(d). Find the area of the region enclosed by the graphs of f(x)= x³ and g(x)=x²+2x. [Verify your answer by MATHEMATICA and attach the printout of the commands and output (e). Find the area of the region enclosed by the graphs of y = 3/X and y=4-X. [Verify your answer by MATHEMATICA and attach the printout of the commands and output

Answers

Answer 1

Answer:

d .  37/12 unit^2.

Step-by-step explanation:

d) First find the points of intersection of the the 2 graphs, by solving them simultaneously:

x^3 = x^2 + 2x

x^3 - x^2 - 2x) = 0

x(x^2 - x - 2) = 0

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

So they intersect at x = -1, x = 0 and x = 2.

Take the area from x = 0 to x = 2)

           2                        2

Area =  ∫ x^2 + 2x dx -   ∫  x^3 dx

            0                       0

   2

=  [ x^3/3 + x^2 ) - x^4/4]

   0

=   ((8/3 + 4) - 0) - (16/4 - 0) -

=   8/3 unit^2

Now calculate the area  from x = -1 to x = 0.

   0

=    (x^3/3 + x^2 ) - x^4/4 )

   -1

=   (( 0 +1/3 - 1) ) - (0 - 1/4)

=  5/12 unit^2

So the total area of the region =  8/3 + 5/12 = 37/12 unit^2.


Related Questions

Emmalie is 32 inches tall. If her brother Joshua was 3.5 inches taller, he would be exactly twice Emmalie's height. How tall is Joshua? Enter your answer as a decimal in the box.

Answers

Answer:

60.5in

Step-by-step explanation:

32(2) - 3.5 = 60.5

Answer:

HERES ALL THE QUIZZES ANSWERS!

Question One/1:

9.5(w+5.7)=77.9

Question Two/2:

The scuba diver is 27 feet below sea level.

Question Three/3:

25.50

YOUR QUESTION: Question 4:

60.5 inches (in)

Question Five/5:

58 3/4 (mi)

Step-by-step explanation:

k12

MATH,

MIDDLE SCHOOL,

7TH GRADE,

HALFWAY.

YOU'RE SO WELCOME!

sorry, caps lol.

PHOTOS TOO!

(Crown?)

(i appreciate it!)

Thanks, bye!

PLEASE HELP ILL GIVE BRAINLIEST


Matt ate 2005 calories. The next day he ate 1920 calories. What is the percent change in the number of calories from day 1 to day 2?​

Answers

Answer:

85%

Step-by-step explanation:

a meal came to $16.41 without tax. calculate the 6% sales tax, and then calculate the 15% tip based on the sum of the meal and the tax. what is the total cost of the meal?

Answers

Answer:

$20

Step-by-step explanation:

correct me if im wrong(┬┬﹏┬┬)

When asked a certain question in a poll, 72% of the people polled answered yes. If 56 people did not answer yes to that question, what is the total number of people who were polled?

Answers

Answer:

i think its 200

Answer:

200people

Step-by-step explanation:

28 percent=56people100=?100 multiplied by 56=5600 5600 divide by 28=200

The difference of twice a number and 7 is 20. Find the number.

Answers

Answer:

twice the difference gives 2(difference). 7 = 14  20 = 40

Step-by-step explanation:


???????????????????????????????????????

Answers

Answer:

Its C (Third Multiple Choice Answer)

Step-by-step explanation:

The reason being that x + 1 / 2 (6x - 4) = 6 is the way it is instead of the first step being x + 6x / 2 - 4 / 2 = 6 is because it is using legal manipulation by multiplying the 1 / 2 out.

Math:

First

2 * (x + 1 / 2 (6x - 4) = 6 * 2 [In this case the x gets multiplied by 2 and multiplies 2 to the other side as well. The reason why it isn't a Distributive Property in the first place is because we are using multiplication only and the equation is not 1 / 2 (6x - 4).

Then

2x + 6x - 4 = 12 will then equal to 8x - 4 = 12 which is adding like terms

Thirdly

(+ 4) + 8x - 4 = 12 (+ 4) [The parenthesis is to identify that the 4 is positive]

will then turn into 8x = 16

Finally

By dividing 8 on both sides of the previous equation

8x / 8 = 16 / 8 equaling x = 2.

NO LINKS!!!

Complete the following problems to the best of your knowledge. Show all your work. Part 1

Answers

Step-by-step explanation:

#1

a. -6, -9, 12

There is no sequence since the difference between the terms is not common and the ratio of the terms is not common

b. t(n) = 0.5 - 6

There is no sequence as all the terms are same regardless the value of n

c. 32, 16, 8

The sequence is geometric as common ratio is 1/2, each next term is half the previous one#2

a. 8, 16, 32, 64, ...

This is a geometric sequence as the common ratio is 2

b. 1, 1, 2, 3, 5, 8, ...

This is neither one since no common difference or ratio between the consecutive terms

c. 5, 5, 5, ...

This is neither one since common difference is zero or common ratio is 1

d. -101, -99, -97, -95, ...

This is a arithmetic sequence since the common ratio is 2#3

According to question the sequence is:

200000, 100000, 50000, ...

We see each number is half the previous one so this is a GP with common ratio of 1/2

calculate lim F(X)
[tex] {x }^{2} + 1 - 3 \frac{ ln(x) }{x} [/tex]

Answers

[tex]Hiya![/tex]

Sokka is here to help!!

Here's the step:

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

[tex]Mutiply[/tex] [tex]by:[/tex] [tex]3[/tex]

[tex]. \frac{In(x)}{x} :\frac{3In(x)}{x}[/tex]

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

ANSWER:

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

Hopefully, this helps you!!

[tex]Sokka[/tex]

use the correct trig function to find the value of x. SOH, CAH, TOA​

Answers

Answer:

About 11.025

Step-by-step explanation:

[tex]\sin{58^\circ}=\dfrac{x}{13}\\\\x=13\cdot\sin{58^\circ} \approx11.025[/tex]

Complete the equation to show how many tenths are equivalent to 1/2

Answers

Answer:

5/10

Step-by-step explanation:

Mary burns 35 calories when she rides her bicycle to the park. After riding, she
burns 9.5 calories per minute while running.
Write a linear equation for the total amount of calories, C, that Mary will burn if
she cycles to the park and runs m minutes.

Answers

Answer/Step-by-step explanation:

C = 35 + 9.5m --> This means that she burns an initial 35 calories plus 9.5 calories for every minute she runs. This will tell us the total amount of calories she burns for a given amount of time.

Answer:

C = 35 + 9.5m

Step-by-step explanation:

This means that she burns an initial 35 calories plus 9.5 calories for every minute she runs. This will tell us the total amount of calories she burns for a given amount of time.

What is 953 divided by 6

Answers

The answer is 158.8333333333333

Answer

158 with a remainder of 5 ( also expressed as 953/6 OR 158.333333333333)

Step-by-step explanation:

I wasn't sure if you wanted a fraction, so I put two forms of the answer.

fkjlfljkfleruhgowjfgwklgnerql;ng;

Answers

Answer:

THX for points XD

Step-by-step explanation:

Solve
-12 + 23

A. -35

B. -11

C. 11

D. 35

Answers

Answer:

C. 11

Step-by-step explanation:

This can be rewritten as

23 - 12

This is equal to 11.

Answer:

11

Step-by-step explanation:

-12 + 23 = 11

since the 12 is negative subtract it from 23 and you get 11 as your answer

If
x
=
2
and
y
=
5
, evaluate the following expression:
2
(
3
y

4
x
)

Answers

The answer is 14 that should work

16/20 - (- 1.8) - 4/5 =​

Answers

Simplify 16/20 to 4/5
Remove parentheses
4/5 + 1.8 - 4/5



=9/5

Which is the verbal expression for 11 - 2/n?


Answers

Answer:

(a.)

Step-by-step explanation:

(we talked abt it in the comment haah)

2 short questions 20 POINTS

Answers

Step-by-step explanation:

13.

oh, come on !

you never had and solved the situation "one piece costs that much, how much will be 2 or 5 or 10 of them ?"

it is a simple multiplication.

and hence the answer B.

the first hint is already in the table with 1 pizza costing $5.25.

2 pizzas are then 2×$5.25, 3 pizzas 3×$5.25, ...

so, the cost c = number of pizzas × $5.25

or short

c = p×5.25 or 5.25p

14.

the domain is the interval or set of valid values for the input variable (x) of a function/relation.

and the range is the interval or set of valid values for the result variable (y) of a function/relation.

so, the domain is the set {-3, -1, 0, 1, 3}.

and the range is the set {-4, 0, 2, 4}.

In mathematics, a function is a binary relation between two intervals or sets that associates each element of the first interval/set (domain) to exactly one element of the second interval/set (range).

and that's what is done here.

it is a function.

each value of x is associated exactly with 1 result value of y.

a y value can be associated with more than one x value - no problem.

but no x value can have more than one associated y value - otherwise that would break the principle of a function.

find the value of x for which f(x)=4

Answers

[tex] \: \: \: [/tex]

[tex]f(x) = 4[/tex]

The domain of a constant function is the set of all real numbers

[tex]x = R[/tex]

hope it helps

[tex] \: \: \: [/tex]

What equation represents this sentence? 5 less than a number is 12. n−5=12 5=12−n 5=n−12 5−n=12

Answers

Answer:

n-5=12

This is the answer

The algebraic equation n - 5 = 12 represents the sentence " 5 less than a number is 12" and the solution of the equation is the value of variable n is 17.

What is Algebra?

Algebra is the estimation of mathematical representations, while logic is the manipulation of those symbols.

The given statement is "5 less than a number is 12"

According to the given question, translate the phrase into an algebraic form :

⇒ n - 5 = 12

Thus, the algebraic equation n - 5 = 12 represents the sentence " 5 less than a number is 12"

Now the above equation solves for variable n,

⇒ n - 5 = 12

Add 5 to both sides of the above equation,

⇒ n = 12 + 5

⇒ n = 17

Therefore, the algebraic equation n - 5 = 12 represents the sentence " 5 less than a number is 12" and the solution of the equation is the value of variable n is 17.

To learn more about the Algebra link is given below.

brainly.com/question/953809

#SPJ2

A shirt cost $24.92 with 10% discount if the sales tax is 6.35% how much will the shirt cost?

Answers

Cost 24.92*10/100
= 2.492
Sale tax 6.35+2.492
The total Cost of shirt is = 8.732


Translate the English phrase into an algebraic expression: four times the difference of v and one.

Answers

Answer:

4(v-1)

Step-by-step explanation:

the answer is 4(V-1)

Answer:

the answer is 4(v-1)

¿A donde llegas si sales de la escuela y avanzas PORFAVOR ES PARA MAÑANA

Answers

Answer:

a mi casa aunque no es lejos

What is the slope of any line that is perpendicular to the line that contains the points (8,8) and (12,12)

Answers

Answer: 1

Step-by-step explanation:

12-8=4

12-8=4

4 over 4 is 1

if it perpendicular then it's the opposite reciprocal

hope that help

Solve the inequality. 53(2x + 2) – 10 ≥ 2x + 2(23x + 2) please help

Answers

Hope this helps!!!!!!!!!!!!

A relationship between two expressions or values that are not equal to each other is called 'inequality. inequality 53(2x + 2) – 10 ≥ 2x + 2(23x + 2)  is x≥-92/58.

What is Inequality?

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is

53(2x + 2) – 10 ≥ 2x + 2(23x + 2)

Apply the distributive property

106x+106-10≥ 2x + 46x+4

Add the like terms

106x+96≥ 48x+4

Take all common variables on one side

106x-48x≥4-96

106x-48x is 58 and 4 minus 96 is minus 92.

58x≥-92

x≥-92/58

Hence inequality 53(2x + 2) – 10 ≥ 2x + 2(23x + 2)  is x≥-92/58.

To learn more on Inequalities click:

https://brainly.com/question/28823603

#SPJ5

Is the ordered list 26, 39, 52, 65, 78 an arithmetic sequence?

Answers

Answer:

Yes

Step-by-step explanation:

It is an arithmetic sequence since it has a common difference which is 13.

78-65 = 13

65-52 = 13

52-39 = 13

39-26 = 13

Part 2 out of 2
Heather's mom says that they would save more than $100 if they buy tickets for their family on opening
weekend. Do you agree or disagree with Heather's mom? Complete the explanation of how to find how
much they would save.
You ? v with Heather's mom.
The regular price tickets would cost them $80 x 4 people, which equals $
The discounted tickets would cost them $ * 4 people, which equals $224.
To find the difference subtract the discounted tickets total $224 from the regular price tickets total $
which equals $
They would save
which is less than $100.
Next
✓ Check
Next
? A
А
Question 18 of 21

Answers

Answer:

i agree I can't really explain why though sorry

Heather's mom's estimation is wrong, as they will only save $96.

What is a percentage?

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

Given that, The special price for the amusement park ticket costs $56. This is 70% of the regular price, Heather's mom says that they would save more than $100 if they bought tickets for their family on opening weekend.

Let the original price of the ticket be x,

70% of x = 56

x = 56x100/70

x = 80

That means, the regular price is $80

On a regular day, ticket will cost = 80x4 = $320

On the special ticket price cost = 56x4 = $224

The saved priced = 320-224 = $96

Hence, Heather's mom's estimation is wrong, as they will only save $96.

For more references on percentage, click;

https://brainly.com/question/29306119

#SPJ1

In the base ten number 4325 , how many times
greater than the value represented by the digit 2 is the value represented by the digit 4 ?

Answers

Using the concept of place value, the digit 4 is 200 times greater than the digit 2.

Given the number :

4325

The digit 2 is in the tens place = 2 × 10 = 20

The digit 4 is in the thousand place = 4 × 1000 = 4000

The number of times greater can be obtained thus :

4000 / 20 = 200

Hence, the digit 4 is 200 times greater than the digit 2.

Learn more : https://brainly.com/question/14760328

original price of a truck $ 17,100.00 Tax 2.5%

Answers

Answer:

Sales Tax Only: $427.50

Total Price: $17,527.50

URGENT: HELP ME WITH THE MATH PROBLEMS!!

(Note This Needs To Be Done Tonight!)

Answers

Answer:

1. 3 and 1/5 improper: 11/15

2. 3 and 3/4 improper: 15/16

3. 1 and 2/3 improper: 5/6

4. 2 and 1/2 improper: 5/6

5. 3 and 2/10 improper: 32/40

6. 3 and 3/9 improper: 30/36

7. 1 and 2/6 improper: 8/12

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