Properties of Definite Integrals A definite integral is a function that assigns a value to the area under a curve on a given interval.

Answers

Answer 1

Properties of Definite Integrals A definite integral is a function that assigns a value to the area under a curve on a given interval are additive , linearity , continuity , monotonicity and upper and lowersums.

1. Additivity: The definite integral of a sum is equal to the sum of the definite integrals.

2. Linearity: The definite integral of a linear function is equal to the product of the function's slope and the length of the interval.

3. Continuity: The definite integral of a continuous function is equal to the area under the curve between two points.

4. Monotonicity: If a function is increasing or decreasing on a given interval, then the definite integral of the function is also increasing or decreasing.

5. Upper and Lower Sums: The upper and lower sums of a function are the sums of the areas of rectangles constructed under or over the curve between two points. The definite integral of the function is equal to the difference between the upper and lower sums.

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Related Questions

(-3, -4) and (-5, y); m = -9/2

Answers

Answer:

the answer would be y= -40

PLEASE HELP ASAP ITS DUE SOON

Lines R and S are parallel Find the value of x, then find the measure of m<1 and m<2.
m<1=(70-2x)"
m<2 = (82-3x)
x=
m<1=
m<2=


m<1 and m<2 are corresponding angle​

Answers

Answer:

im very confused aadly

What is the greatest common factor of 12a and 9a2

Answers

Answer:

For these types of problems, You must look at the coefficients and variables separately and find the GCF for each. Then, combine the two

First, take 12 and 9

Factors of both

9- 1, 3, 9

12- 1, 2, 3, 4, 6, 12

So the gcf of 12 and 9 is 3

Now do the variables a and a^2

a^2 is just a twice

The GCF is a

Now combine a and 3

Answer: GCF is 3a

Answer:

GCF is 3a

Step-by-step explanation:

I just know LOLLL

A unit of electricity costs 13.2 pence. On average, Tanya uses 90 units of electricity per week. She pays for her bill in 12 weeks. How much will her electricity bill be then? £

Answers

Answer:

90*12=1080

1080*13.2=14256

14256:100=142,56pounds

HELP ME SOLVE THIS!!!

HELP ME SOLVE THIS!!!

Answers

m= - 2, (5, - 1) = 4

Answer:

what are u solving for????????

Step-by-step explanation:

6. There are 30 students doing an
experiment in Science class. If 40% are
measuring the chemicals for an experiment,
what percent are NOT measuring chemicals?
a. 12%
C. 40%
b.
18%
d. 60%

Answers

Answer:

60%

Step-by-step explanation: THeres 30 students, 40% are measuring so that leaves 60% not measuring because in order to have 100% students you'll need 60 to add to the current 40% of students already doing the measuring.

Answer:

The correct option would be D. 60%

Step-by-step explanation:

This is because if only 40% percent of the students are measuring the chemicals then, out of 100%, 60% of students are not measuring chemicals.

Hope this helps!

A yard dart is thrown from a height of 3 feet with an initial velocity of 25 feet per second at an elevation angle of 70°.

How long is the dart in the air? Round to the nearest tenth

A. 0.7

B. 0.8

C. 1.5

D. 1.6

Answers

Answer:

D

Step-by-step explanation:

Plugged it into a projectile motion calc, got 1.58. So 1.6 (rounded).

Which set of angles will be complimentary

Which set of angles will be complimentary

Answers

∠1 + ∠3 + 90° = 180°

∠1 + ∠3 = 90°

∠3 = ∠4 (vertically opposite angles)

∠1 + ∠4 = 90°

Therefore, the answer is ∠1 + ∠4

4 3/8 + 5 1/2= in fractions

Answers

Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

A plane is flying over your head at 30, 000 feet. You calculate the angle of elevation to be 65 degrees . At that time how far is the plane from you?(round to the nearest foot)

Answers

Answer:

33101 ft

Step-by-step explanation:

Let the distance is x.The height is 30000 ft.The angle of elevation is 65°

Use trigonometry to solve.

x is the hypotenuse and 30000 ft is the opposite side of 65° angle:

sine = opposite / hypotenusesin 65° = 30000 / xx = 30000 / sin 65°x = 33101 ft (rounded)

Refer to the attachment

A plane is flying over your head at 30, 000 feet. You calculate the angle of elevation to be 65 degrees

help please thanks very much​

help please thanks very much

Answers

Answer:

the right answer is 18 because 120 divided by 20 is 6 so the you do 6 times 3

Answer:

the answer is 18

Step-by-step explanation:

20:3=workers:casiers

120:x

cross multiply so that means 3 multiplied by 120 which is 360 divided by 20 which is 18

hope this helps :)

Twenty-five people in a survey were asked to give their current checking account balances. Use the balances shown in the following list to complete the frequency distribution table.
$220
$337
$29
$60
$201
$519
$462
$290
$131
$572
$227
$111
$124
$509
$331
$306
$439
$28
$504
$431
Fill in the missing information.
Class Intervals
Class Frequency
(Account Balances) (Number of People)
$0-$99
$431
$83
$451
$417
$341
CIP

Answers

Twenty-five people in a survey were asked to give their current checking account balances and the frequency = 4.

What is frequency and example?

The frequency of a particular data is the number of times the data value occurs. We represent the frequency of a data value by f. For example, if five students got an A in science, and then the grade A is said to have a frequency of 5.

Given that;

Class intervals              Class frequency

(Account Balance)          (No of people)

 $0 - $99                                ?

Entries in this ($0 - $99) range are $29 , $60 , $28 , $83 = 4

Therefore, class frequency (no of people) = 4

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Shawn and Nick are both selling t-shirts to raise money for their school trip. Shawn spent $250 on supplies and charges $35 per shirt. Nick spent $100 in supplies and charges $25 per shirt. How many shirts must be sold in order for Shawn to earn the same as Nick?​

Answers

Answer:

15

Step-by-step explanation:

Shawn: 35x - 250

Nick: 25x - 100

35x - 250 = 25x - 100

          10x = 150

              x = 15

What is the image of the point (6,-4) after a rotation of 90 degrees counterclockwise about the origin?

Answers

Answer: (4, 6)

Step-by-step explanation:

You change the numbers places (x to y and y to x) while switching the sign of the original y value.

what does the global climate change have to do with mcr

Answers

Answer:

Everything bro

Step-by-step explanation:

which value of x is the solution of the equation 2/3x + 1/2 = 5/6?

Answers

Answer:

2

Step-by-step explanation:

2/3(2) + 1/2 = 5/6

If it's 2/3 * X then x is equal to 1/2.

Order the following values from least to greatest |-2| |4.5| -7 3

Answers

Answer:

-7, |-2|, 3, |4.5|

Step-by-step explanation:

-7 is the lowest number, since it is a negative. The absolute value of -2, or |-2|, is 2 making it the second lowest. 3 comes next. The absolute value of 4.5 is 4.5, being the greatest number.

Answer:

-7, |-2|, 3, |4.5|

Step-by-step explanation:

First, let's find -2 and |4.5| .

Absolute value of a number is its distance from 0. Remember, absolute value is always zero or positive.

Now, let's use a number line to order the numbers. Numbers to the left are less than numbers to the right.

The values in order from least to greatest is as follows: -7, |-2|, 3, |4.5|.

Five less than twice the sum of a number n and twelve

Answers

5-2(n+12) that’s the equation. I hope this helped

How does an angle complementary to acuate angle A compare with an angle supplementary to angle A?

Answers

The angle complementary to an acute angle A is always acute and smaller than 90 degrees, while the angle supplementary to angle A is always larger than 90 degrees, they cannot be equal since they are adding up to 90 degrees and 180 degrees respectively.

What is Complementary Angle

A complementary angle is a pair of angles that add up to 90 degrees. Two angles are said to be complementary if the sum of their measures is 90 degrees. The two angles are called complementary angles because they "complete" a right angle.

An angle is considered acute if it measures less than 90 degrees. A complementary angle is an angle that, when added to another angle, will sum up to 90 degrees. So, if angle A is acute, then its complement angle will also be acute.

On the other hand, an angle supplementary to angle A is an angle that, when added to angle A, will sum up to 180 degrees.

So, an angle complementary to an acute angle A is always acute and smaller than 90 degrees, while an angle supplementary to angle A will always be larger than 90 degrees. They can't be equal since they are adding up to 90 degrees and 180 degrees respectively.

For example, if angle A measures 60 degrees, its complementary angle will measure 30 degrees (90 - 60 = 30) and its supplementary angle will measure 120 degrees (180 - 60 = 120).

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Meals are cooked in a process with two resources. The first resource has a capacity of 28 meals per hour. The capacity of the second resource is 24 meals per hour. The first resource has 9 workers and the second resource has 8 workers. Demand for this process is 31 meals per hour. Wages are $24 per hour. Instruction: Round your answer to four decimal places. What is the cost of direct labor (in $s)? _____________ per unit

Answers

Answer:

The cost of direct labor (in $s) is $7.85 per unit.

Step-by-step explanation:

First resource total wages per hour = Number of workers in first resource * Wages per hour = 9 * $24 = $216

Second resource total wages per hour = Number of workers in second resource * Wages per hour = 8 * $24 = $192

Total wages of the process per hour = First resource total wages + Second resource total wages = $216 + $192 = $408

Cost of direct labor per unit = Total wages of the process per hour / (Capacity of first resource + Capacity of second resource) = $408 / (28 + 24) = $7.85

Therefore, the cost of direct labor (in $s) is $7.85 per unit.

w
courses/22406/quizzes/25030/take
OPA
Education Galaxy
D
Ennis 150
Unblocked Games
New tab 4th bone game
1. Francine can decorate 3 cakes in 20
minutes. At this rate, how many cakes can
Francine decorate in one hour?
None of the Above

Answers

Answer:

Francine can decorate 9 cakes in 1 hour.

Step-by-step explanation:

Since there are sixty minutes in an hour, knowing that 20 × 3 = 60, all you have to do is multiply 3 by itself to get 9.

HELP ASAP DUE TODAY I DON"T KNOW I AM NOT REALLY SMART SO HELLLLLLLLLLLLLP ME!!!! WORTH 50 POINTS

HELP ASAP DUE TODAY I DON"T KNOW I AM NOT REALLY SMART SO HELLLLLLLLLLLLLP ME!!!! WORTH 50 POINTS

Answers

Answer:16

Step-by-step explanation: I took the same quiz

Sam buys 4 boxes of the Crispy Crunch Cereal at Store A. What
fraction of the original price of each box of cereal does he pay per
box? Enter your answer and explanation in the box.
B 1 u
X, Ω
Store Discounts
Sam shops at three stores and each store is having its own
sale as described below.
Store A Crispy Crunch Cereal: Buy 3 boxes, get 4th free!
Store B: Take off the original price of one item!
Store C: Mystery Discount! Percent off your total purchase will
be revealed at the register!

Answers

Answer: 3/4 of the original price.

Step-by-step explanation:

Ok, so Sam buys 4 boxes in Store A.

We know that in Store A you can get 4 boxes paying only for 3.

If P is the price of a Box, then he got 4 boxes and paid 3*P

then the amount that he paid for each box is equal to the total amount that he paid divided the number of boxes that he received.

this is: 3P/4 = (3/4)*P

Meaning that he paid 3/4 of the original price for each box.

The model below illustrates what problem

Answers

The problem illustrated by the model given is B. x = 1 + 2 - 6

Which model shows the problem ?

The model that shows the problem would be the one that explains the movement of the problem in the number line.

The problem starts at 1 and then moves to 3 and then moves to - 3.

From the options, the only model to represent this would be  x = 1 + 2 - 6. This is because the initial position of 1 corresponds with the first value of 1. The movement to 3 happens when 2 is added to 1. And finally, the movement to - 3 happens when - 6 is added.

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The model below illustrates what problem

The measure of ∠BAC is π/3 radians and the measure of ∠CAD is π/2 radians. What is the measure of ∠BAD?

The measure of BAC is /3 radians and the measure of CAD is /2 radians. What is the measure of BAD?

Answers

9514 1404 393

Answer:

  5π/6 radians

Step-by-step explanation:

The whole is the sum of the parts.

  ∠BAD = ∠BAC +∠CAD

  ∠BAD = π/3 + π/2 = π(2/6 + 3/6)

  ∠BAD = 5π/6



simplify 1 1/6 + 2 1/4 -1/3​

Answers

The fraction expression 1 1/6 + 2 1/4 -1/3​ when simplified is 3 1/12

How to simplify the expression

Given that

1 1/6 + 2 1/4 -1/3​

Connvert the fractions to improper numbers

so, we have the following representation

1 1/6 + 2 1/4 -1/3​ = 7/6 + 9/4 - 1/3

Take the LCM and evaluate

1 1/6 + 2 1/4 -1/3​ = (14 + 27 - 4)/12

So, we have

1 1/6 + 2 1/4 -1/3​ = 37/12

Convert to mixed numbers

1 1/6 + 2 1/4 -1/3​ = 3 1/12

Hence, the solution is 3 1/12

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PLEASE HELP
The table of values represents an exponential function.

What is the y-coordinate of -3f(x-1) when x = 0
Enter your answer in the box.
SEE PHOTO

PLEASE HELPThe table of values represents an exponential function.What is the y-coordinate of -3f(x-1)

Answers

The y-coordinate of -3f(x-1) when x = 0 is -63

What is the y-coordinate of -3f(x-1) when x = 0

From the question, we have the following parameters that can be used in our computation:

The table of values

So, we have

-3f(x - 1)

When x = 0, we have

y = -3f(0 - 1)

This gives

y = -3f(-1)

From the table, we have

y = -3 * 21

Evaluate

y = -63

Hence, the y-coordinate is -63

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Point A is located at (1, 2). Point B is located at (4, 6). Use this information to determine the length of the line, rounded to the nearest whole number.

Answers

If Point A is located at (1, 2) and Point B is located at (4, 6), the length of the line between points A and B is 5 units.

To determine the length of the line between points A and B, we can use the distance formula, which is a formula used to calculate the distance between two points in a coordinate plane. The distance formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points and d is the distance between them.

Using the coordinates of points A and B, we can substitute their values into the distance formula to find the length of the line between them:

d = √((4 - 1)² + (6 - 2)²)

d = √(3² + 4²)

d = √(9 + 16)

d = √25

d = 5

Rounded to the nearest whole number, the length of the line is also 5 units.

In conclusion, we can use the distance formula to find the length of the line between two points in a coordinate plane. The distance formula uses the coordinates of the two points to calculate the distance between them. The resulting distance can be rounded to the nearest whole number, if needed.

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If a recipe for 24 cookies needs 2 cups of flour, how many cups would we need to make 42 cookies?

Answers

Answer:

3 1/2 cups

Step-by-step explanation:

24=2

42=x

24x=84

/24   /24

3.5

Explain
Find all the values of x for which the statement is true, |x^2+9|=x^2+9​

Answers

the 2 statements are identical even if one has absolute value
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