6. A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again. If the ball continues to rebound and fall in this manner, find the total distance the ball has travelled after it hits the ground the 5th time. This may be answered in decimal form. Round your answer to 2 decimal places.

Answers

Answer 1

Answer:

The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient of consecutive terms is the same. The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term and [tex]q[/tex] is the common ratio.

A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again.

This means that:

[tex]q = 0.7, a_1 = 25*0.7 = 17.5[/tex]

Then

[tex]a_n = a_1q^{n-1}[/tex]

[tex]a_n = 17.5(0.7)^{n-1}[/tex]

First 5 terms:

[tex]a_1 = 17.5[/tex]

[tex]a_2 = 17.5(0.7)^{2-1} = 12.25[/tex]

[tex]a_3 = 17.5(0.7)^{3-1} = 8.58[/tex]

[tex]a_4 = 17.5(0.7)^{4-1} = 6[/tex]

[tex]a_5 = 17.5(0.7)^{5-1} = 4.2[/tex]

Find the total distance the ball has travelled after it hits the ground the 5th time.

[tex]T = 17.5 + 12.25 + 8.58 + 6 + 4.2 = 48.53[/tex]

The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.


Related Questions

Hiiioo! Can someone please help me out! :)❤️

Answers

Answer:

-2/3

3/2

Step-by-step explanation:

slope is m in the equation y = m*x+b.

3y=-2x-3

y=-2/3x-1

parallel lines have the same slope, so slope of parallel lines is -2/3

perpendicular lines have negative the inverse

so -(-3/2)=3/2

3/2 is the correct answer to your question

Which of the following represents the factorization of the trinomial below?
-3x2 – 18x2 – 24x

Answers

Answer:

-3x(7x+8)

Step-by-step explanation:

-3x^2-18x^2-24x

-3x(x+6x+8)

-3x(7x+8)

Please help ASAP. Differentiating polynomials

Answers

Answer:

Step-by-step explanation:

If the function is

[tex]y=x^2-4x[/tex], then its derivative is

y' = 2x - 4. This is equal to 0 where

2x - 4 = 0 and

2x = 4 so

x = 2. When x = 2 in the original equation:

[tex]y =2^2-4(2)[/tex] so

y = -4. So the coordinate is (2, -4). On to the next one:

If the function is

[tex]y=25x +\frac{1}{x}[/tex] then its derivative is

[tex]y'=25-\frac{1}{x^2}[/tex]. This is equal to 0 where

[tex]25-\frac{1}{x^2}=0[/tex] and

[tex]-\frac{1}{x^2}=-25[/tex] or, in simpler terms:

[tex]\frac{1}{x^2}=\frac{25}{1}[/tex] so

[tex]25x^2=1[/tex] and

[tex]x^2=\frac{1}{25}[/tex] so

x = ±[tex]\sqrt{\frac{1}{25} }[/tex] so

x = [tex]\frac{1}{5},- \frac{1}{5}[/tex]. When you plug those into the original equation, you get the coordinates

[tex](\frac{1}{5},10)[/tex] and [tex](-\frac{1}{5},-10)[/tex]

HELP PLEASEEEE !!!!!

Answers

Answer:

5%

Step-by-step explanation:

5 customers ordered large cold drinks so the probability would be 5/100

To convert 5/100 to percent, just do 5/100 x 100%

If f(x) = x^2 + 1 find f (a+1)

Answers

Answer:

f(a + 1) = a² + 2a + 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/CoefficientsFunctionsFunction NotationExpand by FOIL

Step-by-step explanation:

Step 1: Define

Identify

f(x) = x² + 1

Step 2: Evaluate

Substitute in x [Function f(x)]:                                                                           f(a + 1) = (a + 1)² + 1Expand [FOIL]:                                                                                                  f(a + 1) = a² + 2a + 1 + 1Combine like terms:                                                                                         f(a + 1) = a² + 2a + 2

Answer:

[tex]{ \tt{f(x) = {x}^{2} + 1 }} \\ { \tt{f(a + 1) = {(a + 1)}^{2} + 1 }} \\ { \tt{f(a + 1) = ( {a}^{2} + 2a + 1) + 1 }} \\ { \tt{f(a + 1) = {a}^{2} + 2a + 2}}[/tex]

What is the area, in square inches, of the shape below?

Answers

Answer:

27.44 in²

Step-by-step explanation:

The formula for area of a triangle is a=[tex]\frac{bh}{2}[/tex], where a is area, b is base length, and h is height.

We can sub in the base and height lengths we know to work out the area. This gives a=[tex]\frac{5.6*9.8}{2}[/tex] or [tex]\frac{54.88}{2}[/tex].

This solves to 27.44 in².

**This content involves area of triangles, which you may wish to revise. If you are required to do this by hand, you may also like to review multiplying and dividing decimals. I'm always happy to help!

Answer: 27.44

Step by step explanation


203 cm
196 cm
Question 1:
The formula to calculate the perimeter of the banner is
(a) 2 (1+ b)
(b) 2xrh + 2A
(c) a + (21 + b)
(d) 2 (1 + b) + ar​

Answers

Answer:

πr + (2l + b)

Step-by-step explanation:

The figure is a composite figure, consisting of a semicircle and a rectangle :

The perimeter of a rectangle is the sum of the sides ;

Perimeter of semicircle is the 2πr/2 (Circumference / 2)

For the triangle, we take the sum of 3 sides ;

Length + length + breadth = 2l + b

Hence, the perimeter is :

2πr/2 + 2l + b

πr + (2l + b)

I need some help

A rectangular prism with 6 square faces is called

A)square

B)polygon

C)Cube

D)Rhombus

Answers

Answer:

cube

Step-by-step explanation:

prisms are 3d figures just like cubes are

the other options are just 2d figures

[tex]\huge\tt\pink{Answer}[/tex]

C. Cube or Cuboid

A cuboid is a solid that has six rectangular faces--think of a typical box. All faces are either parallel or perpendicular to each other. Further, a cuboid is a right rectangular prism. A cuboid with six square faces is a cube, whereas a cuboid with at least two square faces is known as a square cuboid.

х
3
3(x+4) represents the area of the rectangle above. Which expression below is equivalent by the Distributive Property?
O 3x+12
O (3 + x) +4
O (x + 4) - 3
O 3x + 4

Answers

Answer:

O 3x+12

Step-by-step explanation:

3(x + 4) = (3 · x) + (3 · 4)

= 3x + 12

Answer O 3x+12
Hope this helps

What portion of shared $7500 security costs should be apportioned to store A?

Answers

Answer:

3,750

Step-by-step explanation:

2500+1250+625+625=5000

2500/5000=.50 or 50%

7500X.50=3750

Calculate the following:

5 +0,3 +0,04 + 0,008 in steps ​

Answers

Answer:

5.348

Step-by-step explanation:

5 + 0.3 + 0.04 + 0.008

If you find this difficult to calculate put zeroes in Hundredths place and thousandths place

=> 5.000 + 0.300 + 0.040 + 0.008

=>5.348

What is the volume of the cube below?

Answers

Answer:

D. 9h

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Geometry

Volume of a Cuboid Formula: V = a²h

a is the sides of the cubeh is the height

Step-by-step explanation:

Step 1: Define

Identify variables

a = 3

h = h

Step 2: Find Volume

Substitute in variables [Volume of a Cuboid Formula]:                                 V = 3²hEvaluate exponents:                                                                                         V = 9h

Answer:

D. 9h

Step-by-step explanation:

Volume of a cube = Length × Width× Height

= 3×3×h

= 9h

Sam had $42 to spend on 12 raffle tickets. After buying them he had $6 left. How much did each raffle ticket cost?

Answers

Answer:

Each raffle ticket cost $3.

No files just type it in please and thank you

Answers

9 is being added together 5 times, which is equal to the expression 9 x 5. The answer is A, 9 x 5

Answer:

The answer is A - 5×9 I think so..

find the derivative of the following function, with a positive index (differentiation)
pls help there’s a picture

Answers

Answer:

2nd option

Step-by-step explanation:

Using the power rule

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]

Given

f(x) = [tex]\frac{3}{2\sqrt[3]{x} }[/tex] = [tex]\frac{3}{2x^{\frac{1}{3} } }[/tex] = [tex]\frac{3}{2}[/tex] [tex]x^{-\frac{1}{3} }[/tex] , then

f'(x) = - [tex]\frac{1}{3}[/tex] × [tex]\frac{3}{2}[/tex] [tex]x^{-\frac{4}{3} }[/tex]

      = - [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{x^{\frac{4}{3} } }[/tex]

      = - [tex]\frac{1}{2x^{\frac{4}{3} } }[/tex] = - [tex]\frac{1}{2\sqrt[3]{x^4} }[/tex] [ Note there should be a leading negative ]

−5x+2y=9
y=7x


solve the system of equation

Answers

Here to solve the equation we need to plug in the value y as given. -5x+2(7x)=9. -5x+14x=9. 9x=9. X=1.

what is the equation of the red graph? g(x)=? A. g(x)=-x^2 B. g(x)=x^2 C. g(x)=(4-x)^2 D. g(x)=(8-x)^2

Answers

the answer of course is bobbies

Answer

the answer if b in the above

what is the answer to 7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8)

Answers

Answer:

m=-2

Step-by-step explanation:

A factory makes orange paint by mixing red paint and yellow paint in the ratio 7:2. The factory makes 2700 litres of orange paint every day. How many litres of yellow paint does the factory use every day?

Answers

Answer:

2700÷9=300

300×2=600liters yellow paint

1, 3, 2, 2, 1, 3, 3, 1

Part A: What is the mean of the data? Show your work. (4 points)

Part B: Use your answer from Part A to calculate the mean absolute deviation for the data. Show your work. (6 points)

Answers

Answer:

(I only know part A. sorry) The mean is 2.

Step-by-step explanation:

To find the mean of data you have to add all of the numbers and then divide by the total number of numbers being added. (I hope that made sense)

So you have to do- 1+3+2+2+1+3+3+1=16 -and then- 16÷8=2 -so you're answer is 2.

The area of a rectangular painting is 5049 cm. If the width of the painting is 51 cm, what is its
length?

Answers

Answer:

The length is 99 centimeters.

Step-by-step explanation:

The area of a rectangle is found by multiplying:

A = Length • width

We also know that the area of the rectangular painting is 5,049 cm^2

An equation to represent this is:

51w = 5049

To find w, divide:

5049/51 = 99

CHECK YOUR ANSWER:

Formula tor area of a rectangle:

Length x width

Use formula with the measurements:

99 x 52 = 5049

So the length is 99 centimeters.

HOPE THIS HELPS!

Which statement is NOT true concerning the graphing of a linear system?
------------------------------------------------------------------------------------------------------------------------------
Systems of linear equations that contain coordinates with fractions or decimals can be challenging.

You need to be careful and plot straight lines.

You can only graph a system of linear equations with a graphing calculator.

The point of intersection of lines that intersect at a shallow angle is difficult to determine.

Answers

You can only graph a system of linear equations.

Find the area of the circle. Round your answer to two decimal places, if necessary.​

Answers

Answer:

379.94 in.²

Step-by-step explanation:

To find the area of a circle, multiply the radius by itself twice, then multiply the product by pi.

[tex]a=\pi r^2[/tex]

In the image, the diameter is shown.

To find the radius of a circle, divide the diameter by 2.

[tex]22/2=11[/tex]

The radius of this circle is 11 inches.

Next, multiply the radius by itself twice.

[tex]11*11=121[/tex]

Lastly, multiply the product by pi (3.14).

[tex]121*3.14=379.94[/tex]

Therefore, the area of this circle is 379.94 inches squared.

A college had a tuition of $35,000, then increased it by 10%, then decreased it by 5%. What is the new tuition of the college after this increase and decrease?

Answers

Can you help me with the last question write the equation 3x^2 - 27 = -6x in vertex form

Answer:

$36,575 is the new tuition

* please help*
What are the solutions of equation (x — 2)^2 = -3x + 6
Select all that apply.
A X= -3
B. X= -2
C. X= -1
D. x= 3
E. x= 1
F. X= 0
G. X= 2

Answers

Answer:

C and G

Step-by-step explanation:

Given

(x - 2)² = - 3x + 6 ← expand left side using FOIL

x² - 4x + 4 = - 3x + 6 ( subtract - 3x + 6 from both sides )

x² - x - 2 = 0 ← in standard form

(x - 2)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2 → G

x + 1 = 0 ⇒ x = - 1 → C

If this trapezoid is moved through the
translation (x+3, y-2), what will the
coordinates of D' be?
5
B
С
4
3
2
A
D
1
-7 -6 -5 -4
-3 -2
-10
1
2
3
4
D' = ([?], [ ]
-2.

Answers

9514 1404 393

Answer:

  D'(4, 0)

Step-by-step explanation:

  (x, y) ⇒ (x +3, y -2)

  D(1, 2) ⇒ D'(1+3, 2-2) = D'(4, 0)

Find the probability that a randomly
selected point within the circle falls
in the red shaded area.
Ir = 4cm
2.5 cm
3 cm
3 cm
[?]%
Round to the nearest tenth of a percent.

Answers

Answer:

38.8%

Step-by-step explanation:

Area of the triange:

6*6.5*.5= 19.5

Area of the circle:

π*16= 16π

19.5/16π= .387940174

38.8%

Answer:

38.8%

Step-by-step explanation:

Recall that variables represent changing values. In this unit, you will work with
equations that contain two different variables. What types of situations might be
modeled with equations containing two or more variables? If the value of one variable
changes, must the value of the other variable change for the equation to remain true?
How would the number of solutions for an equation with two variables differ from the
number of solutions for an equation with only one? Explain




Answers

Answer:

It depends on the equations and the variables.

Example of an equation in 2 variables with infinitely many solutions:

sin2x - cos2y + cos2x - sin2y = 0

Example of an equation in 1 variable with 2 solutions:

(x - 1)(x - 2) = 0

Example of 2 equations in 2 variables with no solution:

The intersection of the lines given by

y = 3x + 1

y = 3x + 2

Example of an equation in 1 variable with 1 solution:

5x - 4 = 15

Example of an equation in 1 variable with no real solution:

x2 + 49 = 0

We can go on and on with examples like this. The question is way too general.

Step-by-step explanation:

please mark as brainliest

please mark as brainliest

i need help with this asap !!

Answers

Answer:

x^2-2x-13

Step-by-step explanation:

f(x) = 2x-5

g(x) = x^2 -4x-8

f(x) +g(x) = 2x-5 +  x^2 -4x-8

Combine like terms

              = x^2+2x-4x-5-8

               =x^2-2x-13

hope your having a good day!

Answers

Answer:

yes im am gydyd6rrfxjdjsjwjejwhwwehebrhrhhrrhrhrhdhrhehrhehrhrhdhdhdhdhddhdgdgdhr

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