Which is the area between the x-axis and y=x from x=1 to x=5

Answers

Answer 1

Answer:

[tex]\displaystyle A = 12[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra I

FunctionsFunction NotationGraphing

Calculus

Integrals

Definite IntegralsArea under the curve

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Area of a Region Formula:                                                                                     [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

y = x

Interval: x = 1 to x = 5

Step 2: Sort

Graph the function. See Attachment.

Bounds of Integration: [1, 5]

Step 3: Find Area

Substitute in variables [Area of a Region Formula]:                                   [tex]\displaystyle A = \int\limits^5_1 {x} \, dx[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]:                     [tex]\displaystyle A = \frac{x^2}{2} \bigg| \limits^5_1[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:           [tex]\displaystyle A = 12[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Which Is The Area Between The X-axis And Y=x From X=1 To X=5

Related Questions

Consider function f. (-412 + 6.3 + 36, 1 < -2 15, 2 < I 4 Are the statements about the graph of function ftrue or false? true false 2 false The graph crosses the y-axis at (0.–15). The graph has a point of discontinuity at I = The graph is increasing over the interval (4, co) The graph is decreasing over the interval (-12, -2). false The domain of the function is all real numbers. false​

Please help

Answers

Answer:

Behold.

Step-by-step explanation

The answer to the statement is 1)false 2) false 3) true 4) true and 5) false.

Given functions,f

1) For x ≤ -2: f(x) = -12 + 6x

2) For -2 < x < 1: f(x) = 41 - 15x

3) For x ≥ 1: f(x) = 31 - 4x

1) The graph crosses the y-axis at (0, -15).

This is false because if x = 0, the function value would be -12 + 6 * 0 = -12, not -15.

2) The graph has a point of discontinuity at x = 1.

This is false because the function is defined at x = 1 there is no space, so there is no point of discontinuity at x = 1.

3) The graph is increasing over the interval (4, ∞).

This is true because the coefficient of x in the function's expression is negative, showing that it is decreasing. Therefore, as x increases, the function values decrease.

4) The graph is decreasing over the interval (-12, -2).

This is true because the coefficient of x in the first piece of the function (-12 + 6x) is positive, showing an increasing trend. Therefore, as x decreases from -12 to -2, the function values increase.

Statement 5: The domain of the function is all real numbers.

This is false because the domain of the function is limited by the intervals in its definition. The function is defined differently for different intervals of x.

So, the answer to the statement is

1) false

2) false

3) true

4) true

5) false

Learn more about functions here:

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Yesterday, the snow was 2 feet deep in front of Archie’s house. Today, the snow depth dropped to 1.6 feet because the day is so warm. What is the percent change in the depth of the snow?
The percent change in the depth of snow from yesterday to today is
%.

Answers

1.6/2 * 100 = 80%
100% - 80% = 20%

So the snow depth decreased 20%.

Geometry, please answer question ASAP

Answers

Answer:

It's 5 which is A.

Step-by-step explanation:

Tutorial
Emmy already owns 22 hair bands, and additional hair bands are priced at 1 for a dollar.
How much money does Emmy need to spend on new hair bands in order to own a total of
38 hair bands?

Answers

Answer:

16

Step-by-step explanation:

38-22=16

Anyone wanna help with this please ?

Answers

Answer:

y = mx + b

m = slope = -2

To find the y-intercept(b), substitute the points into the function:

-3 = -2(-5)  + b

-3 = 10 + b

b = -3 - 10 = -13

Therefore, y = -2x - 13

Answer:

Step-by-step explanation:

The length of a rectangle is six times its width. If the area of the rectangle is 384^2, find its perimeter.

Answers

Answer:

Perimeter, P = 112 meters

Step-by-step explanation:

Let the length of the rectangle be L.Let the width of the rectangle be W.

Translating the word problem into an algebraic expression, we have;

L = 6W  ...... equation 1

Given the following data;

Area of rectangle = 384 m²

To find the perimeter of the rectangle;

First of all, we would determine the dimensions of the rectangle using its area.

Mathematically, the area of a rectangle is given by the formula;

Area of rectangle = LW  ..... equation 2

Substituting eqn 1 into eqn 2, we have;

384 = 6W(W)

384 = 6W²

Dividing both sides by 6, we have;

W² = 384/6

W² = 64

Taking the square root of both sides, we have;

W = √64

Width, W = 8 meters

Next, we would find the length;

L = 6W

L = 6 * 8

Length, L = 48 meters

Lastly, we would determine the perimeter of the rectangle using the above dimensions;

Mathematically, the perimeter of a rectangle is given by the formula;

Perimeter = 2(L + W)

Substituting the values into the formula, we have;

Perimeter, P = 2(48 + 8)

Perimeter, P = 2(56)

Perimeter, P = 112 meters

what is the result of converting 1260

Answers

Answer:

hiyupbhhhhkigkzblbbbgedvflr

7(8+a)=189 please help and give me step by step ​

Answers

Answer: a = 19

Step-by-step explanation:

Given

7 (8 + a) = 189

Divide 7 on both sides

7 (8 + a) / 7 = 189 / 7

8 + a = 27

Subtract 8 on both sides

8 + a - 8 = 27 - 8

a = 19

Hope this helps!! :)

Please let me know if you have any questions

Well, we can use the distributive property:
56 + 7a = 189
7a = 133
a = 19

rachel rides her bicycle due east at 9 miles per hour amos rides his bicycle due north at 12 miles per hour if they left from the same point at the same time how far apart will they be after 1 hour

Answers

The distance between Rachel and Amos after one hour is 15 miles.

What is an equation?

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

Distance travelled by Rachel after one hour = 9 mph * 1 h = 9 miles

Distance travelled by Amos after one hour = 12 mph * 1 h = 12 miles

Let x represent the distance between Rachel and Amos, hence:

x² = 9² + 12²

x = 15

The distance between Rachel and Amos after one hour is 15 miles.

Find out more on equation at: https://brainly.com/question/2972832

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Using the Pythagorean Theorem, they will be 15 miles apart after one hour.

What is the Pythagorean Theorem?

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

For this problem, considering their directions, their distance is the hypotenuse of a right triangle of legs 9 miles and 12 miles, hence:

[tex]d^2 = 9^2 + 12^2[/tex]

[tex]d = \sqrt{9^2 + 12^2}[/tex]

d = 15 miles

More can be learned about the Pythagorean Theorem at https://brainly.com/question/654982

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URGENT HELP PLS AND THANK U

Answers

Answer: a= 1

Step-by-step explanation:

a * b = b

Divide by “b” on both sides

a= b/b

“b/b” is equal to 1

a=1

Hope that helps

Lmk if you need a better explanation.

1 because anything times 1 will equal it self so b times 1 will equal 1 there the answer is one. Hope this helps!


What is the surface area of a sphere with a diameter of 14 cm?
1961 cm2
287 cm2
7841 cm2
981 cm2

Answers

Answer:

??

Step-by-step explanation:

how

did you get 616? are you even looking at the 4 answers?????

75.072 divided by 9.6

Answers

Answer:

7.82

Step-by-step explanation:

I solved it

The answer is 7.82 :)

(4y¹²) (3y)
Please help me​

Answers

12y with as the 13 square root

Someone plz help me on this

Answers

Answer:

9²+x²=13²

81+x²=169

x²= 169-81

x²=88

X= 9.38

x=9.4

[tex]x = \sqrt{88} [/tex]

In algebraic expression


The sum of a number and six, divided by eight.

Answers

Answer:

x + 6 / 8

Step-by-step explanation:

The sum of a number is the answer to addition. So that means an unknown number and 6 are being added together. Lets make this unknown number x.

x + 6

The sum of this is being divided by 8. Since we already know what division is, we can just add the line and 8.

x + 6 / 8

Which expression is equivalent to 4x +4y

Answers

Answer:

C. 4(x + y)

Step-by-step explanation:

Use the distributive property.

4(x + y) = 4x + 4y

Answer:

C. 4(x + y)

Step-by-step explanation:

If you multiply this answer out (4 times x and 4 times y) it is the equivalent to 4x + 4y.

I need help to find n =

Answers

Answer:

n = √108

Step-by-step explanation:

Use similar triangles or the right triangle altitude theorem.

18/n = n/6

n^2 = 18 * 6

n^2 = 108

n = √108

Which of the following is a correct sine ratio for the figure? Question 20 options: A) C = 5∕12 B) C = 5∕13 C) C = 12∕13 D) C = 13∕12

Answers

Answer:

B

Step-by-step explanation:

Sine is opposite/hypotenuse. Sine C  would be 5/13 so option B is correct.

Help pls, I need Help :D

Answers

Answer:

5

Step-by-step explanation:

Step 1. Get two points off the graph

Points: (-70, 0) and (-60, 50)

Step 2. Use the two points to find the slope

m = slope

m = change in y/change in x

m = y2 - y1/x2 - x1

m = 50 - 0/-60 - -70

m = 50/10

m = 5/1

m = 5

The slope is 5

Angela works a basic week of 40 hours and her hourly rate of pay is $12.50. Calculate her weekly wage.

Answers

Answer:

$500

Step-by-step explanation:

Answer:$500

Step-by-step explanation:

To calculate the weekly wage, take the hourly rate and multiply it by the number of hours worked. For this question it would be:

$12.50 x 40

=$500

That is your weekly wage

Hope this helped! <3

Simplify the following equation

4−8÷2+3 ​

Answers

This is NOT an equation because it has no =
The correct order to evaluate it is:
4 - (8 / 2) + 3 = (4 - 4) + 3 = 0 + 3 = 3

Hi there!  

»»————- ★ ————-««

I believe your answer is:

3

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Simplifying...}}\\\\4-8\div2+3\\\\---------------\\\text{Follow PEMDAS:}\\\\\\\rightarrow4-8\div2+3\\\\\rightarrow 4 - 4 + 3\\\\\rightarrow 0 + 3\\\\\rightarrow \boxed{3}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

2 plus 2 is 22???????

Answers

Answer:

NO

Step-by-step explanation:

Quesdon 8 of 10
Which of the following is a polynomial?

Answers

Answer:

B

Step-by-step explanation:

It has two or more terms.

i need help asap im timed

Answers

Answer:-

Refer to attachment for the required solution.

Answer:

Step-by-step explanation:

When f(x)=4, what is the value of x?
O zero
O 2
O 3
O4

Answers

Answer:

x = 2

Step-by-step explanation:

f(x) is the range and values of x the domain

When f(x) = 4 the corresponding value of x in the domain is x = 2

Answer:

2

Step-by-step explanation:

this might not be the best explanation but this is how I thought of it.

f(0)=4?   any number multiplied by zero equals zero so it is not the first answer.

f(2)=4?   if f were to be 2, then 2*2 can equal 4 so this is a pretty good answer.

f(3)=4?  there isn't a whole number you can multiply with 3 that will make 4 so this is not the answer.

f(4)=4?  if f were to be 1 then this could be a possible answer.

so we know that it is either the 2nd or 4th answer. look at the table. if you look, 2 forms into 4 (because they multiplied 2 by 2). but 4 doesn't remain at 4 (because they did not multiply it by 1). so we know the answer is 2.

{(3,1),(-2,-1),(-3,2)}

Domain:

Range:

Answers

Answer:

Domain { -3,-2,3}

Range{ -1,1,2}

Step-by-step explanation:

The domain is the input

Domain { -3,-2,3}

The range is the output

Range{ -1,1,2}

One number is six times another number. Their difference is 35. Whàt are the two numbers?

Answers

Answer:

7 and 42

Step-by-step explanation:

The difference 35 is actually equivalent to 5 units if you draw it out into a model, thus 35 divide 5 is 7 and the other number is 7x6 which is 42

A gray crayon is made with 5 mL of black wax for every 6 mL of white wax

Which of the following wax mixtures will create the same shade of gray?

choose 2 answers:

A 10 mL of black wax mixed with 24 mL of white wax
B 15 mL of black wax mixed with 18 mL of white wax
C 35 mL, of black wax mixed with 42 mL of white wax
D 20 mL of black wax mixed with 26 mL of white wax
E 45 mL of black wax mixed with 48 mL of white wax

Answers

Answer:

B and C

Step-by-step explanation:

The ratio of black to white is 5:6

The only mixtures that have this ratio is B and C

B and c are the correct answers

If x-2y=6 and x+y=10.Find 2x+2y.

Answers

Answer:

20

Step-by-step explanation:

x-2y=6 and x+y=10

Multiply the second equation by 2

2x+2y = 20

Find the length of the missing side:

Answers

Answer:

x = 15.8

Hope this helps...Have a good day!!

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