The position of a ball after it is kicked can be determined by using the function f left parenthesis x right parenthesis equals negative 0.11 x squared plus 2.2 x plus 1f(x)=−0.11x2+2.2x+1​, where​ f(x) is the​ height, in​ feet, above the ground and x is the horizontal​ distance, in​ feet, of the ball from the point at which it was kicked. What is the height of the ball when it is​ kicked? What is the highest point of the ball in the​ air?

Answers

Answer 1

Answer:

When kicked, the height of the ball is 1 feet. The highest point for the ball's trajectory is 12 feet.

Step-by-step explanation:

We are given that the height is given by [tex]f(x)=-0.11x^2+2.2x+1[/tex]. The distance between the ball to the point where it was kicked is 0 right at the moment the ball was kicked. So, the height of the ball, when it was kicked is f(0) = -0.11*0 + 2.2*0 +1  = 1.

To determine the highest point, we will proceed as follows. Given a parabola of the form x^2+bx + c, we can complete the square by adding and substracting the factor b^2/4. So, we get that

[tex] x^2+bx+c = x^2+bx+\frac{b^2}{4} - \frac{b^2}{4} +c = (x+\frac{b}{2})^2+c-\frac{b^2}{4}[/tex].

In this scenario, the highest/lowest points is [tex]c-\frac{b^2}{4}[/tex} (It depends on the coefficient that multiplies x^2. If it is positive, then it is the lowest point, and it is the highest otherwise).

Then, we can proceed as follows.

[tex] f(x) = -0.11x^2+2.2x+1 = -0.11(x^2-20x)+1[/tex]

We will complete the square for [tex]x^2-20x[/tex]. In this case b=-20, so

[tex] f(x) = -0.11(x^2-20x+\frac{400}{4}-\frac{400}{4})+1 = -0.11(x^2-20x+100-100)+1[/tex]

We can distribute -0.11 to the number -100, so we can take it out of the parenthesis, then

[tex] f(x) = -0.11(x^2-20x+100)+1+100*0.11 = -0.11(x^2-20x+100)+1+11 = -0.11(x-10)^2+12[/tex]

So, the highest point in the ball's trajectory is 12 feet.

Answer 2

Answer:

Initial height = 1ft

Heighest height = 12ft

Step-by-step explanation:

In order to solve this problem, we can start by graphing the given height function. This will help us visualize the problem better and even directly finding the answers, since if you graph it correctly, you can directly find the desired values on the graph. (See attached picture)

So, the initical height happens when the x-value is equal to zero (starting point) so all we need to do there is substitute every x for zero so we get:

[tex]f(x)=-0.11x^{2}+2.2x+1[/tex]

[tex]f(0)=-0.11(0)^{2}+2.2(0)+1[/tex]

which yields:

[tex]f(0)=1 [/tex]

so the height of the ball when it is kicked is 1 ft.

In order to find the highest point of the ball in the air, we must determine the x-value where this will happen and that can be found by calculating the vertex of the parabola. (see the graph)

the vertex is found by using the following formula:

[tex]x=-\frac{b}{2a}[/tex]

in order to find "a" and "b" we must compare the given function with the standard form of a quadratic function:

[tex]f(x)=ax^{2}+bx+c[/tex]

[tex]f(x)=-0.11x^{2}+2.2x+1[/tex]

so:

a=-0.11

b=2.2

c=1

so the vertex formula will be:

[tex]x=-\frac{b}{2a}[/tex]

[tex]x=-\frac{2.2}{2(-0.11)}[/tex]

so we get that the highest point will happen when x=10ft

so the highest point will be:

[tex]f(10)=-0.11(10)^{2}+2.2(10)+1[/tex]

f(10)=12ft

so the highes point of the ball in the air will be (10,12) which means that the highest the ball will get is 12 ft.

The Position Of A Ball After It Is Kicked Can Be Determined By Using The Function F Left Parenthesis

Related Questions

I need help please help

Answers

Answer:

a) 60 times

b) 0.24

c) 150 times

Step-by-step explanation:

A rectangle is sometimes, always, never similar to another rectangle

Answers

Two rectangles can be similar, but that's not always guaranteed.

In fact, similar shapes have the same angles and correspondant sides in proportion.

All rectangles will always have four right angles, so we only have to worry about the sides.

Let [tex]a,b[/tex] be the sides of a rectangle, with [tex]a\leq b[/tex]. Let [tex]c,d[/tex] be the sides of a rectangle, with [tex]c\leq d[/tex].

Then, the two rectangles are similar if and only if

[tex]a\div c=b\div d[/tex]

So, for examples, a rectangle with dimensions 3 and 7 is similar to a rectangle with sides 6 and 14 (both sides have been doubled), but it's not similar to a rectangle with sides 6 and 21 (one side has been doubled, the other has been tripled).

Place parentheses around one operation and two numbers to make this equation true. Then solve it, showing all of your steps. 64 - 8 + 12 x 2 + 9 = 188

Answers

Answer:

64 - 8 + 12 x (2 + 9) = 188

Step-by-step explanation:

64 - 8 + 12 x 2 + 9 = 188

Putting parentheses around two numbers and one operation:

64 - 8 + 12 x (2 + 9) = 188

Following the BODMAS principle

Solving the bracket or parentheses first

(2 + 9) = 11

64 - 8 + 12 × 11

Then multiplication:

12 × 11 = 132

64 - 8 + 132

Then addition:

-8 + 132 = 124

64 + 124 = 188

Hence the proof

The owner of a car wash combines x gallons of a 2% liquid soap and 98% water mix with y gallons of a 7% liquid soap and 93% water mix to make 500 gallons of a 5% liquid soap and 95% water mix. Write a system of linear equations that represent the situation.

Answers

X(2+98) + y(7+93)= 500(5+95)

Not sure if it’s right or not!!!

Chuck says that he can draw a cylinder on his polyhedron poster because it has a pair of base that are congruent.Is chuck correct?Explain your reosining.

Answers

Answer:

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

Please have a look at the attached photo.  

My answer:

1. Chuck wants to draw three-dimensional figures whose lateral faces are rectangles. He says he can draw prisms and pyramids. Do you agree

No, I do not agree because:

The lateral faces of a pyramid are triangles The lateral faces of a prism are rectangles

2. Part B. Chuck says that he can draw a cylinder on his polyhedron poster because it has a pair of bases that are congruent.

No, do not agree because:

A  cylinder has two congruent bases but it is not a  polyhedron while a cylinder has a curved surface when a polyheron has faces that are polygons

Hope it will find you well.

What is the value of x in the equation 3-2x=-1.5x?
оооо
-6

Answers

Answer:

x=6

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

x = 6

Step-by-step explanation:

In this equation, we are told to solve for the value of x. Thus, we must isolate the variable x (poor x... we're always trying to isolate it).

3 - 2x = -1.5x

(I'm going to swap sides to make it easier for me to solve. This doesn't change anything mathematically due to the associative laws. It's purely cosmetic.)

-1.5x = 3 - 2x

First, we can add 2x to both sides of the equation to get all algebraic expressions containing the variable x on one side of the equation alone.

0.5x = 3

For our next part here, let's convert 0.5 to a fraction to make life easier for us.

[tex]\frac{1}{2}[/tex]x = 3

When isolating x in this, we are trying to get rid of 1/2. How can we do this? We can multiply is by 2!

[tex]\frac{1}{2}[/tex]x · [tex]\frac{2}{1}[/tex] = 1x (or simply x)

What we do to one side we must do to another.

x = 3 · 2

x = 6

Our answer is x = 6. Woo!

please help i will mark brainly !

Answers

Answer:

1 hour and 20 minutes

Step-by-step explanation:

Answer:

Total time taken by Natalie to reach the airport is 1 hour and 20 minutes

The height of a cone is twice the radius of its base.
What expression represents the volume of the cone, in
cubic units?
orx?
2/3 pi x ^3
4/3 pi x ^2
2 pi x^3
4 pi x ^3

Answers

Answer:

This first expression is correct

V= 2/3*pi*r³

Step-by-step explanation:

This problem bothers on the volume of a cone

We know that the volume of a cone is expressed as

V= 1/3πr²h

Given that h= 2r

Let us substitute h=2r in the formula above

V= 1/3πr²*2r

V= 2/3πr³

The Answer Is:

2/3pix^3

Elimination method using multiplication
1. x+3y=6 and x+2y=5
2. 3x-y=2 and x+2y=3
3. 4x X 5y=6 and 6x-7y=-20
4. 4x+2y=8 and 16x-y=14

Answers

Answer:

1. x=3, y=1

2. x=1, y= 1

3.( i dont know what the first expression means, are you multiplying 4x and 5y or adding it?)

4. x=1 , y=2

Step-by-step explanation:

This is simple simultaneous equations. You need to eliminate one element in each of the two equations, either y or x and the calculate for the other value.

Which angle is coterminal to 2pi/3

Answers

the correct answer is -4π/3.

PLEASE HELP !!! ASAP

Answers

11.88x=172.26
11.88x/11.88=172.26/11.88
X=14.5
To the nearest tenth
X=15
She has to work 15 hours to pay for the new scooter

Can you plz answer question on the screenshot?

Answers

Answer:

Step-by-step explanation:

Please help I will give Brainliest please. Just tell what I need to do or solve I need help ASAP *image*

Answers

Answer:

Step-by-step explanation:

Hard to figure out huh

Use the correct inverse trig function to find the missing angle, round to the nearest whole number.
15
?
31

Answers

Answer:

61 degrees is the missing angle measure

Step-by-step explanation:

[tex]cos^{-1} (\frac{15}{31})[/tex]     Use this equation to find the missing angle

61 degrees is the missing angle measure

If this asnwer is correct, please make me Brainliest!

What integer represents a drop in temperature of 12°

Answers

Answer:

Integer; - 12

Step-by-step explanation:

If we are considering a situation were there is a drop in temperature, this integer representation would contain a negative;

At the same time the temperature drops by 12 degrees ( ° ) such that this integer is;

Answer; - 12

helppppppppppppppp meeeeeee

Answers

1x1x1.  That's pretty much the definition of

Answer: 1 cubic foot, last choice

A factory sells backpacks for $40.00 each. The cost to make 1 backpack is $10.00. In addition to the cost of making backpacks, the factory has operating expenses of $12,000 per week. The factory’s goal is to make a profit of at least $9,800 per week. Which inequality represents the number of backpacks, x, that need to be sold each week for the factory to meet this goal?

Answers

Answer:

300 Backpacks each week]

Step-by-step explanation:

dont have an explanation srry but the answer is totally 300 backpacks a week

Answer:

30

Step-by-step explanation:

The table represents the equation y=8x what y-value is missing from the table

Answers

Answer:

Step-by-step explanation:

There must be an attachment. I have no knowledge of what to solve for, unless you can tell or show me the missing pieces.

Answer: 1, 3 , 5, and 6

I took the test have a great day!

             

which one would you choose and please explain why

Answers

I’d choose the larger down payment because then you know that you’re going to get your car more quickly paid off and more efficiently
larger down payment so the monthly fees aren’t as much

Pythagorean theorem :

There’s no diagram or anything. You can just make a triangle ? :)
Looking for A
A= ?

Answers

The correct answer is 4.

A sphere has a radius of 6. Using 3.14 for pi, what is the volume?

Answers

Answer:

v= 904.78

Step-by-step explanation:

Answer:

904.77868423386 feet^3

Step-by-step explanation:

Step one the formula is 4/3 Pie R ^3

Step two you do 4/3 x PI x 6^3

Step three do exponents first so 6x6x6=216

Step four multiply 4/3 x 3.14 which equals 4.187

Step four finally you are going to multiply 216 by 4.187 to get   904.77868423386 feet^3

I need this done please help in the picture

Answers

Answer

7.85

but I not sure JutMon21 know the problem

Answer:

I got 7.85

Step-by-step explanation:

First, I took the center angle which is 90 degrees in this case and divided by 360 and I got 0.25 Then, I multiplied that number by the radius which is 5 and I got 1.25. After that I multiplied 1.25 with 2π and the final answer that I got is 7.85

ZB=
Round your answer to the nearest hundredth.
С
2
А
3
?
B

Answers

Answer:

B = 41.81

Step-by-step explanation:

sin B = opposite/ hyp

sin B = 2/3

Take the inverse sin of each side

sin ^-1 sin (B) =sin ^-1 (2/3)

B =41.8103149

To the nearest hundredth

B = 41.81

Monica's family is thinking about going on a vacation. They are debating about whether
to go to Florida, Italy Mexico, or England. They are also trying to decide whether to go for
1 or 2 weeks. List the sample space (all of the possible outcomes) for their vacation
Destination
Vacation
Florida, Italy,
Mexico, England
1 week, 2 weeks​

Answers

Answer:

{FL1, FL2, IT1, IT2, ME1, ME2, EN1, EN2}

Step-by-step explanation:

This is each location paired with one week, and each location paired with two weeks.

Answer:

c

Step-by-step explanation:

Caleb’s puppy weighs 2,250 grams. If the puppy weighed 600 grams at his last visit to the veterinarian’s office, what is the percent increase in the puppy’s weight rounded to the nearest whole number? Enter your answer in the box.

Answers

Answer:

[tex]73\%[/tex]

Step-by-step explanation:

Given: Present weight of Caleb’s puppy = 2,250 grams

Puppy weighed 600 grams at his last visit to the veterinarian’s office.

To find: percent increase in the puppy’s weight rounded to the nearest whole number

Solution:

Increase in puppy's weight = 2250 - 600 = 1650 grams

Percent increase in the puppy’s weight =( Increase in puppy's weight/Present weight of Caleb’s puppy) × 100 = [tex]\frac{1650}{2250}(100)=73.33 \%[/tex]

[tex]73.33\%[/tex] is rounded to [tex]73\%[/tex]

What is the slope of the line graphed in the picture

Answers

Answer:

-1

Step-by-step explanation:

Take the two points

(-2,4) and (4,-2)

And we can find the  slope

m = (y2-y1)/(x2-x1)

   = (-2-4)/( 4 - -2)

   =(-2-4)/(4+2)

   = -6/6

   = -1

Find the volume of the pyramid.

Answers

Answer:

200cm³

Step-by-step explanation:

Volume=[tex]\frac{LXBXH}{3}[/tex]

so 10×10×6=600

600÷3=200

Consider these triangles with two known angle
measures.
w
Answer the questions about the triangles.
Which equation can be used to determine the measure
of angle Q?
What is the treasure of angle Y?
48°
48R
What can be concluded about the measure of angle Q
and the measure of angle Y?
86x
86
Р
Y

Answers

Answer:

1. 48 + 86 + + Q = 180

2. 46 degrees

3. They are congruent

Step-by-step explanation:

I just got them right on edg

Angle sum property (In ΔPQR, ∠P + ∠Q + ∠R = 180°) can be used to determine the measure of angle Q.

Using angle sum property, ∠Y = 46°.

It can be concluded that ∠Y = ∠Q.

What is angle sum property?

The angle sum property of a triangle states that the sum of the angles of a triangle is equal to 180º.

In ΔPQR,

∠P + ∠Q + ∠R = 180° (angle sum property)

86 + ∠Q + 48 = 180

∠Q = 180 - 86 - 48 = 46°

In ΔXYZ,

∠X + ∠Y + ∠Z = 180° (angle sum property)

86 + ∠Y + 48 = 180

∠Y = 180 - 86 - 48 = 46°

As visible, ∠Q = ∠Y.

Learn more about angle sum property here

https://brainly.com/question/4316040

#SPJ3

Molly wants to put a fence around an area. The fence will follow the diagram of the triangle shown below. (Look at picture) About how much fencing does Molly need?

Answers

Answer:

Step-by-step explanation:

43feet

Two terms of an arithmetic sequence are $a_{12}=70$a12​=70​ and A sub 30 is equal to 124$a_{30}=124$a30​=124​ . Write an explicit rule for the n$n$n​ th term

Answers

Answer:

Tn = 34+3n

Step-by-step explanation:

The formula for finding the nth term of an arithmetic sequence is expressed as shown;

[tex]Tn = a+(n-1)d[/tex]

a is the first term of the sequence

n is the number of terms

d is the common difference

If T₁₂ = 70 and T₃₀ = 124

T₁₂  = a+(12-1)d = 70

T₁₂  = a+11d = 70... (1)

Similarly;

T₃₀ = a + (30-1)d = 124

T₃₀ = a +29d = 124...(2)

Solving equation 1 and 2 simultaneously to get a and d.

Subtracting 2 from 1 we have;

29d - 11d = 124-70

18d = 54

d = 54/18

d = 3

Substituting d = 3 into equation 1 to get a we have;

a + 11(3) = 70

a + 33 = 70

a = 70-33

a = 37

The explicit rule for the nth term of the sequence can be gotten by substituting the value of a and d into the formula Tn = a+(n-1)d

Tn = 37+(n-1)*3

Tn = 37+3n-3

Tn = 34+3n

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