what is the average rate of change of f(x) = (x + 3)2 − 2

Answers

Answer 1

Answer:

When we have a function f(x), the average rate of change in the interval (a, b) is:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

In this case, we have the function:

f(x) = (x + 3)^2 - 2

(but we do not have the interval, and I couldn't find the complete question online)

So if for example, we have the interval (2, 4)

The average rate of change will be:

[tex]r = \frac{(4 + 3)^2 - 2 - (2 + 3)^2 + 2}{4 - 2} = \frac{24}{2} = 12[/tex]

If instead, we want the rate of change in a differential dx around the value x, we need to differentiate the function (this is way more complex, so I will define some rules first).

Such that the rate of change, in this case, will be:

f'(x) = df/dx

For a function like:

g(x) = x^n + c

g'(x) = n*x^(n - 1)

And for:

h(x) = k( g(x))

h'(x) = k'(g(x))*g'(x)

So here we can write our function as:

f(x) = k(g(x)) = (x + 3)^2 - 2

where:

g(x) = x + 3

k(x) = x^2 - 2

Then:

f'(x) = 2*(x + 3)*1 = 2*x + 6

That is the rate of change as a function of x (but is not an "average" rate of change)


Related Questions

In the number 3,941,608,572, which digit is in the hundred millions place?

Answers

Answer:

9

Step-by-step explanation:

A hundred millions is: 100,000,000

looking at the number the number in the place hundred millions place is 9, so the answer is 9.

Answer:900,000,000

The digit is 9

Step-by-step explanation:

what shapes have 2 pairs of parallel sides? Choose all that arw correct.​

Answers

Answer:

can we see the options please

square, rectangular, rhombus

Please show steps, 100 points and Brainliest
Convert vertex form f(x)=(x+2)^2-25 to factored form.

Answers

Answer:

f(x)=x^2+4x-21

Step-by-step explanation:

Answer:

f(x) = (x + 7)  (x - 3)

Step-by-step explanation:

f(x)=(x+[tex]2)^{2}[/tex]-25

(x + 7) (x - 3) we put the 2 x's because of the (x+2)^2

now the + 7 and - 3, multiply the 2 numbers = -21 then use those 2 in

(x+2)^2 to add for the answer = -25

Which Which value of x makes this equation true? -3x+10=5x-8

value of x makes this equation true? -3x+10=5x-8

Answers

Answer:

9/4

Step-by-step explanation:

-3x+10=5x-8

or, -3x-5x = -8-10

or, -8x=-18

or, 8x=18 (i.e. - is cancelled)

or, x=18/8

i.e. x=9/4

Hence, the value of x is 9/4

Answer:

The value of x is 9/4

Step-by-step explanation:

-3x+ 10 = 5x - 8

Add 3x both side

-3x + 3x + 10 = 5x + 3x - 8

10 = 8x - 8

Now, Add 8 both side

10 + 8 = 8x - 8 + 8

18 = 8x

8x = 18

Now, Divide by 8 from both side

8x/8 = 18/8

x = 9/4

Thus, The value of x is 9/4

FOR VERIFICATION ONLY:

-3x + 10 = 5x - 8

-3(9/4) + 10 = 5(9/4) - 8

-27/4 + 10 = 45/4 - 8

-27 + 4 × 10/4 = 45 - 8 × 4/4

-27 + 40/4 = 45 - 32/4

13/4 = 13/4

Hence, L.HS = R.H.S

-TheUnknownScientist

I need the answer fast pls

Answers

Answer:

B

Step-by-step explanation:

It's B because that's the only answer that talks about the highest temperature, which is mentioned in the question

The answer is B




Hope this helps

Find the measure of angle AGE in the figure below. Enter only
the number.

Answers

Answer:

AGE = 129 degrees

Step-by-step explanation:

Portia has purchased a new aquarium for her fish. It is in the shape of a hexagonal prism. 3a) How much water can Portia’s new aquarium hold? * 1 point a) 166.28 cubic inches b) 790.28 cubic inches c) 956.56 cubic inches d) 3120 cubic inches e) 6240 cubic inches

Answers

Answer:

D. 3120

Step-by-step explanation:

How many sides does a hexagon have? Six. Let's begin our equation with 6. The area of a triangle formula would be: 1/2 bh. And a hexagon is just six triangles put together. Now our equation is: 6 (1/2 bh) What's bh then? B (base)= 8in. The base is usually always at the bottom. Now we take 10 and add it into the equation. Next we would multiply this by 13. Our equation is now: 6(1/2*8*10)*13. What do you get then? 3120.

For Part B:  Portia's new fish require complete darkness for 12 hours a day. Rather than buying a blackout curtain for her room, she decides to make an aquarium cover out of a tropical print, with a blackout liner. How much tropical print fabric will she need to purchase in order to cover the top and sides of the aquarium?

Now, we're dealing with surface area. What is surface area, anyway? Surface area is the sum of all faces. There are 2 hexagonal faces and 6 sides.

What is 6*1/2 *8? 24! Now what's 10*24? That's right, 240!

8*13=104

6(104)=624

624+240=864

Please solve!
l = 48.1 m, w = 51.62 m, h = 3.42 m

Answers

Answer:

Volume? Surface area?

Step-by-step explanation:

Volume=8491.59

Surface area=5647.93

solve this: - 6 n = 30​

Answers

Answer:

-6n=30

so find value of n

n=30÷(-6)

n=-5

so, value of n = -5

Answer:

-6 n = 30

or,n=30÷(-6)

or,n=-5

12. Which statement best describes the effects on the graph of f(x) = log2 xwhen f(x) is replaced by
f(x-2) + 1?
a. The graph is vertically stretched by a factor of 3, horizontally translated 2 units right, and
vertically translated 1 unit up.
b. The graph is vertically compressed by a factor of 3, horizontally translated 2 units right, and
vertically translated 1 unit up.
c. The graph is horizontally stretched by a factor of 3, horizontally translated 2 units left, and
vertically translated 1 unit up
d. The graph is vertically compressed by a factor of , vertically translated 2 units down, and
horizontally translated 1 unit left.

Answers

Answer:

B.

Step-by-step explanation:

Hope it helps thx

#CARRYONLEARNING!

Does anyone know how to
Solve this

Answers

Answer:

53.4 cm^2

Step-by-step explanation:

rhombus's have the same formula as a square (B*H)

8.9*6 = 53.4 cm^2

5) Find the measure of the unknown
angle in the triangle
O 100°
O 105
106
0 112
PLEASE HELP

Answers

105 degree , I think but not sure
106
explanation: triangles add up to 180 degrees. in the triangle above, the angles only add up to 74. 180-74=106

Arianna earns $15 for doing yard work for 3 hours. If Arianna charges at the same rate, how many hours will it take her to
earn $35? hours

Answers

Answer:

7 hours

Step-by-step explanation:

15 dollars +15 dollars 30 dollars=2 hours. 5 dollars left 15 divided by 3, 5 dollars. 3 divided by 3 = 1 so 1 hours is 5 dollars. My explaining is not good.

Answer: 7 hours

Step-by-step explanation:

She earns 5 dollars per hour because 5x3=15

and then you do 15x2=30

then 3x2=6

then just add 1 to 6

6+1=7

so there's your answer

7 hours

solve these equations, show all your work x/2=20

Answers

Answer:

x = 40

Step-by-step explanation:

x/2 = 20

x/2(2) = 20(2)

x = 40

Enter the value for x that makes the equation √x-7=-4

Answers

Answer:

Your answer is 9

Step-by-step explanation:

√9=3

3-7=-4

Determine the rate of change of the function given by the table.
A) 2
B) 1
C) -1
D) -2

Answers

Hi! The answer is A.
All i did was

5-3=2
6-4=2
7-5=2
8-6=2

They all equal to 2 so the answer is 2 :)

A bag contains 10 marbles: 2 are green, 2 are red, and 6 are blue. Yolanda chooses a marble at random, and without putting it back, choose another one at random. What is the probability that both marbles she chooses are green? Write your answer as fraction in simplest form.

Answers

Answer:

2/10 = 1/5

Step-by-step explanation:

help please i cant do this LOL

Answers

Answer and Step-by-step explanation:

Answer is in picture.

First you need to translate (or move) to the right 1 unit, the translate (or move) downwards 5 units.

Then, reflect the points over the y-axis (reflecting is like when you see your reflection in a mirror, how your hand lines up with the hand in the mirror)

#teamtrees #PAW (Plant And Water)

¿Existen o no existen los números?.

Answers

si existen pero que tipo de números? porque si existen

Paula needs to replace the floor in her family room since her cat peed in several places. She wants to put down both vinyl flooring and carpet in the room. The carpet she selected costs $2 per sq. foot. The vinyl floor covering costs $1 per sq. foot. She has $500 to spend on materials and must cover an area of 300 sq. feet. How much carpet and vinyl flooring will she buy to meet her requirements?

Answers

Answer:

c = amount of carpet flooring; v = amount of vinyl flooring2c + 1v = $500v = 100 sq. ft.c + v = 300c = 200 sq. ft.

Step-by-step explanation:

the anwser

Rob can complete his bus route in 4 hours. Joan can complete her bus route in 3 hours. If they both left the terminal at 3:00 am and after each completed route returned to the terminal, determine the next time they would leave the terminal at the same time.

Answers

Answer:

3:00 pm

Step-by-step explanation:

Given

[tex]Rob = 4\ hrs[/tex]

[tex]Joan = 3\ hrs[/tex]

[tex]Start\ Time = 3:00\ am[/tex]

Required

The next time they leave at the same time

To do this, we first list out the multiples of 4 and 3 (i.e. their time of completing each route)

So, we have:

[tex]Rob: 4, 8, 12, 16, 20...[/tex]

[tex]Joan: 3,6,9,12,15,18....[/tex]

The least common multiple in the above is:

[tex]Least = 12hrs[/tex]

This means that they will meet at the terminal after 12 hours

So, their meeting time is:

[tex]Time = 3:00am + 12\ hrs[/tex]

[tex]Time = 3:00\ pm[/tex]

The length of one rectangle in a quilt is 6 inches. Its width is 3 inches. About how many of these rectangles do you need to cover an area of 7,500 square inches?

Answers

Step-by-step explanation:

Area=2(L+W)

A=2(6+3)

A=2(9)

A=18in²

therefore, 7500/18

=416.66in²

What is the correct ratio?

Answers

D)32/40

Hope it helps you

Answer:

[tex]\frac{24}{40}[/tex]

Step-by-step explanation:

Sin = [tex]\frac{opposite}{hypotenuse}[/tex] (relative to the angle asked for)

The opposite of Angle Z is 24

The hypotenuse no matter what would always be 40; therefore,

Sin(Z) = [tex]\frac{24}{40}[/tex]

Hope this helps!

please help this is overdue and i get my grades tmr

Answers

Answer:

162 sq

Step-by-step explanation:

6 x 9 x 3 = 162

unless im wrong :/

Answer:

The surface area is 198 square centimeters.

Step-by-step explanation:

A = 2 · (wl + hl + hw)

2 · (6 · 9 + 3 · 9 + 3 · 6)

198

An account is compounded continuously at 4.5% interest. What was the initial amount deposited if after 8 years it is worth $1720?

Answers

9514 1404 393

Answer:

  $1200.00

Step-by-step explanation:

The balance is given by the formula ...

  A = Pe^(rt) . . . . . principal P invested at annual rate r for t years

Using your numbers, we can find P to be ...

  P = Ae^(-rt) = $1720·e^(-0.045·8) = $1720·e^-0.36

  P ≈ $1200.00

Find the volume of the pyramid. v=

Answers

Answer:

240 mi^3

Step-by-step explanation:

Base area = length x width = 10 x 8 = 80 mi^2

V = (base area x height)/3 = (80 x 9)/3 = 240 mi^3

find 11/25 of a liter

Answers

Answer:

0.44l

Step-by-step explanation:

a litre=1l

11/25 of it=11/25×1l

=0.44l

Answer:

A litre=1 l

Or, 1/25×1

=0.44.

if x=-4 and y=3 what is the value of x-3y^2

a: -13
b: -31
c: -23
d: -85​

Answers

Answer:

b -31

Step-by-step explanation:

Step-by-step explanation:

x-3y²4-3×3²4-27-23

hope it helps

stay safe healthy and happy..

Solve for x.
4x - 14
x + 85
x = [?]

Answers

Answer:

x = 33

Step-by-step explanation:

4x - 14  = x + 85

3x = 99

x = 99/3

x = 33

In the following table y is proportional to x.



What is the constant of proportionality?


A. 5/14


B. 5/7


C. 7/5


D.20/7

Answers

D there’s a 20 and a 20 is missing
D ggccccccccccvccccccccc
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