1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ANEK [815]
3 years ago
8

Ja'Von kicks a soccer ball into the air. The function f(x) = –16(x – 2)2 + 64 represents the height of the ball, in feet, as a f

unction of time, x, in seconds. What is the maximum height the ball reaches?
Mathematics
1 answer:
Dima020 [189]3 years ago
3 0

Answer:

The maximum height the ball reaches is 64 feet

Step-by-step explanation:

The given function is f(x) = -16·(x - 2)² + 64

From the equation, the path described by the ball is an inverted n-shaped parabola

The maximum height is therefore, the tip of the parabola

At the maximum height, the slope = 0 because the tip is momentarily flat

Since the slope (y₂ - y₁)/(x₂ - x₁)  = The derivative Δy/Δx, we find the derivative of the function and equate it to zero to find the coordinates at the  maximum height

Δy/Δx = dy/dx = d(-16·(x - 2)² + 64)/dx = -32·(x - 2) = -32·x + 64

To check if it is a maximum, we have;

d²y/dx² = d(-32·x + 64)/dx = -32 which is negative, indicating that the slope is reducing and we at the maximum point of the slope

Therefore for the maximum height Δy/Δx = dy/dx = -32·x + 64 = 0

64 = 32·x

x = 64/32 = 2 seconds

We now have the x-value at the slope, the f(x) value, is therefore;

f(2) = -16·(2 - 2)² + 64 = 64 feet

Therefore, the maximum height the ball reaches is 64 feet.

You might be interested in
Will give Brainliest
geniusboy [140]

Answer:

The y intercept is 2

Step-by-step explanation:

Y = mx + b where b is the y intercept. Since b = 2 here, the y intercept is 2. Yes, the line crosses the y-axis at the point (0,2).

3 0
3 years ago
The table shows the steps for solving the given inequality for x.
slavikrds [6]

Given inequality -3(4-6x) < x+5.

We have -3 in front of Parenthesis.

That represents multiplication of -3 and Parenthesis.

The multiplication of Parenthesis could be done by applying distributive property.

On distributing, we get

-12+18x < x+5

x is added on right side of the inequality. The reverse operation of addition is subtraction. So we need to subtract x from both sides, we get

-12+18x-x < x-x+5

-12+17x < 5

Now, we need to get rid -12 from left side.

So, we need to apply addition property of equality, we need to add 12 on both sides, we get

-12+12+18x < x+5+12

17x < 17

We need to get rid 17 from left side. So we need to apply division property of equality.

On dividing both sides by 17, we get

17x/17 < 17/17

x<1.

8 0
3 years ago
Which equation can be used to find the measurement of ∠C? To the nearest degree, what is the measurement of ∠A? A) 5sin∠C = 2; 2
egoroff_w [7]
First guy is incorrect.Answer is actually B

7 0
3 years ago
Read 2 more answers
WILL MARK BRAINLIEST
Levart [38]

Answer:

Part 1:

The solution set of the system of equations is x = 1, y = 1

Part 2:

The solution set is x = 1, y = 1

Part 3:

The similarity of the system of equations in Parts 1 and 2 is that they have the same solution set

The difference of the system of equations in Parts 1 and 2 is that they are arranged differently

Step-by-step explanation:

Part 1:

The system of equation is given as follows;

2·x + y = 3...(1)

x = 2·y - 1...(2)

The above system of equations can be written in terms of the variable, y, as follows;

For equation (1), we have;

y = 3 - 2·x

For equation (2), we have;

y = (x + 1)/2

From the attached graph created with Microsoft Excel, we have;

The solution set (the point of intersection) of the system of equations is x = 1, y = 1

To accurately find the common solution, we have;

(x + 1)/2 = 3 - 2·x

x + 1 = 2·(3 - 2·x) = 6 - 4·x

x + 1 = 6 - 4·x

x + 4·x = 6 - 1

5·x = 5

x = 5/5 = 1

x = 1

Therefore, y = 3 - 2·x = 3 - 2× 1 = 1, at the common solution

Part 2:

y = -2x + 3

x - 2y = -1

∴ x = 2y -1

y = -2(2y -1) + 3

y = -4y + 2 + 3

5y = 5

y = 1

x = 2y - 1 = 2 - 1 = 1

x = 1

The solution set is x = 1, y = 1

Part 3

The system of equations are similar in terms of their solution

The system of equations are different in terms of their arrangement

6 0
2 years ago
WILL GIVE BRAINLEIST NEED TO TURN IN BY 9 P.M. PLS HURRY SUPER EASY
Klio2033 [76]

Answer:

1. true

2. false

Step-by-step explanation:

1.there are no restrictions on what makes it true so it can be any number

2. only one answer because

m+8=12

subtract 8

m=4

3 0
3 years ago
Read 2 more answers
Other questions:
  • Mara and Taylor need to rent a car for 6 days. If the cost of the car is $105 for each day, which of the following expressions c
    10·2 answers
  • Given points A (-3,-4) and B (2,0), points P (-1,-12/5) partitions line AB in the ratio
    9·1 answer
  • How do I solve: -20&lt;4-2x
    7·1 answer
  • By recycling 1 ton of paper,6,953 gallons of water are saved.How many gallons of water are saved by recycling 4 tons of paper?
    8·2 answers
  • Help me pleaseeeeeeeee
    12·1 answer
  • A ​ 75 inch is cut into two pieces. One piece is four times the length of the other. Find the length of the shorter piece.
    12·1 answer
  • Please help BRAINIEST ANSWER ❤️❤️
    9·1 answer
  • Which of the following shows the inverse of {(0, 4), (5, -2), (-1, 8), (2, 5)}?
    10·1 answer
  • Can I get provided with an explanation of how to work this out as well with the answer please ?
    11·1 answer
  • White shapes and black shapes are used in a game some of these shapes are circles and all the rest of the shapes are squares the
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!