years ago
7 0

Answer:

y = (-1/15)(x - 3)2 + 15

Step-by-step explanation:

The general equation of a parabola is

y = a(x - h)2 + k

If the halfway line if the origin, i.e. (x, y) = (0, 0), then the ball is kicked at (-12, 0) and it lands at (18, 0). By symmetry, the ball reaches its greatest height halfway between the starting and ending x values, or at x = 3. So, we know three points on this parabola: (-12, 0), (18, 0) and (3, 15).

Let us plug the first point into the generalized equation:

y = (x - h)2 + k

0 = (-12 - h)2 + k

So, k = -(-h - 12)2

or

k = -(h + 12)2, since we can factor out -1 and it becomes squared.

We can also plug (18, 0) into the generalized equation, and get:

0 = (18 - h)2 + k

So, k = -(18 - h)2

Since we have two expressions both equal to k, we can set them equal to each other and eliminate k:

-(h + 12)2 = -(18 - h)2

We can cancel out the negative signs and square out the terms on each side of the last equation.

h2 + 24h + 144 = h2 - 36h + 324

We can cancel out h2 and then solve for h.

24h + 144 = -36h + 324

60h = 180

h = 3

Therefore, the generalized equation becomes

y = a(x - 3)2 + k

We know that if x = 3, y = 15 from out third point.

15 = a(3 - 3)2 + k

So, k = 15

Thus, the equation becomes

y = a(x - 3)2 + 15

We can then pick one of the other points, plug in the corresponding x and y and then solve for a. I choose (18, 0).

0 = a(18 - 3)2 + 15

0 = 152a + 15

Divide this equation through by 15.

0 = 15a + 1

or

a = -1/15

Therefore, the generalized equation is

y = (-1/15)(x - 3)2 + 15

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657

Step-by-step explanation:

pemdas

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3 years ago
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.. y = kx^2
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7 0
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James won 9 out of 12 games in a school competition. What percent of competitions did James win
ratelena [41]
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5 0
3 years ago
Mrs. Gomes found that 40% of students at her high school take chemistry. She randomly surveys 12 students. What is the probabili
zlopas [31]

Answer:

The correct answer to the following question will be "0.438".

Step-by-step explanation:

Just because Mrs. Gomes finds around 40% of students in herself high school are studying chemistry.  

Although each student becomes independent of one another, we may conclude:  

"x" number of the students taking chemistry seems to be binomial to p = constant probability = 0.40

Given:

Number of surveys

= 12

Exactly 4 students have taken chemistry:

=P(X\leq4)

=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)

=\Sigma_{0}^{4} C_{r}(0.4)^r(0.6)^{12-r}

On substituting the above equation, we get the probability of approximately "0.438".

So that the above would be the appropriate answer.

5 0
3 years ago
If a cubic container has a side length of 50.0cm, what is the volume in liter?
zimovet [89]

Answer:

The answer is

<h2>125 litres</h2>

Step-by-step explanation:

To find the volume in liter we must first find the volume in cm³

Since the container is cubic

Volume = l³

where l is the length of one side

From the question

l = 50.0 cm

Volume = 50³

= 125000 cm³

Next we use the conversion

1cm³ = 0.001 L

If 1 cm³ = 0.001 L

Then 125,000 cm³ = 125,000 × 0.001 L

We have the final answer as

<h3>125 litres</h3>

Hope this helps you

3 0
3 years ago
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