Calculate the average rate of change of function on the interval (a,a+h). simplify your expression.Show all steps.
f(x)=3x+2/2x-1

Calculate The Average Rate Of Change Of Function On The Interval (a,a+h). Simplify Your Expression.Show

Answers

Answer 1

Answer:

Please check the explanation.

Step-by-step explanation:

Given the function

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

at x₁ = a,

[tex]f\left(x_1\right)=f\left(a\right)=\frac{3a+2}{2a-1}[/tex]

at x₂ = a+h,

[tex]f\left(x_2\right)=f\left(a+h\right)=\frac{3\left(a+h\right)+2}{2\left(a+h\right)-1}[/tex]

Using the formula to determine the average rate of change

Average rate = [f(x₂) - f(x₁)] / [ x₂ - x₁]

                      [tex]=\:\frac{\frac{3\left(a+h\right)+2}{2\left(a+h\right)-1}-\frac{3a+2}{2a-1}}{a+h-a}\:\:\:\:\:\:\:[/tex]

as a+h-a = h, so    

                      [tex]=\frac{\frac{3\left(h+a\right)+2}{2\left(h+a\right)-1}-\frac{3a+2}{2a-1}}{h}[/tex]

Thus, the everarge rate of chnage:  [tex]\frac{\frac{3\left(h+a\right)+2}{2\left(h+a\right)-1}-\frac{3a+2}{2a-1}}{h}[/tex]

We can further simplify such as:

[tex]=\frac{\frac{3\left(h+a\right)+2}{2\left(h+a\right)-1}-\frac{3a+2}{2a-1}}{h}[/tex]

[tex]=\frac{-\frac{7h}{\left(2a-1\right)\left(2\left(h+a\right)-1\right)}}{h}[/tex]

[tex]=-\frac{\frac{7h}{\left(2a-1\right)\left(2\left(h+a\right)-1\right)}}{h}[/tex]

[tex]=-\frac{7h}{\left(2a-1\right)\left(2\left(h+a\right)-1\right)h}[/tex]

Cancel the common factor h

[tex]=-\frac{7}{\left(2a-1\right)\left(2\left(h+a\right)-1\right)}[/tex]            


Related Questions

deb Found 56 tulips for $8. Please help Deb figures out the ratio

Answers

Answer: 7:1

To find the unit rate or unit ratio, divide 56 by 8.

56/8 = 7.

So, per 7 tulips it costs 1 dollar, or $1.

So the ratio, 7:1 represents this problem.

Dj Jacqueline is making a playlist for a friend: she is trying to decide what 15 songs to play and in what order they should be played. If she has her choices narrowed down to 10 pop. 25 reggae, and 10 blues songs, and she wants to play an equal number of pop. reggae, and blues songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place

Answers

Answer:

4.4 * 10^21

Step-by-step explanation:

Given :

Number of pop, n(p) = 10

Number of reggae, n(r) = 25

Number of blues, n(b) = 10

Total number of songs to select (n) = 15

If she wants equal Number if the 3 genres

Each genre will have : 15/3 = 5 songs each

Hence,

(10C5 * 25C5 * 10C5) * n!

Combination formula :

pCr = p! / (p-r)! r!

Using calculator to save computation time :

(10C5 * 25C5 * 10C5) * n!

(252 * 53130 * 252) * 15!

= 4412050844368527360000

= 4.4 * 10^21

If BD bisects ∠ABC, find each value

Answers

Answer:

x=14

y=10

AD=19

CD=19

Step-by-step explanation:

x:

5x-6=64

   +6   +6

5x=70

x=14

y:

3y-11=y+9

   +11    +11

3y=y+20

-y   -y

2y=20

y=10

AD:

3y-11

3(10)-11

30-11

19

CD:

y+9

(10)+9

19

If x=-3 what does 6+5x

Answers

Answer:

-9

Step-by-step explanation:

Plug in -3 for the x value to get 6 + 5 (-3).  Multiply 5 by -3 to get -15 and subtract that number from 6 to get -9 as your final answer.

Mr. Garza had 178 pencils in a storage room. He put 46 more boxes of pencils in the storage room. Each box contained 12 pencils. Which of these is the best estimate of the number of pencils Mr. Garza now has in his storage room?

Answers

Answer: 730

Step-by-step explanation:

46x12+178= 730

What is -20 + 1/2 in a decimal form

Answers

Answer: The answer is -19.5

Step-by-step explanation: This is because 1/2 is .5 in decimal form. A negative PLUS a positive = is negative since the -20 is larger than .5

Answer:

the answer would be -19.5 :)

Step-by-step explanation:

Can someone help me with this please

Answers

Answer:

the picture is upside down

Step-by-step explanation:

I can’t see right please do it again

please help me i cant under stand this

Answers

Answer:

Plot the same points that are on the table

Step-by-step explanation:

when given a table you are also given ordered pairs , so for example , the first pair on the table is (1,3) so plot that as your first point , then your second is (2,6) and so on . write these on the blank spaces aswell ! hope this helps :))))

Use equivlant ratios 7/= 21/27

Answers

Answer:

7/9 = 21/27 hope this helps

Step-by-step explanation:

7/? = 21/27
= 7 * 3
= 21

? * 3
= 27
?= 9

Write in lowest terms:
4rs2/(6s)

Answers

Answer:

2rs/3

Step-by-step explanation:

PLZ HELP WILL GIVE V=BRIANLYEST

Answers

i also agree to this question

Answer:

i also agree to this question

Step-by-step explanation:

A population of rabbits on a farm grows by 12% each year. Assume that this increase occurs as new baby rabbits at the beginning of each new year. Define a sequence {rn} describing the rabbit population at the beginning of each year. Suppose that the sequence starts with r1 = 30. for the first year. As the sequence is a model for the actual population, we accept fractional numbers in the sequence. (a) Determine r12. Determine a formula for rn, for general n. (b) If each rabbit consumes 10 pounds of rabbit food each year, then how much rabbit food is consumed during the 10th year? How much rabbit food is consumed in total for the 1st through 10th years? Express this as a summation and as an exact number.

Answers

Answer:

a) r₁₂ = 104.36

In general, rₙ = arⁿ⁻¹

b)

- rabbit food consumed during the 10th year is approximately 832 pounds

- rabbit food consumed in total for the 1st through 10th years is approximately 5265 pounds

Step-by-step explanation:

Given that:

r1 = 30 and a farm grows by 12%

a = 30 and the common ratio r = 1.12

now

n           r

1        30.00

2       33.60

3       37.63

4       42.15

5       47.21

6       52.87

7       59.21

8       66.32

9       74.28

10      83.19

11       93.18

12      104.36

Therefore r₁₂ = 104.36

In general, rₙ = arⁿ⁻¹

b)

if each rabbit consume 10 lbs of rabbit food each year

n           r                food consumed(lbs)

1        30.00               300

2       33.60               336

3       37.63                376

4       42.15                422

5       47.21                472

6       52.87               529

7       59.21                592

8       66.32               663

9       74.28               743

10      83.19                832

total                          5265

Therefore, the rabbit food consumed during the 10th year is approximately 832 pounds

And the rabbit food consumed in total for the 1st through 10th years is approximately 5265 pounds

write the slope of x+2y=16 pls help fast

Answers

Answer: [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

To find the slope, let's turn the equation into slope-interept form. In slope intercept form, y=mx+b, we know that m=slope.

[tex]x+2y=16[/tex]             [subtract both sides by x]

[tex]2y=-x+16[/tex]          [divide both sides by 2]

[tex]y=-\frac{1}{2}x+8[/tex]

Now, we know that [tex]m=-\frac{1}{2}[/tex]. That tells us [tex]-\frac{1}{2}[/tex] is the slope.

Step-by-step explanation:

x+2y=16

-× -×

2y=-x+16

÷2. ÷2

y=-1/2x+8

slope is -1/2

A ball rolls 12 meters in 3 seconds. What is its speed?​

Answers

Step-by-step explanation:

speed = distance/time

= 12/3 m/s

= 4 m/s

4

V = s/t

= 12/3

=4

S = move

T = time

V = speed

Write an equation for line L in point-slope form and slope-intercept form.
L is perpendicular to y=4x.

Answers

Answer:

[tex]y = -\frac{1}{4}x + c[/tex] --- Slope intercept

[tex]y - y_1 = -\frac{1}{4}(x - x_1)[/tex] --- Point slope

Step-by-step explanation:

Given

Perpendicular to [tex]y = 4x[/tex]

Required

Determine its equation

The general form of an equation is:

[tex]y = mx + c[/tex]

Where

[tex]m = slope[/tex]

By comparison:

[tex]m = 4[/tex]

Next, we calculate the slope of L.

Because L is perpendicular to [tex]y = 4x[/tex], the relationship between their slopes is:

[tex]m_2 = -\frac{1}{m}[/tex]

Substitute 4 for m

[tex]m_2 = -\frac{1}{4}[/tex]

The equation of L in slope intercept form is: [tex]y = mx + c[/tex]

Substitute -1/4 for m

[tex]y = -\frac{1}{4}x + c[/tex]

In point slope form, we have:

[tex]y - y_1 = m(x - x_1)[/tex]

Substitute -1/4 for m

[tex]y - y_1 = -\frac{1}{4}(x - x_1)[/tex]

Answer:

y-4=-1/4(x-1)

y=-1/4x+17/4

Step-by-step explanation:

solve the question below, please

Answers

Answer:

carios has greater angle

Step-by-step explanation:

hope this helps

need help plzzzzzxsss​

Answers

with whatttttt ( i can edit my answer )

Ernesto has already baked 3 pies, and he can bake 2 pies with each additional cup of sugar
he buys. Write an equation that shows the relationship between the additional cups of sugar
x and the number of pies y.
Write your answer as an equation with y first, followed by an equals sign.

Answers

Answer:

igcwochcd chocho dhvohov dochvo

Which of the following correctly shows the quotient of 55 divided by5 ?

Answers

Answer:

Quotient is 11

Step-by-step explanation:

In this question, we need to find the quotient of 55 divided by 5. In this case, 5 is divisor, 55 dividend. Let Q be the quotient of this.

On dividing 55 by 5, the quotient of this sum is 11. In this case, remainder is 0.

We know that,

11 × 1 = 11

And 11 × 5 = 55

So, the quotient in this case is 11. Hence, this is the required solution.

Have A Wonderful Day !!

Please help! Or if someone can explain how to find the answer

Answers

Answer:

If the equation is in the form, ax + b = c, where x is the variable, you can solve the equation as before. First “undo” the addition and subtraction, and then “undo” the multiplication and division. Solve 3y + 2 = 11. Subtract 2 from both sides of the equation to get the term with the variable by itself.

Answer: x = 20

All this is exaple hople it help

the answer to this is20, hope it helps <3

The formula for the velocity of an object is v=d/t, where v is the velocity of an object, dis the distance traveled, and t is the time elapsed, while the distance is traveled. If you had only this formula to work with, what should your first step be in determining how long it takes for light to reach Earth from the Sun? What additional information do you need to calculate this?

Answers

Answer:

To know the distance between the sun and the earth you need isolate d of the equation:

[tex]v = \frac{d}{t} \\ d = vt[/tex]

and the additional information needed is the velocity of light and the time elapsed to be in the earth

Why is a sample used more often more than a population

Answers

Answer:

A number which describes a characteristic of a population. ... Uses a sample to find conclusions, analyzations, and probability about a population. Why is a sample used more often than a population? Because it is more difficult to get an accurate population where as a sample is smaller and easier to assess.

Two angles are complementary if their sum is 90o. If one angles measure is xo and the other angle is (2x – 3)o find the measure of each angle.

Answers

x + (2x - 3) = 90
3x - 3 = 90
3x = 93
x = 31
angle 1 = 31
angle 2 = 59

If 1,200 students participated in the survey, how many rated the cafeteria food “poor”?
200 students
300 students
400 students
600 students

Answers

Answer:

The answer is 300

Answer:

300 students

Step-by-step explanation:

hope this helps!

b. How much information could be transmitted in 30,000 packets?

Answers

Answer:

45'000,000 45 million

Step-by-step explanation:

The answer is 45 million 45000000

Which statement explains why the two systems of equations below have the same solution

Answers

Answer: "B"

The first equation B is the sum of the equations in A, while the other is obtained by multiplying the first equation in A by 2.

The first equation B is the sum of the equations in A, while the other is obtained by multiplying the first equation in A by 2 hence, the correct option is second.

What is a system of equations?

An equation is an expression that shows the relationship between two or more numbers and variables.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We are given the system of equation as;

A,  { 6x + 8y = -10}

      {2x - 5y = 12}

B, {8x + 3y = 2}

    {12x + 16y = -20}

If we add the first two equations that shown in A, then;

6x + 8y + 2x - 5y = -10 + 12

8x + 3y = 2

Now the first equation in A would be multiplied by 2, So

2(6x + 8y = -10)

12x + 16y = -20

Therefore, the correct option is Option B.

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ6

When Josh babysits, he charges a flat fee of $14 plus an
hourly rate of $9. How long would Josh need to babysit if he
wants to earn $86 in one night?

Answers

Answer:

8

Step-by-step explanation

86-14=72 this is the hourly rate before the flat fee is added on. Now you have to divide $72 by $9 to see how many hours josh needs to work. Josh gets paid $9 an hour so he needs to work for 8 hours in order to get $72. Then add the flat fee of 14 and you get $86

Which equation is graphed below?

Answers

Hope it will help you

Find the measure of angle YTG

Answers

The angle is 30 degrees
Answer= 30 degrees.

A farm has 5 brown cows and 10 white cows. A fence is open and a cow escapes. What is the probability that it will be a brown cow?

Answers

1/15 because if just one cow escapes out of all the cows then it will be 1 out of 15 cows all together.

Answer:

D

Step-by-step explanation:

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