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
ASHA 777 [7]
2 years ago
5

NO LINKS!!!!

Mathematics
1 answer:
statuscvo [17]2 years ago
5 0

The instructions for these problems seem incomplete. I'm assuming your teacher wants you to find the equation of each parabola.

===============================================================

Problem 1

Let's place Maya at the origin (0,0) on the xy coordinate grid. We'll have her kick to the right along the positive x axis direction.

The ball lands 40 feet away from her after it sails through the air. So the ball lands at (40,0). At the halfway point is the vertex (due to symmetry of the parabola), so it occurs when x = 40/2 = 20. The ball is at a height of 18 feet here, which means the vertex location is (20,18).

The vertex being (h,k) = (20,18) leads to...

y = a(x-h)^2 + k\\y = a(x-20)^2 + 18

Let's plug in another point on this parabola, say the origin point. Then we'll solve for the variable 'a'.

y=a(x-20)^2+18\\\\0 = a(0-20)^2 + 18\\\\0 = a(-20)^2 + 18\\\\0 = 400a + 18\\\\-18 = 400a\\\\400a = -18\\\\a = -\frac{18}{400}\\\\a = -\frac{9}{200}

So we can then say,

y = a(x-h)^2 + k\\\\y = -\frac{9}{200}(x-20)^2 + 18\\\\y = -\frac{9}{200}(x^2-40x+400) + 18\\\\y = -\frac{9}{200}x^2-\frac{9}{200}*(-40x)-\frac{9}{200}*400 + 18\\\\y = -\frac{9}{200}x^2+\frac{9}{5}x-18 + 18\\\\y = -\frac{9}{200}x^2+\frac{9}{5}x\\\\

The final equation is in the form y = ax^2+bx+c where a = -\frac{9}{200}, \ b = \frac{9}{5}, \text{ and } c = 0

x = horizontal distance the ball is from Maya

y = vertical distance the ball is from Maya

Maya is placed at the origin (0,0)

The graph is shown below. Refer to the blue curve.

===============================================================

Problem 2

We could follow the same steps as problem 1, but I'll take a different approach.

Like before, the kicker is placed at the origin and will aim to the right.

Since the ball is on the ground at (0,0), this is one of the x intercepts. The other x intercept is at (60,0) because it lands 60 feet away from the kicker.

The two roots x = 0 and x = 60 lead to the factors x and x-60 respectively.

We then end up with the factorized form y = ax(x-60) where the 'a' is in the same role as before. It's the leading coefficient.

To find 'a', we'll plug in the coordinates of the vertex point (30,20). The 30 is due to it being the midpoint of x = 0 and x = 60. The 20 being the height of the ball at this peak.

y = ax(x-60)\\\\20 = a*30(30-60)\\\\20 = a*30(-30)\\\\20 = -900a\\\\a = -\frac{20}{900}\\\\a = -\frac{1}{45}

Let's use this to find the standard form of the parabola.

y = ax(x-60)\\\\y = -\frac{1}{45}x(x-60)\\\\y = -\frac{1}{45}(x^2-60x)\\\\y = -\frac{1}{45}*x^2-\frac{1}{45}*(-60x)\\\\y = -\frac{1}{45}x^2+\frac{4}{3}x\\\\

Refer to the red curve in the graph below.

===============================================================

Problem 3

We can use either method (similar to problem 1 or problem 2). The second problem's method is probably faster.

Logan is placed at (0,0) and kicks to the right. The ball lands at (30,0). Those x intercepts are x = 0 and x = 30 respectively, which lead to the factors x and x-30. This leads to y = ax(x-30)\\\\

The midpoint of (0,0) and (30,0) is (15,0). Eight feet above this midpoint is the location (15,8) which is the vertex. Plug in (x,y) = (15,8) and solve for 'a'

y = ax(x-30)\\\\8 = a*15(15-30)\\\\8 = a*15(-15)\\\\8 = -225a\\\\a = -\frac{8}{225}\\\\

So,

y = ax(x-30)\\\\y = -\frac{8}{225}x(x-30)\\\\y = -\frac{8}{225}(x^2-30x)\\\\y = -\frac{8}{225}*x^2-\frac{8}{225}*(-30x)\\\\y = -\frac{8}{225}x^2+\frac{16}{15}x\\\\

The graph is the green curve in the diagram below.

Like with the others, x and y represent the horizontal and vertical distance the ball is from the kicker. The kicker is placed at the origin (0,0).

Once we know the equation of the parabola, we can answer questions like: "how high up is the ball when it is horizontally 10 feet away?". We do this by plugging in x = 10 and computing y.

Side note: We assume that there isn't any wind. Otherwise, the wind would slow the ball down and it wouldn't be a true parabola. However, that greatly complicates the problem.

You might be interested in
?????????????????????????????????????????????????
Vladimir [108]
Number 15- The total is 350
                    A discount of 70% off
                    The answer : 245

4 0
3 years ago
Read 2 more answers
Suppose that 15 inches of wire costs 90 cents. At the same rate, how many inches of wire can be bought for 48 cents?
tamaranim1 [39]
This can be solved by making an equivalent ratio.
The original ratio is what we know, 15 inches of wire for 90 cents.
In a ratio of inches of wire:cents, this would be 15:90.

Now for the equivalent ratio.
We don't know the number in the inches place but we do know it for the cents place.
Let's use x to represent inches of wire.
x:48 is our new ratio, and we need to find x.

Since x:48 and 15:90 are equivalent, that means the same thing that was done to 90 to get 48 has to be done to 15 to get the value of x, since the same thing must be applied to both sides.
We can find what 90 was divided by (which is what we'll have to divide 15 by) by dividing 90 by 48.
90 / 48 = 1.875

This means 48 • 1.875 = 90 and x • 1.875 = 15.
Since we don't know x though, we can isolate it by dividing both sides by 1.875.
x • 1.875 = 15
x • 1.875 / 1.875 = x
15 / 1.875 = 8
So x is 8.

Answer:
While you can be 15 inches of wire for 90 cents, you can buy 8 inches of wire for 48 cents at the same rate.
3 0
3 years ago
Use the elimination method to solve the system of equations. Choose the
hichkok12 [17]

Answer:

the ordered pair is (2,-1)

Step-by-step explanation:

We need to solve the system of equations using elimination method

12x - y = 25     eq(1)

9x + y = 17      eq(2)

Adding eq(1) and eq(2)

12x - y = 25

9x + y = 17

___________

21x = 42

x = 42/21

x= 2

Now, putting value of x in equation 1

12x - y = 25

12(2) -y = 25

24 -y = 25

Adding -24 on both sides

24 -y-24 = 25-24

-y = 25-24

-y = 1

Multiply both sides by -1

y = -1

the value of x = 2 and y = -1

So, the ordered pair is (2,-1)

5 0
3 years ago
Read 2 more answers
Write -15 as a rational number
LiRa [457]
-15 is already rational itself, but it as a fraction:
-15/1
7 0
3 years ago
Which steps could be used to solve this story problem? The librarian was organizing some books on some shelves. She had 200 fict
VashaNatasha [74]
Hi there! The answer is A. Add together 200 and 100. Then divide the sum by 6.

In this problem we want to know how many books there are on 1 shelf. Therefore we must first now the total amount of books and so we add up 200 and 100 (which makes a total of 300 books)

Finally we divide this total amount of books by the amount of shelfs (300 / 6), and then we've found the answer to our question. Hence, the answer is A.
5 0
3 years ago
Other questions:
  • Write in exponential form. 3a • 3a • 3a
    5·1 answer
  • Polygon ABCD is translated to create polygon A′B′C′D′. Point A is located at (1, 5), and point A′ is located at (-2, 1). What is
    13·1 answer
  • Identify the sequence as arithmetic, geometric, both, or neither. 50, –50, 50, –50, . . . both arithmetic geometric neither desc
    6·1 answer
  • I have to give the answer in by 8pm
    10·1 answer
  • Use the expression 8a + 16c.
    13·1 answer
  • WILL MARK BRAINLIEST IF CORRECT! A mini-cone has a diameter of 2 inches and holds 12.5 in3 of ice cream. A mega-cone holds 133.1
    7·1 answer
  • A plane is a _ figure
    10·2 answers
  • Suppose 540 people visit the zoo.Predict how many people will choose the monkey exhibit as their favorite
    5·2 answers
  • Select all values equivalent to -10/7
    10·1 answer
  • Surface area,<br>pls help ​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!