What is the average rate of change of the function over the interval x = 0 to x = 6? f(x) = (2x - 1) / (3x + 5)

Answers

Answer 1

Answer:

The average rate of change of the function over the interval x = 0 to x = 6 is [tex]\frac{34}{195}[/tex].

Step-by-step explanation:

Geometrically speaking, the average rate of change ([tex]r[/tex]) of the function over a given interval is determined by equation of secant line, that is:

[tex]r = \frac{f(b)-f(a)}{b-a}[/tex] (1)

Where:

[tex]a[/tex], [tex]b[/tex] - Lower and upper bounds.

[tex]f(a)[/tex], [tex]f(b)[/tex] - Function evaluated at lower and upper bounds.

If we know that [tex]f(x) = \frac{2\cdot x -1 }{3\cdot x + 5}[/tex], [tex]a = 0[/tex] and [tex]b = 6[/tex], then the average rate of change of the function over the interval is:

[tex]f(a) = \frac{2\cdot (0)-1}{3\cdot (0) +5}[/tex]

[tex]f(a) = -\frac{1}{5}[/tex]

[tex]f(b) = \frac{2\cdot (6)-1}{3\cdot (6)+5}[/tex]

[tex]f(b) = \frac{11}{13}[/tex]

[tex]r = \frac{\frac{11}{13}-\left(-\frac{1}{5} \right) }{6-0}[/tex]

[tex]r = \frac{34}{195}[/tex]

The average rate of change of the function over the interval x = 0 to x = 6 is [tex]\frac{34}{195}[/tex].


Related Questions

Solve the question below

Answers

Answer : x is equal to 0 hope that’s correct

Saniya bought a new outfit for the holidays. She paid $15.00 for the shirt, $32.00 for the pants and $75.00 for the shoes. If she had a 30% off coupon, how much was her subtotal?

Answers

Answer:

$99.5

Step-by-step explanation:

Add up all the dollar amounts and subtract 30%

Answer:

Subtotal: $122     Total: $36.60

Step-by-step explanation:

Since you're only looking for the subtotal and not the actually total, you just have to add $15.00 + $32.00 + $75.00 and you should get $122. Although if you were looking for the total then you would have to know what 30% of 122 is and you should get 36.60 as the result so it would cost $36.60

Hope this helps you :D

2(4+9w)=
answer pls
kkkkkk

Answers

Answer:

simplify the expression:

8 + 18w

Step-by-step explanation:

i hope this helps!

Answer: 8 + 18w

Step-by-step explanation: PLs mark me as brainlisti have great day

A line is parallel to y=4x-2 and intersects the point (-1, -2) what is the equation of this parallel line?

Answers

Answer:

y = 4x + 2

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

Grayson is going to invest $710 and leave it in an account for 17 years. Assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for Grayson to end up with $920?

Answers

Answer:

1,3%

Step-by-step explanation:

[tex]x^{20} * 710 = 920\\x^{20} = 1.3\\x = 1.013[/tex]

find minimum value for the perimeter of the rectangle.​

Answers

Answer:

possible lengths

45 and 2

3 and 20

5 and 18

15 and 6

10 and 9  

there perimeter will be

94

46

46

27

38

answer to this question is  15 and 6

3
A robot can complete 5 tasks in hour. Each task takes the same amount of time.
10
a. How long does it take the robot to complete one task?
b. How many tasks can the robot complete in one hour?

Answers

Answer:

a) 12 minutes

b) 5 tasks

Step-by-step explanation:

Eddie has $45. He needs a new bike tire that costs $70. Write and then evaluate a subtraction expression to determine how much more Eddie needs in order to get the bike tire.

Answers

Answer:

70-45=25

70-25=45

Step-by-step explanation:

45+25=70

forty-five plus twenty-five equals seventy because if you ignore the fives and save those for later you will have forty and twenty and forty and twenty makes sixty and then you bring back the fives and add those together and get ten, then you add ten to sixty and you get seventy.  

A teacher worked out a gym continuously for 70
minutes. The graph shows the remaining percentage of
the workout as a linear function of x, the time in
minutes. Which answer choice best describes the
domain and range of the function for this situation?

Answers

Answer:

NO CLUE

Step-by-step explanation:

UR WELCOME

Find the missing variables

Answers

Answer:

Solution,

tan45 = [tex]\frac{u}{v}[/tex]

or, 1 =  [tex]\frac{u}{v}[/tex]

or, v = u

Now,

Using Pythagoras Theorem,

[tex](8\sqrt{2})^{2} = u^{2} +v^{2}\\or, 128 = u^{2} +u^{2}\\or, 128 = 2u^{2}\\or, u^{2} = 64\\\\or, u = 8cm = v[/tex]

Step-by-step explanation:

[tex] \underline{ \underline{ \text{Given}}} : [/tex]

Hypotenuse ( h ) = 8√2Perpendicular ( p ) = uBase ( b ) = v [tex] \tt{ \theta = 45 \degree}[/tex]

[tex] \underline{ \underline {\text{To \: find}}} : [/tex]

Value of u & v

[tex] \underline{ \underline{ \text{Solution}}}\: [/tex] :

[tex] \tt{sin \: \theta = \frac{p}{h}} [/tex]

⟶ [tex] \tt{ \sin(45 \degree) = \frac{u}{8 \sqrt{2} } }[/tex]

⟶ [tex] \tt{ \frac{1}{ \sqrt{2} } = \frac{u}{8 \sqrt{2}} } [/tex]

⟶ [tex] \tt{ \sqrt{2 \: } u = 8 \sqrt{2}} [/tex]

⟶ [tex] \tt{u = \frac{8 \sqrt{2} }{ \sqrt{2}} } [/tex]

⟶ [tex] \tt{u = 8}[/tex]

Again ,

[tex] \tt{tan \: \theta = \frac{p}{b}} [/tex]

⟶ [tex] \tt{ \tan(45 \degree) = \frac{8}{v}} [/tex]

⟶ [tex] \tt{1 = \frac{8}{v}} [/tex]

⟶ [tex] \tt{v = 8}[/tex]

[tex] \red{ \underline{ \boxed{ \boxed{ \text{Our \: final \: answer : \boxed{ \tt{u = 8 \: and \: v = 8}}}}}}}[/tex]

Hope I helped ! ♡

Have a wonderful day / night ! ツ

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Help me plssss!!!!!!!

Answers

The answer is The first option bc
#1 adds up to 200/8 and that’s 25
#2 adds up to 140/8 and that’s 17.5
25-17.5 is 7.5

the scale map says that 10cm represents 2km what distance on the map in centimeters represent an actual distance of 15 kilometers

Answers

Answer:

75cm

Step-by-step explanation:

Well, I can't see a photo, so I'll have to assume that the description provides enough info.

10cm/2km = x/15km,

where x is the distance on the map (in centimeters) of a real-life distance of 15 kilometers.

10cm/2km = x/15km

10/2 = 5/1

This means we have to multiply 5 by 15 to find x.

x = 5 · 15

x = 75

Let's plug the new value back in...

10cm/2km = x/15km

10cm/2km = (75cm)/15km

(Simplify each side to its simplest form)

10cm/2km = 75cm/15km

5/1 = 5/1

It works! So x = 75cm.

Hope this helps! :)

What is the rate of change of 8y=3x+64

Answers

Answer:

The range is the set of all valid y values. Use the graph to find the range.

Interval Notation:

(−∞,∞)

Set-Builder Notation:

{y|y∈R}

Step-by-step explanation:

Answer:

0.125

Step-by-step explanation:

Hope this is helpful

Kyle is 16 shorter than his brother his brother is 64 inches tall how tall is kyle.

Answers

Answer:

48 inches

Step-by-step explanation:

64 - 16 = 48 inches

find x of the triangle

Answers

Answer:

X=4

Step-by-step explanation:

8*2=16

since equilateral it has to be 4*4

welcome brainliest pls

i will give brainliest to correct answer and explanation ah help i don’t understand it

Answers

Answer:

15 degrees

Step-by-step explanation:

So you know that the sum of the two angles is 90 degrees, so you can make an equation:

[tex]3x + 45 =90[/tex]

Then, solve:

subtract 45 from both sides

[tex]3x = 45[/tex]

divide both sides by 3

[tex]x = 15[/tex]

This means that x = 15 degrees

Answer:

The answer is 15 degrees.

Step-by-step explanation:

1) Do you see the little square symbol at the bottom right corner? That represents that the angle is a right angle, or a 90 degree angle, in other words.

2) If you know that the first part of the angle is 45 degrees, as it is already labeled, then subtract 90 degrees - 45 degrees = 45 degrees, which is the angle that is left.

3) Set 3x equal to 45 degrees, and solve.

4) So, the equation is 3x = 45; divide by 3 on both sides to get x = 15 degrees.

Hope this helps! Feel free to give me Brainliest if you feel this helped. Have a good day, and good luck on your assignment. :)

what is 12% of 40

i will give brainliest

Answers

Answer:

it is 4.8 .................

Question 1
Which statement best describes and justifies the symmetry of the graph shown?

Answers

ANSWER
B I think... I hope it’s right

Graph y + 2 = -1(x + 3).

Answers

Answer: y=−x−5

Step-by-step explanation: -4+-4

Y=-x-5 I think that’s the correct answer.

Plzzzz helppppp I will mark you as a brainliest

Answers

Answer:

A, 4

B, 0

Step-by-step explanation:

gcf = 4

32-28 = 4 (4-4) = 4(0) = 0

can i get brainliest?

Answer: a4 b0

Step-by-step explanation:

gcf = 4

32-28 = 4 (4-4) = 4(0) = 0

Very easy math problem need fast please

Answers

Answer:

C. 36π

Step-by-step explanation:

π·r^2=area

An appropriate metric unit to measure the distance from tagaytay city to Manila would be a. millimeter b. Centimeter c.meter d.kilometer

Answers

Answer:

Meter is the answer as per the question

Write the fractional equivalent (in reduced form) of each number.

Answers

Answer:

1) 1/10

2)16/100

3)6..../10

4) 3/5

Pls give me brainliest I rly need it!

Step-by-step explanation:

[cos(x)cos(y)][tan(x)+tan(y)]=sin(x+y)​

Answers

Answer:

this is a required answer.

The given identity is proved.

What is trigonometric identities?

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation

According to the given question we have a trigonometry identity.

[tex]cos(x)cos(y)[tan(x)+tan(y)] = sin(x+y)[/tex]

To prove the above the identity, we show that R.H.S = L.H.S

So,

[tex]L.H.S = [cos(x)cos(y)][tan(x)+tany(y)][/tex]

[tex]\implies L.H.S = [cos(x)cos(y)][\frac{sinx}{cosx} +\frac{siny}{cosy} ][/tex]

[tex]\implies L.H.S = [cos(x)cos(y)][\frac{sinxcosy+sinycosx}{cosxcosy} ][/tex]

[tex]\implies L.H.S = cos(x)cos(y) \frac{sin(x)cos(y)+sin(y)cos(x)}{cos(x)cos(y)}[/tex]

[tex]\implies L.H.S = sin(x)cos(y)+ sin(y)cos(x)[/tex]

[tex]\implies L.H.S = sin(x+y)...(i)[/tex]

And from the given trigonometry identity,

[tex]R.H.S = sin(x+y)..(ii)[/tex]

Therefore,

L.H.S = R.H.S

⇒ [tex]cos(x)cos(y)[tan(x)+tan(y)] = sin(x+y)[/tex]      (proved)

Hence, the given identity is proved.

Find out more information about trigonometric identities here:

https://brainly.com/question/12537661

#SPJ3

Simplify the following expression by combining like terms. Select the most simplified expression: 2w + 5w - 6 + 4w
A. 5w
B. 11w-6

Answers

Answer:

Your answer is B

Step-by-step explanation:

Here you go mate

Step 1

2w + 5w - 6 + 4w  Equation/Question

Step 2

2w + 5w - 6 + 4w  Simplify

2w + 5w - 6 + 4w

Step 3

2w + 5w - 6 + 4w  Combine the like terms

(2w+5w+4w)+(-6)

Step 4

(2w+5w+4w)+(-6)  Add them

Answer

11w-6

Hope this helps

Janie has $3. She earns $1.20 for each chore she does and can do fractions of chores. She wants to earn enough money to buy a CD for $13.50.

The expression is “3+1.2c is equal to or greater than (the great symbol with a line at the bottom)13.50

The number line is

8.5 (closed circle) pointing to greater direction :)

I just did it so yeah

Answers

Answer:

3+1.2c≥13.50       c≥8.75

Step-by-step explanation:

3 angles of a quadrilateral measure 25 degree and 40 degree and 90 degree wwhat is the measure of the 4th angel

Answers

A quadrilateral has 4 sides and 4 angle.

The sum of the 4 angles need to equal 360 degrees.

4th angle = 360 - 25-40-90

4th angle = 205 degrees.

wich statement is true.​

Answers

Answer:

c

Step-by-step explanation:

Monica is selling a house where she earns a commission equal to 3.25% of the final selling price of the house. If Monica sells a house for $256,000, what is her commission fee?

Answers

Answer:

$8320

Step-by-step explanation:

3.25% of 256000 = 0.0325 × 256000 = 8320

last one of the night correct answer gets brainilest

Answers

The answer is the second table
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