Mathematics College

Evaluate the integral ∫2−1|x−1|dx

Answers

Answer 1

I think you might be referring to the definite integral,

$\displaystyle \int_{-1}^2|x-1|\,\mathrm dx$

Recall the definition of absolute value:

$|x| = \begin{cases}x&\text{if }x\ge0\\-x&\text{if }x<0\end{cases}$

Then $|x-1|=x-1$ if $x\ge1$, and $|x-1|=1-x$ is $x<1$. So spliting up the integral at x = 1, we have

$\displaystyle \int_{-1}^2|x-1|\,\mathrm dx = \int_{-1}^1(1-x)\,\mathrm dx + \int_1^2(x-1)\,\mathrm dx$

The rest is simple:

$\displaystyle \int_{-1}^2|x-1|\,\mathrm dx = \left(x-\dfrac{x^2}2\right)\bigg|_{-1}^1 + \left(\dfrac{x^2}2-x\right)\bigg|_1^2 \\\\ = \left(\left(1-\frac12\right)-\left(-1-\frac12\right)\right) + \left(\left(2-2\right)-\left(\frac12-1\right)\right) \\\\ = \boxed{\frac52}$

Related Questions

There is a mother-daughter tea that will be attended by 20 mother-daughter pairs, including the hosts. The rules of conduct are very strict; the host mother-daughter will greet everyone, all the guest mothers will greet everyone, and all the guest daughters will greet all the mothers only. How many greetings will there be?

Answers

In total, the number of greetings will be 1159.

Why do you use the term "numbers"?

Mathematical symbols used to represent quantities or values include numbers. They are employed in the measurement, comparison, addition, subtraction, multiplication, and division processes in mathematics. According to their qualities and properties, numbers can be categorized into a variety of groups, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers. There are specific properties and guidelines for mathematical operations for each group of numbers. Mathematics depends on numbers, which are also utilized in many other disciplines, including science, engineering, economics, and statistics.

The number of greetings exchanged between the host and the other mothers and daughters must be counted first. Since there is only one host, the number of mother-daughter pairs is 20 - 1 = 19. There are thus a total of 38 greetings, 19 between the host and the other moms, and 19 between the host and the other daughters.

The number of pleasantries exchanged between the guest mums and everyone else must next be tallied. The host, the other mothers, and the daughters must all be greeted, making a total of 20 - 1 = 19 guest mothers. Thus, each host mother must extend 1 + 19 + 20 = 40 greetings. There will be 760 greetings exchanged between the guest mothers and everyone, or 19 x 40.

The number of pleasantries exchanged between the mothers and the invited girls must also be tallied. Moreover, there are 20 guest girls, so 19 of them must welcome the mothers. As a result, there will be 361 pleasantries exchanged between the mothers and the guest daughters.

In total, the number of greetings will be 38 + 760 + 361 = 1159.

To know more about numbers visit:

https://brainly.com/question/26856218

#SPJ1

What is the area, measured in square centimeters, of the triangle below? Do
not include units in your answer.

Answer here

Answers

Answer:

The area of this triangle is (1/2)(9)(8) = 36.

Simplify the expression -3÷(-2/5). A. -7 1/2 B. -1 1/5 C. 1 1/5 D. 71/2

Answers

Answer: The answer is D: 7 1/2.

Step-by-step explanation:

Find the missing height.
units Plss help

Answers

Answer:

Step-by-step explanation:

The area of a parallelogram is

A = bh

A = 5*h

30 = 5h

Divide each side by 5

30/5 =5h/5

6 =h

The formula for the area of a parallelogram is A = bh.

Since we know the parallelogram has an area of 30 units and a height of 5 units, we can plug this information into the formula to get 30 = 5h.

Now, dividing both sides of the equation by 5, we find that 6 = h.

So the height of this parallelogram is 6 units.

Pls help
With thissss

Answers

Answer:

Ion know lol

Step-by-step explanation:

The answer is An estimate so it’s B

Something that I need to remember about converting time/capacity is?

PLSSS HELPPP

Answers

We have to remember that 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day and the base unit for capacity is the liter (L).

There are 1,000 milliliters (mL) in a liter, and 1,000 liters in a kiloliter (kL).

Time Conversions:

There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day.

To convert from smaller to larger units, divide the value by the appropriate conversion factor.

To convert from larger to smaller units, multiply the value by the appropriate conversion factor.

Capacity Conversions:

In the metric system, the base unit for capacity is the liter (L).

There are 1,000 milliliters (mL) in a liter, and 1,000 liters in a kiloliter (kL).

To convert from smaller to larger units, divide the value by the appropriate conversion factor.

To convert from larger to smaller units, multiply the value by the appropriate conversion factor.

Remembering these conversion factors and units will help ensure accurate conversions when dealing with time and capacity measurements.

To learn more on Conversions click:

https://brainly.com/question/9414705

#SPJ1

Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students.a) 91.69 < μ < 98.31b) 92.95 < μ < 97.05c) 91.68 < μ < 98.32d) 92.03 < μ < 97.97

Answers

Answer: c) 91.68 < μ < 98.32

Step-by-step explanation:

Let μ be the mean score of all students.

Let $\overline{x}$ represents the sample mean score.

As per given , we have

Sample size : n= 30

Sample mean : $\overline{x}=95$

Sample standard deviation: $s=6.6$

Significance level $\alpha=0.01$

Now, Confidence interval of mean when population standard deviation is unknown is given by :-

$\overline{x}\pm t_{\alpha/2, df}\dfrac{s}{\sqrt{n}}$

Degree of freedom = n-1 = 29

Critical two-tailed t-value : $t_{0.01/2,29}=t_{0.005,29}=2.756$ [By students' t distribution table]

Confidence interval of mean will be:

$95\pm (2.756)\dfrac{6.6}{\sqrt{30}}\\\\=95\pm (2.756)\dfrac{6.6}{5.47722557}\\\\=95\pm (2.756)(1.205)\\\\=95\pm 3.32\\\\= (95-3.32, 95+3.32)\\\\=(91.68,\ 98.32)$

i.e. a 99% confidence interval for the mean score of all students : 91.68 < μ < 98.32

So correct option is c) .

3 6 9 12 15 18 21 24 27 30 is odd or even numbers?

Answers

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

whats is 1+1+3+7+8+33542

Answers

Answer:

33562, You could have used a calculator, or used your head, why

Step-by-step explanation:

Kyle submits a design for the contest, but his explanation was misplaced. How can figure A be mapped onto figure B? Can any other transformation be used to map figure A onto figure B

Answers

Answer:

Step-by-step explanation:

ita a bc i know its I did this before

20 points! For students majoring in Hospitality Management, it was determined that 5% have visited 1–10 states, 16% have visited 11–20 states, 45% have visited 21–30 states, 19% have visited 31–40 states, and 15% have visited 41–50 states. Suppose a Hospitality Management student is randomly selected. What is the probability that the student has visited 21 or more states?

0.15
0.21
0.45
0.79

Answers

Answer:

So i feel like the answers is .79

Step-by-step explanation:

asking for the ones that visited 21 or more so thats .45+.19+.15=.79

Answer:

.55

Step-by-step explanation:

What are the answers to this?

Answers

Answer:

u should better search the google or this site www.edkasa.edu.pk u will defiantly find the answer.

4
(Graphing Proportional Relationships LC)
The table shows a proportional relationship.
x 12 8 24
y 3 26
Describe what the graph of the proportional relationship would look like.
O Aline passes through the point (0, 0) and continues through the point (3, 12).
O Aline passes through the point (0, 0) and continues through the point (2,8).
A line passes through the point (0, 0) and continues through the point (6, 24).
A line passes through the point (0, 0) and continues through the point (12, 3).
Question 2(Multiple Choice Worth 2 points)
(Graphing Proportional Relationships MG)

Answers

The correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3)

For the first question:

The table shows a proportional relationship between x and y. To describe what the graph of this proportional relationship would look like, we can examine the given data points.

The data points are (12, 3), (8, 26), and (24, ?). We can observe that as x increases, y also increases. This indicates a positive correlation between the variables. Additionally, we can see that the ratio of y to x remains constant for each data point.

Now, let's analyze the answer options:

A. A line passes through the point (0, 0) and continues through the point (3, 12).

This answer option does not align with the given data because there is no data point with an x-value of 3 and a corresponding y-value of 12.

B. A line passes through the point (0, 0) and continues through the point (2, 8).

This answer option aligns with the given data because (2, 8) is a valid data point from the table, and the line passes through the origin (0, 0).

C. A line passes through the point (0, 0) and continues through the point (6, 24).

This answer option does not align with the given data because there is no data point with an x-value of 6 and a corresponding y-value of 24.

D. A line passes through the point (0, 0) and continues through the point (12, 3).

This answer option aligns with the given data because (12, 3) is a valid data point from the table, and the line passes through the origin (0, 0).

Based on the analysis, the correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3). This accurately represents the graph of the proportional relationship given in the table.

For the second question, I'm sorry, but you didn't provide the multiple-choice options or the complete question. Could you please provide the question and options so that I can assist you further?

for more such question on point visit

https://brainly.com/question/1859113

#SPJ8

What is the domain of this function ?

Answers

Domain is x so I believe it would be a

Q1 ? Help Robert is 7 ½ years old. How many months old is he?

Answers

Answer:

Step-by-step explanation:

If Robert is 7 1/2 months old you need to multiply 7 1/2 by 12 because there are 12 months in a year.

7x12=84

1/2x12=6

6+84=90

Two types of tickets are available for a charity ball event: $18 for a reserved seat and $9 for general admission. The number of reserved seats available is 85 less than the number of tickets available for general admission. If the sale of tickets for the day was $3,600, how many seats were allotted for general admission?

Answers

Answer:

# of reserved seats = R; # of general admission seats = G

G - R = 85

$18R + $9G =$3600

Multiply 1st equation by 18: 18G - 18R = 1530

Rearrange 2nd equation: $9G + $18R =$3600

Combine the equations: 27 G = 5130

G = 190

R = 105

Step-by-step explanation:

The difference between the squares of two numbers is 35. Twice the square of
the first number increased by the square of the second number is 73. Find the
numbers.

Answers

Answer:

Los números son

7 y 8

Explicación paso a paso:

Si el número menor es "x" , el mayor es "x + 1"

entonces

( x + 1 )² - x² = 15

x² + 2x + 1 -x² = 15

2x + 1 = 15

2x = 15 - 1

2x = 14

x = 14/2

x = 7 ( número menor )

x + 1 = 7 + 1

x + 1 = 8 ( número mayor )

find the value of x in the following equation 8x- 6=50

Answers

Answer:

x = 7

Step-by-step explanation:

8*7 - 6 = 50

1.3.1 1.3.2 1.3.3 1.3.4 Government receives income from various sources, like tax and loans. This income is then distributed to the different sectors. TABLE 3 below shows the source of the income and the expenditure for the 2019/20 tax year. SOURCE Tax INCOME Loans ASC QP Other income Non-tax income AMOUNT (in billion rand) 1370 242.7 180.3 31.5 EXPENDITURE SECTOR Social Development Basic Education Health Peace and safety Economic development Community Development Debt service cost AMOUNT (in billion rand) Further Education and Training Other 278.4 262.4 222.6 211.0 209.2 208.5 202.2 APRIL 2021 112.7 B 1823.72 TOTAL A Write the amount received from loans as a number in millions (1) (3) (3) Calculate the missing value A Calculate the missing value B. Show ALL calculations. Determine the amount allocated for Community Development as a percentage of the total expenditure. (4)

Answers

The amount received from loans as a number in millions is 242,700 million rand.

How to calculate the value

Deducing value A requires computation of collective income sources, for which the following summation suffices:

Total Income = Tax + Loans + ASC + QP + Other income + Non-tax income = 1370 + 242.7 + 180.3 + 31.5 + A + 0 = 1825.5 + A

In this context, it follows that A amounts to (1825.5 - 1370 - 242.7 - 180.3 - 31.5) = 0 million rand.

Conversely determining missing value B necessitates subtraction of total expenditure from accumulated revenue, giving rise to the subsequent formula:

Total Income - Total Expenditure = B

(1825.5 - 112.7 - 278.4 - 262.4 - 222.6 - 211.0 - 209.2 - 208.5 - 202.2 - 0) = B

Following calculation, B equates to -77.1 million rand, indicating an overage in expenses during fiscal year 2019/20.

Learn more about word problem on

https://brainly.com/question/21405634

#SPJ1

please help! maths hyperbolic functions

Answers

Answer:

See attachments.

Step-by-step explanation:

The quickest way to sketch the given functions, given that the coordinate plane is restricted to -5 ≤ x ≤ 5, is to substitute the values of x into the functions to find the points for the given interval. Plot these points on the given coordinate plane, and draw a continuous curve through the points.

Part (a)

Given function:

$y=\dfrac{5}{x}-2, \quad x > 0$

Substitute the values of x = 1, x = 2, x = 3, x = 4 and x = 5 into the function:

$\begin{aligned}x=1 \implies y&=\dfrac{5}{1}-2\\&=5-2\\&=3\end{aligned}$

$\begin{aligned}x=2 \implies y&=\dfrac{5}{2}-2\\&=2.5-2\\&=0.5\end{aligned}$

$\begin{aligned}x=3 \implies y&=\dfrac{5}{3}-2\\&=-0.333...\end{aligned}$

$\begin{aligned}x=4 \implies y&=\dfrac{5}{4}-2\\&=1.25-2\\&=-0.75\end{aligned}$

$\begin{aligned}x=5 \implies y&=\dfrac{5}{5}-2\\&=1-2\\&=-1\end{aligned}$

Plot the points (1, 3), (2, 0.5), (3, -0.333...), (4, -0.75) and (5, -1) on the given coordinate plane and draw a continuous curve through them.

End behaviour:

As x approaches 0 from the positive side, x tends to ∞.As x approaches ∞, y approaches -2.

$\hrulefill$

Part (b)

Given function:

$y=\dfrac{-2}{x+1}+3, \quad x < -1$

Substitute the values of x = -2, x = -3, x = -4 and x = -5 into the function:

$\begin{aligned}x=-2 \implies y&=\dfrac{-2}{-2+1}+3\\&=2+3\\&=5\end{aligned}$

$\begin{aligned}x=-3 \implies y&=\dfrac{-2}{-3+1}+3\\&=1+3\\&=4\end{aligned}$

$\begin{aligned}x=-4 \implies y&=\dfrac{-2}{-4+1}+3\\&=0.666...+3\\&=3.666...\end{aligned}$

$\begin{aligned}x=-5 \implies y&=\dfrac{-2}{-5+1}+3\\&=0.5+3\\&=3.5\end{aligned}$

Plot the points (-2, 5), (-3, 4), (-4, 3.666...) and (-5, 3.5) on the given coordinate plane and draw a continuous curve through them.

End behaviour:

As x approaches -1 from the negative side, x tends to ∞.As x approaches -∞, y approaches 3.

L
9) Consider the following equations:
x= 10-t
t + 50 = x2 + 50
What equation would result from
combining the given equations?

Answers

pic po please please please please

an airplane flew for one hour and landed 100 miles north and 80 miles east from its origin. what was the distance traveled, speed and angle of direction from its origin?

Answers

The distance traveled by airplane is 180 miles.

The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°

The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.

Then, the total distance traveled by airplane will be:

= 100 miles + 80 miles = 180 miles.

The speed can be defined as the distance traveled by the total time taken.

Speed = distance/time

Speed = 180 miles/ 1 hour

Speed = 180 miles/60 minutes

Speed = 3 miles per minute

The angle of direction from its origin will be:

tan (x) = 100 miles/80 miles

x = tan⁻¹ ( 100/80)

x = tan⁻¹ ( 10/8) = tan⁻¹ ( 5/4)

x = 51.34°

Learn more about speed here:

brainly.com/question/13943409

#SPJ1

A box contains 3 chocolate chips, 5 oatmeal raisin ,and 4 peanut butter cookies.one cookie is randomly selected.what is the probability that a peanut butter cookie will be selected

Answers

Answer:

1/3 or .333 or 33%

Step-by-step explanation

You take the 4 (peanut butter cookies) divided by the total number of cookies (12)

My favorite Pokemon card has a mass of about one and a half
_____
grams
kilograms
millimeters
or inches

Answers

Answer:

grams cause its is really small

Enter the decimal represented by the shaded square.
The shaded square represents

Answers

Answer: the shaded squares are equal to 0.3

Find the sticker price and the dealer's cost for the Bobcat SX with a base price of $13,568.00. Options include air conditioning for $765.00, turbo for $643.00, towing package for $236.00, and custom wheels for $422.00. Destination charges total $365.00. The dealer pays 90% of the base price and 65% of the options.

Answers

Sticker price = 15,999
Dealer’s Cost=13,910.10

A building has 6 homes per floor and 3 floors. On the first floor, there are 4 penguins per home. On the second and third floor, there are 3 penguins per home.
Which equation can we use the total number of penguins living in the building?

Answers

The equation that represent the number of penguins is (6 × 4) + (3 × 6) + (3 × 6) = p.

How to find the equation to represent a situation?

A building has 6 homes per floor and 3 floors. On the first floor, there are 4 penguins per home. On the second and third floor, there are 3 penguins per home.

Therefore, the equation that can be used to find the total number of penguins living in the building is as follows:

Hence,

(6 × 4) + (3 × 6) + (3 × 6) = p

where

p = number of penguins

learn more on equation here: https://brainly.com/question/27022155

#SPJ1

Describe the series of rigid motion transformations which map polygon A to Polygon A'''. Are the two polygons congruent? Explain how you know.

(someone please help me!)

Answers

The series of rigid motion transformations that map polygon A to Polygon A''' are;

A rotation of 145° about the origin to map A to A'A reflection across the x-axis to map A' to A'A translation of four units to the right and one unit down

What is a rigid transformation?

A rigid transformation is a transformation in which the distance between all pairs of points on the pre-image is preserved following the transformation.

The series of rigid motion transformations that map polygon A to polygon A''' are;

Transformation from A to A'

The angle in the diagram in the question indicates the rotation of polygon A to produce polygon A' is a rotation of 145° about the origin.

Transformation from A' to A''

The coordinates of the vertices of triangle, A' (0.9, 4.1), (3.1, 5.9), (5.5, (2.5) and the vertices of triangle A'' (0.9, -4.1), (3.1, -5.9), (5.5, -2.5), indicates that the transformation is a reflection about the x-axis

Transformation from A'' to A'''

The arrow of the translation transformation indicates that the transformation is a translation of four units to the right and 1 unit down.

Learn more about rigid transformations in geometry here:

https://brainly.com/question/2222755

#SPJ1

Will mark brainlist and give extra points bth grade math