Mathematics College

100 Points
Use geometry to evaluate the integral from negative 2 to 6 of f of x, dx where f of x equals the absolute value of x for x between negative 2 and 2 inclusive, equals 2 for x greater than 2 and less than or equal to 4, and equals negative x plus 4 for x greater than 4 and less than or equal to 6.

Answers

Answer 1

Answer:

[tex]\int\limits^{6}_{-2} {f(x)} \, dx=6[/tex]

Step-by-step explanation:

Review the attached graph

Answer 2

By using geometry to evaluate the given integral, the value is equal to 6 units.

How to use geometry to evaluate an integral?

In order to use a geometry to evaluate a definite integral, you should identify the portion of a graph which corresponds to the given integral.

Also, you'll mark out the geometric shapes that are formed on the graph, so as to enable you calculate their areas. Finally, you'll add the areas together.

From the graph of the integral shown in the image attached below, the geometric shapes that are formed are rectangle and triangles.

For the area of rectangle, we have:

Area of rectangle = L × B

Area of rectangle = 2 × 2

Area of rectangle = 4 units.

For the area of triangle, we have:

Area of triangle = 1/2 × b × h

Area of triangle = 1/2 × 2 × 2

Area of triangle = 2 units.

Total area = 4 + 2

Total area = 6 units.

Read more on integrals here: https://brainly.com/question/5898524

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Related Questions

Which statement is true?

Answers

Answer:

your right

Step-by-step explanation:

Two sides of a triangle have lengths 5 and 4. Which of the following can NOT be the length
of the third side?
A.1
B.4
C.2
D.3

Answers

Answer:

im guessing b.4

Step-by-step explanation:

It is not possible to have a) 1 as one f the third side of the triangle

What is triangle inequality theorem ?

It defines the relationship between the sides `of a triangle .

The triangle inequality theorem states that sum of length of two sides of a triangle is greater than the length of the third side .

a + b > c

correct answer option a) 1

it is not possible to make a triangle if one side is 1 because triangle inequality theorem will be violated

1 + 4 = 5 and not greater than 5

hence , not possible

learn more about triangle inequality theorem

https://brainly.com/question/1163433?referrer=searchResults

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(1-cos^2 60°)+(1-sin^2 60°)=tan^2 60°

Answers

(1-cos^2 60°)= sin^2 60°
(1-sin^2 60°) = cos^2 60°
Sin^2 60° + cos^2 60°= tan^2 60°

What are the reasons you would "flip" or reverse the inequality symbol in your answer?

Answers

When you multiply both sides by a negative value you make the side that is greater have a "bigger" negative number, which actually means it is now less than the other side! This is why you must flip the sign whenever you multiply by a negative number.

Andre paid $13 for 3 books. Diego bought 12 books priced at the same rate.

How much did Diego pay for the 12 books?

PLEASE INCLUDE AN EXPLANATION

Answers

Answer:

$36

Step-by-step explanation:

i dont know how to explain it but heres the number answer

Answer:

well 3÷13= 4.33 and 4.33×12=52

Can someone help me plz

Answers

Answer:

Answer 3

Step-by-step explanation:

Answer:

A. 27

Step-by-step explanation:

trust me

If a polynomial function f(x) has roots 0, 4, and 3+ V11, what must also be a root of f(x)

Answers

Answer:

3-√11 must also be a root of f(x)

Step-by-step explanation:

4 pound tomato cost 14 dollar how much does 1 pound cost

Answers

Answer:$3.50

Step-by-step explanation:

14/4 =3.5. To check answer multiply 3.5 by 4. You get 14

What is the least common multiple of 9, 17, and 51? A. 51 B. 102 C. 153 D. 867

Answers

Answer:

C. 153

Hope this helps

shshsgshsh

Answer:

C. 153

Step-by-step explanation:

I just did this quiz and got it right!! Hope this helps! :D

A restaurant is making hamburgers. The cooks use 2/3 pounds of beef for each hamburger. If the cooks have 46 and 2/3 pounds of beef, how many hamburgers can they make?

Answers

Answer:

They can make 49 hamburgers

Step-by-step explanation:

Answer:

They can make 49 hamburgers

Step-by-step explanation:

5 2/3 multiplied by 4 1/2

Answers

Answer:

[tex] 25\frac{1}{2} [/tex]

Step-by-step explanation:

[tex]5 \frac{2}{3} \times 4 \frac{1}{2} \\ \\ = \frac{5 \times 3 + 2}{3} \times \frac{4 \times 2 + 1}{2} \\ \\ = \frac{15 + 2}{3} \times \frac{8 + 1}{2} \\ \\ = \frac{17}{3} \times \frac{9}{2} \\ \\ = \frac{17}{1} \times \frac{3}{2} \\ \\ = \frac{51}{2} \\ \\ = 25 \frac{1}{2} [/tex]

^ what he said
Can u make me the Brainlyest

According to the Vivino website, the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is $32.48. A New Englandâbased lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for 56 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are $30.15 and $12, respectively.

Required:
a. Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
b. Using the sample from the 60 bottles, what is the test statistic?
c. At Î± = 0.05, what is your conclusion?

Answers

Answer:

The null hypothesis is [tex]H_o : \mu = 32.48[/tex]

The alternative hypothesis is [tex]H_a : \mu < 32.48[/tex]

[tex]t = -1.504[/tex]

There is no sufficient evidence to conclude that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48

Step-by-step explanation:

From the question we are told that

The mean price of is [tex]\mu = \$ 32.48[/tex]

The sample size is n = 56

The sample mean is [tex]\= x = \$30.15[/tex]

The standard deviation is [tex]\sigma = \$12[/tex]

The null hypothesis is [tex]H_o : \mu = 32.48[/tex]

The alternative hypothesis is [tex]H_a : \mu < 32.48[/tex]

Generally the test statistic is mathematically represented as

[tex]t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]

=> [tex]t = \frac{30.15 - 32.48 }{\frac{12 }{\sqrt{60} } }[/tex]

=> [tex]t = -1.504[/tex]

Generally the p-value is mathematically represented as

[tex]p-value = P (t < -1.504 )[/tex]

From the z-table

[tex]P(t < -1.504) = 0.066291[/tex]

[tex]p-value = 0.066291 [/tex]

From the value we obtain we see that

[tex]p -value > \alpha[/tex]

Then we fail to reject the null hypothesis

Hence there is no sufficient evidence to conclude that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48

There is The Question and answers

Answers

m3
—— correct me if I’m wrong please
216

Answer: -1/8

Step-by-step explanation:

A coral reef grows 0.12 minutes every week. How much does it grow in 8 weeks?

Answers

Answer:

0.96

Step-by-step explanation:

0.12 x 8 = 0.96

help. will give brainly to correct answer. please.

Answers

Answer:

Last option; 5/2+ i5/2

What is the rate of change of the function?
O -3. O -1/3. O 1/3. O 3

Answers

Answer:

I think it's 1/3

Step-by-step explanation:

because yo can see that in y-1, x=1 then in y0, x=1.3 and it keep going

i’ve been on this question for 22 minutes please help me

Answers

Answer:

Step-by-step explanation:

I need help please! 7:44 est need rn

Answers

Answer:

B. [tex]3^{6}[/tex]

Step-by-step explanation:

[tex]3^{8} = 6561[/tex] [tex]3^{2} = 9[/tex] 6561 ÷ 9 = 729Option B, [tex]3^{6}[/tex], is equal to 729, so that is the right answer.

I hope this helps!

what is l4x-4l+10=3x

Answers

Answer:

x=−6

Step-by-step explanation:

4x−4+10=3x

Step 1: Simplify both sides of the equation.

4x−4+10=3x

4x+−4+10=3x

(4x)+(−4+10)=3x(Combine Like Terms)

4x+6=3x

Step 2: Subtract 3x from both sides.

4x+6−3x=3x−3x

x+6=0

Step 3: Subtract 6 from both sides.

x+6−6=0−6

Answer:

l4x-

Step-by-step explanation:

Sorry I hope this is it I hoped it help sorry.

please leave a thanks.

i’ll mark brainlest to whoever answers this question first! :)

Answers

Answer:

Step-by-step explanation:

(9x-2y)/xy when x-4 and y=-2

Answers

Answer:

-5

Step-by-step explanation:

Answer:

GIVEN x=4 and y=-2

So, in (9x-2y)/xy when we apply x=4 and y=-2

{9(4)-2(-2)}/(4)(-2)

36+4/-8

40/-8

-5/1

=-5

Rephrase: what is 35% of $120?

Answers

35% of $120 is 42 US$

How do I find x in this equation?

Answers

Answer:

Exact Form:

=29/20

Decimal Form:

x=1.45

Mixed Number Form:

x=1 9/20

Step-by-step explanation:

I did that before trust me I know

A cyclist travels 10 km from home to the park.
She leaves home at 12:20 and arrives at the park at 12:50.
What is her average speed in km/h?

Answers

Answer:

20 km/hr

Step-by-step explanation:

The total time she takes to travel 10 km is 30 minutes of 0.5 hours.

To calculate speed, we can divide the distance traveled by the time it takes.

[tex]s = \frac{10}{0.5} = 20[/tex] km/hr

P= 2/ + 2w Find The Width

Answers

9514 1404 393

Answer:

W = P/2 -L

Step-by-step explanation:

Divide by 2 and subtract L.

P = 2L +2W

P/2 = L +W

P/2 -L = W

The width is ...

W = P/2 -L

50 PONTIS Score for Question 3: ___ of 5 points) 3. Solve the given inequality and graph the solution on a number line. Show your work! -2x + 3 < 5

Answers

Answer:

If x equals -1 or anything less than -1, then the inequality statement is false

Step-by-step explanation:

So to find the number x has to be for the statement to be false, we have to find what number x would be to make it so both sides equal the same thing. So in this case, it would be -1 because 5-3 equals 2 and -2x=2 only if x=-1. So anything greater than -1 would make the statement true.

I hope this helped.

Answer:

x > - 1 or x = (-1, + oo)

Step-by-step explanation:

Given

Inequality

-2x + 3 < 5To findSolve and graphSolution-2x + 3 < 5-2x < 5 - 3-2x < 2x > - 1x = (-1, + oo)

As per above, the graph covers all numbers to the right from the point -1

The graph is attached

i need help in geometry :(

Answers

9514 1404 393

Answer:

82 ft

Step-by-step explanation:

We can find the value of x by making use of the fact that corresponding angles have equal measures.

∠K = ∠N

20x -10 = 15x +15

5x = 25 . . . . . . . . . . add 10-15x

x = 5 . . . . . . . . . . . . divide by 5

Then the side lengths are ...

JK = (4x -4) ft = (4·5 -4) ft = 16 ft

KL = (5x +1) ft = (5·5 +1) ft = 26 ft

And the perimeter is the sum of side lengths:

16 ft + 26 ft + 40 ft = 82 ft

The perimeter of each pool is 82 feet.

If a dose of 100mg is contained in 4cc, how many cubic centimeter are in 40mg?

Answers

the answer to this is 1.6cc

Patty walked 2/5 of a mile in 5 1/2 minutes. At this rate, how long will it take Patty to walk 3 miles?

Answers

Answer:

41.25 minutes i think sorry if its wrong

In an auditorium, the front 39 rows with 53 seats in each row are for kids while all 53 seats in each of the remaining 61 rows are for adults. How many seats are there in the auditorium?

Answers

Answer:

The auditorium has a total of 5,300 seats

Step-by-step explanation:

The seats for kids can be calculated by multiplying the number of rows by the number of seats per row:

Seats for kids=39*53 =2,067 seats

The seats for adults are calculated in a similar way:

Seats for adults = 61*53= 3,233 seats

Total seats: 2,067+3,233 = 5,300

The auditorium has a total of 5,300 seats

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Determine whether the lines are parallel, intersect, or coincide. Al almohadn de plumas ,,tipo de narrador What is the relationship between the lines with the following equations? 2x+6y=12 y=3x8A) The lines are neither parallel nor perpendicular.B) The lines are the same.C) The lines are parallel.D) The lines are perpendicular. help please i am struggling whic of the following When did the water level in Lake Mead become a concern? A review of the ledger of Marin Inc. at December 31 produces the following data for the preparation of annual adjusting entries: 1. Salaries and Wages Payable, $0. There are 8 salaried employees. 5 employees receive a salary of $1,150 each per week, and 3 employees earn $690 each per week. Employees do not work weekends. All employees worked two days after the last pay period and before December 31. 2. Unearned Rent Revenue, $349,860. The company began leasing condos in its new building on November 1. Each tenant has to make a $5,340 security deposit that is not refundable until occupancy is ended. At December 31, the company had the following rental contracts that were paid in full for the entire term of the lease:Date Term (in months) Monthly Rent Number of LeasesNov. 1 6 $3,940 6Dec. 1 6 $10,370 4Prepaid Advertising, $16,560. This balance consists of payments on two advertising contracts. The contracts provide for monthly advertising in two trade magazines. The terms of the contracts are as follows:Contract Date Amount Number of magazines IssuesA650 May 1 $6,960 12B974 Oct. 1 9,600 24The first advertisement runs in the month in which the contract is signed.4. Notes Payable, $78,480. This balance consists of a one year, 8%, note that is dated June 1.Required:Marin is preparing for a meeting with potential investors. What is the net effect of the adjusting entries on net income? In a human somatic cell (normal body cell) that is in G2, what would be true about chromosome number and structure? a. These cells would be considered haploid (n).b. These cells would be considered diploid (2n).c. These cells would be considered tetraploid (4n).d. These cells would contain homologous chromosomes.e. These cells would contain sister chromatids.f. The chromosomes will be aligned in the middle of the cell. a chemist takes a polysaccharide and turns it into many disaccharide. what reaction has the chemist performed and what must he add BRAINLIEST TO FIRST PERSON!!!!!!!!!! 8 POINTS!!!!!! TYSM!!!!!!Why is a soil profile in a tropical rain forest different from one in a desert? he is intelligent _ hard workinga, as well as. c,there foreb, although. d,yet How would you help other people suffering from body image disturbance embrace their physical selve? explain the major differences in beliefs about prophets and messiahs with respect to Christianity, Islam and Judaism. ITS TIMED PLS HELPWhat was the relationship of Islam to Christianity and Judaism?A. It saw itself as a continuation of the Abrahamic traditionB. It did not form any kind of relationship with Christianity or JudaismC. It saw the leaders of Judaism and Christianity as false prophetsD. It rejected the teachings of the other religions Luigi's Pizzeria is having a Pi Day lunch special where you can choose either one 18" pizza or two 12" pizzas. The cost of each option is the same, $14.00. Which option gets you more pizza? Note: Pizza is measured by the diameter so a 10" pizza is 10" in diameter. can any one help? me plz How to write a letter to the Press could someone find a way to reword this????? Mogadishu was advanced in formality. What is 50/45 simplified True or false : the French and Native Americans were business partners?