With the aid of an illustrative example, discuss the relationship between the area of a region and the definite integral. *​

Answers

Answer 1

Suppose there is a function f(x), the definite integral of the function is the difference between the upper and lower x-values.

There are three relationships between the definite integral and the area of the region. The relationships are:

Positive functionNegative functionRegion between two functions

Positive function

The area between the function itself and the x-axis represents the definite integral.

Negative function

The area between the function itself and the x-axis, multiplied by -1 represents the definite integral.

Region between two functions

The definite integral of the function is the difference between the region of both functions.

See attachment for further illustration

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With The Aid Of An Illustrative Example, Discuss The Relationship Between The Area Of A Region And The

Related Questions

ANSWER CORRECTLY FOR BRAINLIEST!!!

ONLY:

8.

9.

10.

11.

Answers

Step-by-step explanation:

8 . 9 + 3x = 6

3x =6 - 9

3x = -3

x =. -1

9 . 9 (x - 1) - 4( 7 - x ) ≤ 10x - ( 2x +1 ) -6

9x -9 - 28 - 4x ≤ 10x - 2x + 1 - 6

C. L. T.

9x - 4x - 10x + 2x ≤ 1 - 6 + 28 + 9

- 3x ≥ 32

x ≥ - 32/3

x ≥ 10⅔

10 b/ 22 =. 16/ 88

cross multiply

88b = 352

b = 4

11. x- 10 / x+2 = 1/5

cross multiply

5x - 50 = x + 2

4x = 52

x = 13

Answer:

Step-by-step explanation:

Which of the following logarithmic expressions are NOT equal?

Answers

Answer:

I say it's the fourth option

Please help and fast!!

Answers

Answer:

-quadratic / parabolic

- y intercept = 0

- x intercepts at 0 and 6

- highest value = 9

- graph is increasing between 0 and 6

Step-by-step explanation:

Which correctly shows how to use the GCF and the distributive property to find an expression equivalent to 45 + 72?
O 3(15 + 24)
O 9(5 + 8)
O (5)(9) + (2)(36)
O (3)(15) + (8)(9)

Answers

Answer:

9(5+8)

Step-by-step explanation:

2+2
middle school kojvs​

Answers

Answer:

answer for this question is 4

Step-by-step explanation:

2+2=4

Answer-is 4

Explanation-2+2 = 4 just like how 1+1+1+1 = 4

Find the radius of this circle please..


Answers

Answer:

r = 3 ft

Step-by-step explanation:

Area = 9π

So, πr²=9π where r is the radius

so, r²=9

or, r=√9

or, r=3, since r can't be negative

Answered by GAUTHMATH

PLEASE IM BEGGING SOMEONE. I NEED HELP FAST!!! SHOW UR WORK PLS!! THANK YOU!! Jimmy, who is five and a half feet tall, sees a bird at the top of a tree and wonders how tall the tree is. Jimmy stands 18 feet from the tree. Jimmy takes an inclinometer (a device used to calculate angles of elevation) and measures the angle created from his horizontal gaze and the bird to be 50 degrees. How tall is the tree?


2. While calculating the height of the tree on the first part, Jimmy drops and breaks his inclinometer. He turns around to find that he is directly in the middle of the first tree with the bird and another tree which he thinks is 20 feet taller than the tree with the bird. What is the angle of elevation created from Jimmy’s horizontal eyeline and the top of the second tree? (Show all work including any equations used)

Answers

Answer:

The height of first tree is

[ 5.5+18tan(50 degrees) ] ft. This is approximately 26.95 ft.

Angle of elevation from Jimmy's eyes to top of tree is arctan([20+18tan(50 degrees)] /18). This is approximately 66.53 degrees.

Step-by-step explanation:

It would help you to draw a picture for both of these.

You have a person whose height is 5.5 ft and from there horizontal gaze they see a bird from a 50 degree angle of elevation. He is standing 18ft ftom the tree.

So we will first want to find the distance from his eyesight level to the top of the tree. We can do this using the tangent ratio since we have the opposite and adjacent measurements.

Let the distance from eyesight level to the top of the tree be r.

tan(50)=r/18

Multiply both sides by 18:

18tan(50)=r

Now the height of the tree is

[5.5+18tan(50 degrees)] ft.

Now if he is the middle of two trees, then he 18 ft from the 2nd tree.

Since he says the height is 20ft taller than the first tree then it's height is

[20+5.5+18tan(50 degrees)] ft.

Now since we want to find his angle of elevation to the top of the 2nd tree we need to take out his height given us the distance from his eyesight level to the top of the tree which is

[20+18tan(50 degrees)] ft..

So again we are using the tangent ratio.

Let this angle if elevation be P.

tan(P)=[20+18tan(50 degrees)] /18

Take arctan() of both sides:

P=arctan([20+18tan(50 degrees)] /18)

Which days are part of line BE?

Answers

Answer:

B) Rays AB and AE

Step-by-step explanation:

Though A-F, A-D, and A-C all meet at one point on line B-E, point A, they aren't a part of it. Point A on line B-E marks the "midpoint" of it, and therefore, ray A-E and A-B are part of line B-E.

the area of a square postcard is 25 square inches. How long is each side postcard?​

Answers

Answer:

5 inches

Step-by-step explanation:

To find the area of a square the formula is A = bh which with a square is essentially one side squared. We know this because every side of a square is the same. We also know that 5 squared is 25 meaning the answer is 5 inches(You could also use the formula A = bh : A = 5 x 5 : A = 25).

Answer:

The side is 5 square inches.

Step-by-step explanation:

Area of square formula:

A = s x s or [tex]s^2[/tex]

To figure out the sides, we use this formula:

A = 25 ÷ s = s

But to figure out s = side, think of factors of 25 like this:

25: 1,5,25

Now let's plug in the factors of 25 to figure out the missing side length.

A = 25 ÷ 1 = 25

This is not true.

A = 25 ÷ 5 = 5

This is true.

A = 25 ÷ 25 = 1

This is not true.

So our answer is 5 square inches on each side.

The triangle below is equilateral. Find the length of side 2 in simplest radical form
with a rational denominator.
x
Submit Answer
Answer: 2
attempt 1 out of 2
PLS HELP

Answers

Answer:

[tex]x=\frac{4\sqrt{3}}{3}[/tex]

Step-by-step explanation:

From the figure attached,

ΔABC is an equilateral triangle.

Therefore, by the property of the equilateral triangle,

Measure of each angle = 60°

By applying tangent rule in the right triangle ADC,

[tex]\text{tan}(60^{\circ})=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

[tex]\sqrt{3}=\frac{4}{x}[/tex]

[tex]x=\frac{4}{\sqrt{3}}[/tex]

[tex]x=\frac{4}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3} }[/tex]

[tex]x=\frac{4\sqrt{3}}{3}[/tex]

Translate this sentence into an equation.
The sum of 22 and Greg's savings is 65.
Use the variable g to represent Greg's savings.

Answers

Answer:

22+g=65

Step-by-step explanation:

take the 22 add (sum) to g (the variable) and have them = 65

Write the equation of the line in slope-intercept form that passes through (5, –4) and (1, 7).

Answers

Answer:

Slope=[tex]\frac{11}{-4}[/tex]

Step-by-step explanation:

Calculate the volume of the following object:

Answers

Answer:

262.44 [tex]m^{3}[/tex]

Step-by-step explanation:

Volume of cylinder = [tex]\pi r^{2}[/tex]h  

Volume of cube = [tex]s^{3}[/tex]

Cylinder  

[tex](\pi )(2.5)^{2}[/tex](7) = 137.44468

Cube

[tex]5^{3}[/tex] = 125

125 + 137.44 = 262.44

Judy is having a birthday party she invited 7 freinds pver and made 98 cookies for party favours how many did each freind get

Answers

Answer:

Number of cookies each friend gets = 14 cookies

Step-by-step explanation:

Total cookies available for the party = 98

Number of friends invited = 7

how many did each freind get

Number of cookies each friend gets = Total cookies available for the party / Number of friends invited

= 98/7

= 14 cookies

Number of cookies each friend gets = 14 cookies

solve 3-x/2 less than or equal to 18

Answers

Answer:

x ≥ -30

Step-by-step explanation:

The equation is 3 - x / 2 ≤ 18.

First, subtract 3 on both sides:

- x / 2 ≤ 15.

Multiply by -2 on both sides and swap the less than or equal to sign:

x ≥ -30

Hope this helps!

Which represents the inverse of the function f(x) = 4x?

Answers

Answer:

The inverse is 1/4x

Step-by-step explanation:

y = 4x

To find the inverse, exchange x and y

x = 4y

Solve for y

1/4 x = 4y/4

1/4x = y

The inverse is 1/4x = y

Answer:

y = x/4

Step-by-step explanation:

y = 4x

x = 4y

y = x/4

Instructions: Find the missing segment in the image below plz help me

Answers

Answer:

56

Step-by-step explanation:

that is the procedure above

The missing segment in the image below is 8.

The missing segment is the side length of the small triangle that is formed by the two red lines and the green line. We can find the length of this side length by using the Pythagorean Theorem.

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the missing segment, and the other two sides are 4 and 5.

missing [tex]segment^2[/tex] = [tex]4^2[/tex] + [tex]5^2[/tex]

missing [tex]segment^2[/tex] = 16 + 25

missing [tex]segment^2[/tex] = 41

missing segment = √41

Therefore, the missing segment is √41.

Here are the steps in detail:

Identify the small triangle that is formed by the two red lines and the green line.

Label the sides of the triangle with the letters A, B, and C, where C is the missing segment.

Substitute the known side lengths into the Pythagorean Theorem.

Solve for the length of the missing segment.

To learn more about segment here:

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#SPJ2

Please help and thank you

Answers

Answer:

Step-by-step explanation:

Let's see how well I can explain this. [tex]\frac{\pi}{6}[/tex] is the same as a 30 degree angle which is in quadrant 1. If you picture the unit circle, right in the center of it is the origin. If you draw a straight line from 30 degrees and through the center (the origin), you will automatically "connect" with the reference angle of 30 (this is true for ALL angles on the unit circle). This puts us in quadrant 3. In quadrant 3, x is negative and so is y. So the terminal point of the reference angle for 30 degrees has the same exact values, but both of them are negative (again, because both x and y are negative in quadrant 3). I can't see your choices but the one you want looks like this:

[tex](-\frac{\sqrt{3} }{2},-\frac{1}{2})[/tex]

Given m || n, find the value of x and y.

Answers

Answer:

[tex]{ \tt{x = 41 \degree}}[/tex]

Interior alternate angles.

[tex]{ \tt{y + x = 180 \degree}} \\ { \tt{y + 41 \degree = 180 \degree}} \\ { \tt{y = 139 \degree}}[/tex]

Answer:

x = 45°

y = 135°

Step-by-step explanation:

Hi, Ace here!

Over here, we have a transversal with m parallel to n. Because those two lines are parallel, we can apply many theorems to this transversal.

First, we can say that m<45° and m<x° are corresponding angles. According to this theorem, that means both these degree measures are equal, thus x = 45°.

To find y, we can do 1 of two things in 1 step. We can name m<45° and m<y° as same side exterior angles, which means that they'd be supplementary angles (add up to 180°).

The second thing we can do is say m<x and m<y supplement each other because the measure of a flat line equals 180°, and according to Part-Whole-Postulate, that means all the parts of the flat line would also equal up to 180°.

Of course, these methods are practically the same due to substitution (m<x=m<45°). So m<y = 180° - m<x or m<y = 180° - 45° = 135°.

Hope this helped, let me know if you have any questions.

WHAT IS THE GRADIENT OF THE BLUE LINE?? NEED HELP URGENTLY

Answers

Answer:

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

Step-by-step explanation:

Calculate the gradient m using the gradient formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (3, 1) ← 2 points on the line

m = [tex]\frac{1-2}{3-(-1)}[/tex] = [tex]\frac{-1}{3+1}[/tex] = - [tex]\frac{1}{4}[/tex]

What's the sum of the infinite geometric series where a1 = 240, and the common ratio is r = 1∕3 ?

A: 600
B: 720
C: 360
D: 480

Answers

I think its B because it is always B

Translate the sentence into an equation.
Six times the sum of a number and 5 equals 4.
Use the variable b for the unknown number.

Answers

6b + 5=4 is correct because I know

Answer:

6(b + 5) = 4

Step-by-step explanation:

To start of we know that by saying six time the sum of a number and five. The problem wants us to put b + 5 in parenthesis to establish that the 6 is being distributed to both the b and the 5. Now that we have the first part, all we have to do is write that this expression is equal to four.

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

2. In equilateral triangle CME, MB is an altitude and DE is an angle bisector.
If BE = 27 - 5x and DM= 5x - 3, what is the length of a side?

Answers

Answer:

24units

Step-by-step explanation:

Since the triangle CME is an equilateral triangle, hence all the sides are equal. This shows that BE =DM

Given that;

BE = 27 - 5x

DM= 5x - 3

On equating, we will have;

27-5x = 5x - 3

-5x-5x = -3-27

-10x = -30

x = 30/10

x = 3

Length of EC = 2BE

EC = 2(27-5x)

EC = 2(27-5(3))

EC = 2(27-15)

EC = 2(12)

EC = 24

Hence the length of a side is 24units

A line passes through the point (8,-5) and has a slope of 5/4. Write an equation in slope intercept form for this line.

Answers

Answer:

y = 5/4x-15

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 5/4x+b

Substitute the point into the equation and solve for b

-5 = 5/4(8)+b

-5 = 10+b

Subtract 10 from each side

-5-10 = b

-15 = b

y = 5/4x-15

Step-by-step explanation:

y-y'=m(x-x')

y-(-5)=5/4(x-8)

y+5=5x/4-10

4(y+5)=4(5x/4)-10(4)

4y+20=5x-40

4y-5x=-40-20

4y-5x=-60

5x-4y-60=0

y=5x/4-15

SOMEONE HELP ME PLEASE

Answers

Answer: P (3 or odd) = 1/2

Step-by-step explanation:

Concept:  

Here, we need to know the idea of probability.  

Probability is a measure of the likelihood of an event to occur.  

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

The numbers on a dice: 1, 2, 3, 4, 5, 6

Total numbers = 6

Number of 3 = 1

Number of Odd = 3

[Since 3 is one of the odd numbers and they are overlapping, so we should subtract 1 from the number of favorable outcomes]

P (3 or odd) = Favorable / Total (refer to the attachment)

P (3 or odd) = [(1 + 3) - 1] / 6

P (3 or odd) = (4 - 1) / 6

P (3 or odd) = 3 / 6

P (3 or odd) = 1/2

Hope this helps!! :)

Please let me know if you have any questions

What is the largest three-digit palindrome divisible by 18?

Answers

Answer:

252

Step-by-step explanation:

mr. Patel travelled from Delhi to Mumbai by road in his car. a). If he travelled in his car 770 km over 22 days, then how many kilometres did he travel in one day?b). A litre of petrol takes Mr Patel’s car a distance of 14 km. How many litres would he need to go 840 km?C). Mr Patel is carrying 326 boxes of sweets in the boot of his car. If each box contains 25 sweets, how many sweets are there in his car?

Answers

Answer:

a. 35 Kilometres.

b. 60 litres.

c. 8150 sweets.

Step-by-step explanation:

Given the following data;

Distance traveled = 770 kmNumber of days = 22 days

a. To find how many kilometres he traveled in one day;

770 km = 22 days

X km = 1 day

Cross-multiplying, we have;

22X = 770

X = 770/22

X = 35 Kilometres.

b. To find how many litres he would need to go 840 km;

1 litre = 14 kilometres

X litres = 840

Cross-multiplying, we have;

14X = 840

X = 840/14

X = 60 litres.

c. To find how many sweets are there in his car;

Number of sweet box, Ns = 326 boxes

Number of sweets in each box, Sw = 25 sweets

Total number of sweets = Ns * Sw

Total number of sweets = 326 * 25

Total number of sweets = 8150 sweets.

Question 6(Multiple Choice Worth 3 points) (08.03)A group of 12 students participated in a dance competition. Their scores are below: Score (points) 1 2 3 4 5 Number of Students 1 2 4 3 2 Would a dot plot or a histogram best represent the data presented here? Why? Histogram, because a large number of scores are reported as ranges Histogram, because a small number of scores are reported individually

Answers

Answer:

Dotplot, because a small number of scores are reported individually.

Step-by-step explanation:

Given the data :

Score (points) _______ 1 _ 2 _ 3 _ 4 _ 5

Number of Students __ 1 _ 2 _ 4 __3_ 2

Both the dot plot and histogram are used to represent graphical representation of data. The histogram uses bars ot represent data values or frequency of data organized or presented as ranges. This means histograms are usually ideal for grouped data which maintain a specified amount of interval between each class Or group. The Dotplot on the other hand handles individual data values using dots that represent the frequency of each. Since the data above are reported as individual data values, then the Dotplot is an ideal choice.

Answer:

small dot plot bb

Step-by-step explanation:

xoxo

Please solve #5 and explain how you solved it

Answers

the answer is y = -2x + 10
2x + y = 10
Subtract 2x from both sides of equation.
y = 10 - 2x
Now put in slope intercept form.
y = -2x + 10
The 2 is negative. The sign stays with it.
Same for the 10. It’s positive and the sign stays with it.

Translating a sentence into a multi-step inequality
Translate the sentence into an inequality.
Four increased by the product of a number and 9 is greater than or equal to 22.

Answers

Answer:

4 + x×9 >= 22

Step-by-step explanation:

that is the word by word "translation".

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Nu iu kin bn bi 1 sng tiu lin AK? Ti sao khi ngm bn v bn bi 1 sng tiu lin AK li thng chn cch ly thc ngm 3 - im ngm chnh gia mp di mc tiu SEE QUESTION IN IMAGE urgent please answer Write one sentence in Spanish to tell what you do after school. (e.g., I start my homework at 5 p.m.)Remember:Use the correct form of one of the following stem-changing verbs: poder, dormir, querer, empezar, decir, jugar.Poder and dormir are o ue stem-changing verbs.Querer and empezar are e ie stem-changing verbs.Jugar is a u ue stem-changing verb.Decir is an e i stem-changing verb and also has an irregular yo form.Add an event time like after school, in the afternoon, at 4 p.m., every day, etc. Write one sentence in Spanish to tell what one of your friends does by himself/herself after school. (e.g., My friend Bryan sleeps for two hours after school.)Remember:Use the correct form of one of the following stem-changing verbs: poder, dormir, querer, empezar, decir, jugar.Poder and dormir are o ue stem-changing verbs.Querer and empezar are e ie stem-changing verbs.Jugar is a u ue stem-changing verb.Decir is an e i stem-changing verb and also has an irregular yo form.Add an event time like after school, in the afternoon, at 4 p.m., every day, etc.I Write one sentence in Spanish to tell what you prefer to do after school. (e.g., I prefer to do yoga in the afternoon.)Remember:Preferir is an e ie stem-changing verb.Add an event time like after school, in the afternoon, at 4 p.m., every day, etc. Write one sentence in Spanish describing an activity you do with someone else after school. (e.g., I run in the park with my dog Sparky at 6 p.m.)Remember:What is the meaning of the preposition con?Add an event time like after school, in the afternoon, at 4 p.m., every day, etc. Write one sentence in Spanish to state what you and your family (or friends) like to do (after school). (e.g., My family and I like to paint.)Remember:You use the indirect object pronouns with the verb gustar. (b) Which dry fruit do people crack on Bhaitika Day? whats does it me study the exercises in which both addends are negative.what do you notice about the sum What is the relationship between coronary artery disease and a heart attack?A. Coronary artery disease is a symptom of heart attacks.B. Heart attacks reduce blood flow to the heart and cause coronary artery disease.C. Coronary artery disease can reduce blood flow to the heart and cause heart attacks.D. Heart attacks occur when coronary artery disease is treated. Is x=-2 a solution for the equation below? A cylinder has a height of 16 cm and a radius of 5 cm.A cone has a height of 12 cm and a radius of 4 cm.if the cone is placed inside the cylinder as shown,what is the volume of the air space surrounding the cone inside the cylinder help please ITS OF TRIGONOMETRYPROVE QUESTION 11Which of the following is an important consideration in setting up the proper environment to complete tasks on time? please help, will give brainliest for correct answer Please help!Which term is best described as a series of ridges and mounds that protect the marshes of Louisiana from hurricanes?A) estuariesB) salt domesC) cheniersD) terraces Which quadrilateral has equal diagonalsSelect one:a. trapezoidb. rectanglec. parallelogramd. rhombus A recipe requires 500 mL of milk. You will make the recipe once a month for the next 4 months. You do not use milk other than for cooking. Which container of milk should you buy? (1L=1000 mL) * What is the image of the point (3, 2) after a rotation of 90 counterclockwise about the origin? what should be done to the people who violate the social rules Amanda has 1 3/4yds of red ribbon and 7/8yds of greenribbon. What is the total amount of ribbon thatAmanda has? (write answer as a fraction) What can the reader infer about the importance the discovery of the shipwrecks has to archaeologists Please answer ASAP!!! A ski store has 60 different boots available, 30 different pairs of skis, and 40 different hats. If a customer were to only buy ONE item, how many different ways can a customer purchase an item from the store?