Cubic equation that has been transformed from the parent function with a vertical compression, reflected over the y-axis and shifted up.

Answers

Answer 1

Question is incomplete

Answer:

See Explanation

Step-by-step explanation:

Let the cubic function be

[tex]f(x) = (x,y)[/tex]

First transformation: Vertical compression

Let the scale factor be a where [tex]0 < |a| < 1[/tex]

The new function becomes:

[tex]f'(x) = (x,ay)[/tex]

Next: Reflection over y-axis

The rule is: [tex](x,y)=>(-x,y)[/tex]

The new function becomes:

[tex]f"(x) = (-x,ay)[/tex]

Lastly: Shifted up

Let the units up be b

The rule is: [tex](x,y)=>(x,y+b)[/tex]

So, the new function becomes:

[tex]f"'(x) = (-x,ay+b)[/tex]

Using the rules states above, assume the cubic function is:

[tex]f(x) = x^3[/tex]

Vertical compress [tex]f(x) = x^3[/tex] by [tex]\frac{1}{2}[/tex]

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

Reflect [tex]f'(x) = \frac{1}{2}x^3[/tex] over y-axis

Rule: [tex]f"(x)= f'(-x)[/tex]

Solving f'(-x)

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

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

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

So:

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

Lastly: Shift [tex]f"(x) = -\frac{1}{2}x^3[/tex] by 3

Rule: [tex](x,y)=>(x,y+b)[/tex]

[tex]f'"(x) = f"(x + 3)[/tex]

Solving: f"(x + 3)

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

Substitute x + 3 for x

[tex]f"(x + 3) = -\frac{1}{2}(x + 3)^3[/tex]

So:

[tex]f'"(x) = f"(x + 3)[/tex]

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


Related Questions

Need help with this;

Answers

Answer:

See below

Step-by-step explanation:

Deposit amount P = $4200Interest rate r = 3 1/2% = 3.5% = 0.035 PA compounded semiannuallyCompound n = 2 per year

Calculations as per following questions

a. I = $4200*(0.035/2) = $73.5b. A = $4200 + $73.5 = $4273.5c. I = $4273.5*(0.035/2) = $74.79d. A = $4273.5 + $74.79 = $4348.29e. I = $4348.29 - $4200 = $148.29f. I = $4200*0.035 = $147

2) Find the median.
4,9, 1, 4, 6, 2, 3,1
A) 1 and 4
B) 3.5
C) 3.75
D) 8
pls help me show work

Answers

Answer:

3.5

Step-by-step explanation:

1-List the numbers from least to greatest

1, 1, 2, 3, 4, 4, 6, 9

2- Then cross off a number from each side unitl you ar with 3 and 4 in the middle.

3- Add 3+4 Together

7

4- Divide by two

3.5

Each of 7 students reported the number of movies they saw in the past year. Here is what they reported.
17, 7, 13, 17, 7, 9, 10
Find the mean number of movies that the students saw.
If necessary, round your answer to the nearest tenth.

Answers

Answer:

11

Step-by-step explanation:

Answer:

11.4  (This is already rounded to the nearest tenth)

Step-by-step explanation

1.) Add all of them

17+7+13+17+7+9+10=80

2.) Divide the sum by how many numbers there are

In this case, there are 7, so 80/7 is 11.42...

3.) Get the answer

80.7 simplifies into 11.42 so rounded to the nearest 10th is 11.4.

Hope this helped. Good luck on your homework!

Find the area of the figure

Answers

Answer: its either 2.5 or 16

Step-by-step explanation: hope this is helpful I don't know if these answers are right...

8.94427191 rounded to the neareast 10th

Answers

Answer:

8.9

Step-by-step explanation:

Answer:

the answer will be 8.9 if im not wrong

Area of composite shapes!!
Find the area
Its geometry
Due Tomorrow
Plz HURRY
Offering brainliest

Answers

Answer:

8/2=4

4*6=24

10*8=80

80+24=104

104

Find m Please let me know if you could help me, with any more questions. I’m struggling in geometry. I wanna get back to doing sports again!

Answers

9514 1404 393

Answer:

  ∠C = 48°

Step-by-step explanation:

The two triangles are congruent by ASA. (The common side BD is between the angles marked congruent.) This means angles A and C have the same measure.

Angle A plus the two given angles will total 180°.

  ∠A = 180° -70° -62° = 48°

  ∠A = ∠C = 48°

Answer:

c=48°

Step-by-step explanation:

...............

Convert 121

5

to mixed fraction.​

Answers

Answer:

24 1/5

Step-by-step explanation:

I'm not sure if u meant 121/5 but I converted it and it's 24 as a whole number and 1/5 for the fraction

24 1/5

Which of the following tables represent exponential functions?

Answers

The top left table is the right answer

Answer:

Step-by-step explanation:

it is the top 2

Sandy pays $120 for 4 violin lessons. How much does she pay for 8 violin lessons?

Answers

Answer:

$240

Step-by-step explanation:

120x2

Answer:

240

Step-by-step explanation:

120x2= 240

or

120+120=240

Anil scored 30 runs in the first innings of a test match. His score changed by +30 runs in the second innings. What was his score in the second innings?

Answers

Answer:

60 runs

Step-by-step explanation:

Given that:

Score in first innings = 30 runs

Change in score during second inning = + 30

The score in the second inning will be :

Score in first inning + change in score during second inning

30 + (+30)

30 + 30

= 60 runs

Andy buys shoes that are on sale for 25% off the regular price. If the sale price is $36.45, what was the regular price of the shoes to the nearest cent?​

Answers

She bought the shoe at a percent of 25

5.
Find the rate of change for the situation. You run 3 miles in one hour and 6 miles in two hours.


A. 3 miles

B. 3 miles per hour

C. 2 hours

D. 2 miles per hour

Answers

Answer:

c

Step-by-step explanation:

c

The momentum of a variable is represented by the rate of change. The rate of change for the situation is 3 miles per hour.

What is the rate of change?

The momentum of a variable is represented by the rate of change, which is used to quantitatively express the percentage change in value over a specific period of time.

Given the distance covered in one hour is 3 miles, while the distance covered in 2 hours is 6 miles. In the given case, the rate of change for the situation, therefore,

Rate of change = (6miles-3miles)/(2hours-1hour) = 3miles/hour.

Hence, the rate of change for the situation is 3 miles per hour.

Learn more about Rate of Change:

https://brainly.com/question/12786410

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A number q divided by 5 is 8

Answers

Answer:

q = 40

Step-by-step explanation:

[tex]\frac{q}{5} = 8[/tex]

multiply 5 on boths sides:

[tex]\frac{q}{5} x 5 = 8 x 5[/tex]

q = 40

to check:

[tex]\frac{40}{5}[/tex] = 8

Answer:

q = 40

Step-by-step explanation:

5,10,15,20,25,30,35,40

1   2  3   4   5    6   7    8

While shopping at a clearance sale, Samantha finds a $60.00 dress on sale for 25% off. Samantha also has a 50% off
coupon. Which statement correctly summarizes her savings?

Answers

It seems most likely that ...

... Samantha will save $37.50 because she must first find the 25% sale price before taking the extra 50% reduction

_____

In the real world, it seems probable that Samantha will be offered the choice of using the coupon or the sale discount. If she chooses tht 50% coupon, her savings will be $30. If she chooses the marked sale discount, her savings will be $15.

The scenario above assumes she gets 50% off the sale price of $45, so saves $15+22.50 = $37.50 off the original price.

Answer:

The answer is B. (Samantha will save $37.50 because she must first find the 25% sale price before taking the extra 50% reduction.)

Step-by-step explanation:

I just took the test! Gl<3

does anyone know the answer?

Answers

Square root of a perfect square

Major arc CBD measures 300 degrees. Which is the radian measure of its corresponding central angle? O 4 pie/3 O 5 pie/6 O 5 pie/3 O 11 pie/6

Answers

Answer:

[tex]\dfrac{5\pi}{3}[/tex]

Step-by-step explanation:

Given that,

Major arc CBD measures 300 degrees.

We need to find the radian measure of its corresponding central angle.

Radian measure is given by :

[tex]R=\dfrac{\pi}{180}\times d\\\\R=\dfrac{\pi}{180}\times 300\\\\R=\dfrac{5\pi}{3}[/tex]

So, the radian measure is [tex]\dfrac{5\pi}{3}[/tex].

is 10y - 4 equivalent to 2 (5y - 2)?
Apply the distributive property to 2(5y - 2).
2 (5y - 2) = 10y - ____ Please answer!! Fast!!

Answers

Answer:

Yes, it is equal10y - 4

Step-by-step explanation:

Yes, it is equal

2 (5y - 2) =

2 x 5y - 2 x 2 -

10y -4

Hope that helps!

Last week, Thomas ran 5 1/4 miles. This week, he planes to run 1/2 as far as he ran last week. How many miles does Thomas plan to run this week?

Answers

Answer:

2.625

Step-by-step explanation:

Last week Thomas ran 5 1/4 miles

This week he plans to run 1/2 miles as far

Therefore the number of miles he plans to run cann be calculated as follows

= 5 1/4 × 1/2

= 21/4 × 1/2

= 21/8

= 2.625

Hence Thomas plans to run 2.625 miles

A bank's electronic management system lacks the ability to protect a client's confidential information. To what type of risk does this expose the client?

market risk
security risk
operational risk
credit risk

Answers

Operational Risk Hope this helps

What is the location of point G, which partitions the directed line segment from D to F into a 5:4 ratio?
D
+
4
F
Sus
7
+
3
+
8
+
9
5
-2
1
0
1
2.
3
4
5
6
10
-1
0
2.
3

Answers

Answer:

2

Step-by-step explanation:

The location of point G  which partitions the directed line segment from D to F into a 5:4 ratio is; x = 3

Division of a Line Segment

The formula for coordinate of a point that divides a line segment in a ration is given by;

x = (mx₂ + nx₁)/(m + n)

We are given the ratio 5:4

Thus m = 5 and n = 4

The endpoints of DF are D(-2) and F(7)

Thus;

x = ((5*7) + 4(-2))/(5 + 4)

x = 27/9

x = 3

Thus, the location of point G  which partitions the directed line segment from D to F into a 5:4 ratio is x = 3

Read more on division of a line segment at; https://brainly.com/question/8009114

Find the perimeter of the rectangle in yards.

Answers

The perimeter is 288 yards

Elizabeth invests $7567 in a savings account with a fixed annual interest rate of 5% compounded quarterly. What will the account balance be after 7 years?

Answers

Answer:

FV= $10,714.81

Step-by-step explanation:

Giving the following information:

Initial investment= $7,567

Number of periods= 7*4 = 28 quarters

Interest rate= 0.05/4= 0.0125

To calculate the future value, we need to use the following formula:

FV= PV*(1+i)^n

FV= 7,567*(1.0125^28)

FV= $10,714.81

Question 13 (5 points)
Keith has $75 from a saved allowance. He needs at least $135 for a new pair of
sneakers. Keith needs no less than more to buy the sneakers.
A) $72
B) $60
O g) 878
D) $56
Question 14 (5 points)

help

Answers

B) $60
keith has $75 he needs at least $135 for his new sneakers so you take $75 and subtract that from $135 and you get $60 .

Ika nilai rata-rata 20 orang murid adalah 7,5. Kemudian, seorang murid menyusul ulangan dan mendapatkan nilai 8. Berapa nilai rata-rata sekarang?

Answers

Answer:

Average grade now = 7.524

Step-by-step explanation:

Given - If the average score of the 20 students is 7.5. Then a student follows the test and gets a grade of 8.

To find - What is your average grade now?

Proof -

Given that,

Average score of 20 students = 7.5

So,

Total value of students = 20 × 7.5 = 150

Now,

Given that, One person added ang his grade is 8

So,

So Total value of 21 students = 150 + 8 = 158

Now,

Average score of 21 students = [tex]\frac{158}{21}[/tex] = 7.5238

∴ we get

Average grade now = 7.524

PLEASE HELP ME NOW!!!! 100 POINTS!!!
Decorative glass balls are being stored in a box. Each ball has a radius of 2 1/3 cm.

How many balls will fit in each layer of a box that is 20 cm by 15 cm?


7 balls

12 balls

48 balls

Answers

Answer: 12 balls i think

Answer:

answer is 12

Step-by-step explanation:

i took the quiz.

Find the missing values in the ratio table. Then write equivalent ratios.
5:3 ?:12 10/3:? ?:5

Answers

Answer:

5 15 10/3 7

3 12 12/3 5

Step-by-step explanation:

The missing values in the ratio table will be;

Pies         5       20      10/3   25/3

Cakes      3       12        2      5

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

The ratio table is;

Pies         5       x      10/3   z

Cakes      3       12     y       5

Now,

Since, The ratios are equivalent to each other.

Thus, We can solve to find the value of x, y and z as;

⇒ 5 : 3 = x : 12

⇒ 5/3 = x/12

Multiply by 12;

⇒ 5 × 12 / 3 = x

⇒ 20 = x

And, 5 : 3 = 10/3 : y

⇒ 5/3 = 10/ (3× y)

⇒ 5/3 = 10/3y

Multiply by 3;

⇒ 5 = 10/y

⇒ y = 10/5

⇒ y = 2

And, 5 : 3 = z : 5

⇒ 5/3 = z/5

Multiply by 5;

⇒ 25/3 = z

⇒ z = 25/3

Therefore, The missing values in the ratio table will be;

Pies         5       20      10/3   25/3

Cakes      3       12        2      5

Learn more about the ratio visit:

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At a birthday party, Vivian counts 15 vanilla ice cream cups and 25 chocolate ice cream cups. Which properties can be used to determine the percent, p, of the ice cream that is chocolate?

Answers

Answer:

62.5 %

Step-by-step explanation:

The percentage, p of the ice cream that is chocolate is p = total number of chocolate ice cream cups/total number of ice cream cups × 100%

Given that there are 25 chocolate ice cream cups and 15 vanilla ice cream cups, total number of ice cream cups  = 25 + 15 = 40

So, p = total number of chocolate ice cream cups/total number of ice cream cups × 100%

p = 25/40 × 100%

p = 25/4 × 10 %

p = 6.25 × 10 %

p = 62.5 %

Ms. Benson is making a jewelry box using 2 identical squares of wood and 4 identical rectangular pieces of wood, as shown below.



What is the surface area of the jewelry box in square inches (sq. in)?

Answers

Length of rectangles = 7 in.

Breadth of 4 rectangles = 3 x 4

                                          = 12 in.

Side of squares = 3 in.

Area of 4 rectangles = length x breadth

                                    = 7 x 12

                              = 84 sq. in.

Area of two squares = 2(side x side)

                                  = 2(3 x 3)

                                  = 18 sq. in.

Therefore, Surface area of the Jewellery box = 84 sq. in. + 18 sq. in.

                                                                              = 102 sq. in.

5. Using the factor tree, What are the prime factors of 36

Answers

Answer:

Step-by-step explanation:

A factor tree is not unique for a given number. Instead of expressing 36 as 2 × 18, we can express 36 as 6 × 6. Prime factorization of 36 using factor tree method is 2 × 2 × 3 × 3 = 2² × 3².

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