The integral that represent the area enclosed by y = x +1, y = 4-X
y = 0,X = 0 is:​

Answers

Answer 1

Answer:

[tex]\displaystyle A = \int\limits^{1.5}_0 {(x + 1)} \, dx + \int\limits^4_{1.5} {(4 - x)} \, dx[/tex]

General Formulas and Concepts:

Algebra I

FunctionsFunction NotationPoints of Intersection

Calculus

Integrals - Area under the curve

Bounds of Integration

Step-by-step explanation:

Step 1: Define

Identify

y = x + 1

y = 4 - x

y = 0

x = 0

Step 2: Identify Info

Graph the functions - See Attachment

Bounds of Integration: [0, 4]

Point of Intersection: x = 1.5

Step 3: Find Area

Set up [Integral - Area]:                                                                                 [tex]\displaystyle A = \int\limits^{1.5}_0 {(x + 1)} \, dx + \int\limits^4_{1.5} {(4 - x)} \, dx[/tex]

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

Unit: Integration - Area under the curve

Book: College Calculus 10e

The Integral That Represent The Area Enclosed By Y = X +1, Y = 4-Xy = 0,X = 0 Is:

Related Questions

Plz help 27 pt this is getting graded plz plz Plz

Answers

Answer:

517.2

Step-by-step explanation:

It has sides you're not seeing so don't forget those.

You need to find the area of the front, back, two sides, and bottom

Front & back:

6*5.2* 1/2

31.2/2 = 15.6 for each

Sides:

27*6 = 162 each

Bottom:

6*27 = 162

162+162+162+15.6+15.6= final answer

Answer: B

Step-by-step explanation:

First, you do 5.2 times 6 divided by two which is 15.6. Now you do 15.6 times two since there are two triangles and get 31.2. Now you do 27 times 6 times two and get 324 + 31.2 = 355.2. Lastly, you do 27 times 6 to get 162. 162+355.2 = 517.2

Please help me!
Will give brainlst :)

Answers

To figure this out we need to plug in the numbers. If the end numbers on both sides equal each other it is the solution.

x = 8 & y = 5

5(8) - 4(5) = 20
40 - 20 = 20
20 = 20

3(5) = 2(8) + 1
15 = 16 + 1
15 = 17

As you can tell the first equation makes sense so that is the solution.

Wavelength and Frequency

A chord consists of notes that sound good together. the C major chord, starting at middle C, has the following frequencies:

C - 262 Hz
E - 330 Hz
G - 392 Hz

Determine the ratio of the frequency of G to C. Express the answer in a simple integer ratio. (Due to rounding the ratio will be approximate. )

a. 5 to 4
b. 3 to 2
c. 6 to 5
d. 9 to 8

Please select the best answer from choices provided

Answers

Answer:

B. 3 to 2

Step-by-step explanation:

I calculated it logically

The ratio of the frequency of G to C is 1.5. So, option b is correct.

What is meant by frequency ?

Frequency of a wave is defined as the number of oscillations completed by the wave in one second.

Here,

The frequency of note G, f(G) = 392 Hz

The frequency of note C, f(C) = 262 Hz

The ratio of the frequency of G to C, r = frequency of G/frequency of C

r = f(G)/f(C)

r = 392/262

r = 1.496 approximately r = 1.5

Hence,

The ratio of the frequency of G to C is 1.5

To learn more about frequency, click:

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The graph of a linear equation is shown. y ОN HNWO -7-6-5-4-3-2-11+1234 5 6 7 -27 -3 가 Place values in the table to show three ordered pairs that are each part of the solution set of the linear equation. 2 P. y – 4 2 -6 -3 - 6​

Answers

Answer:

n

Step-by-step explanation:

s

There were 35 children and 10 adults at a cookout. What is the ratio of adults to children at the cookout?

Answers

Answer:

2:7

Step-by-step explanation:

10:35 can also be written as 2:7

Thenks and mark me brainliest :))

line f has a slope of -3. what is the slope of the line that is parallel to line f

Answers

Answer:

A line parallel has the same slope, so -3

The slope of the line that is parallel to line f is -3.

The given line f has a slope of -3.

We need to find the slope of the line that is parallel to line f.

What are parallel lines slope?

The slope of parallel lines. The slope of parallel lines is equal. The parallel lines are equally inclined with the positive x-axis and hence the slope of parallel lines is equal. If the slopes of two parallel lines are represented as [tex]m_{1}[/tex], [tex]m_{2}[/tex] then we have [tex]m_{1}=m_{2}[/tex].

So, the slope of the parallel line=-3

Therefore, the slope of the line that is parallel to line f is -3.

To learn more about the slope of parallel lines visit:

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It is known that ARST - AWXY. If RS =18, ST = 25, and TR=11 then which of the following is closest
to the ratio of XY to WX?
(1) 0.44
(3) 2.27
(2) 1.39
(4) 0.72

Answers

Answer:

[tex]XY : WX = 1.39[/tex]

Step-by-step explanation:

Given

[tex]RS = 18; ST = 25; TR = 11[/tex]

Required

Which is closest to [tex]XY : WX[/tex]

From the question, we understand that: [tex]\triangle RST[/tex] and [tex]\triangle WXY[/tex] are similar.

This means that, the following sides are similar:

[tex]RS \to WX[/tex]

[tex]ST \to XY[/tex]

[tex]TR \to YW[/tex]

So:

[tex]XY : WX = ST : RS[/tex]

This gives:

[tex]XY : WX = 25 : 18[/tex]

Express as fraction

[tex]XY : WX = \frac{25 }{ 18}[/tex]

[tex]XY : WX = 1.39[/tex] --- approximated

A recent survey showed that 23.3 million adults have cut the cord on cable TV services, a 30% increase fron the previous year. If this trend continues, how many millions if adults can be expected to cut the cord next year?​

Answers

Answer:

30,290,000 people

Step-by-step explanation:

The question is asking if the trend continues from the PREVIOUS year, so we would find the 30% of 23,300,000

23,300,000/100 = 233,000 = 1%

233,000 x 30 = 6,990,000

23,300,000 = 6,990,000 = 30,290,000

If right I’ll mark brainiest if u have questions put it in the comments

Answers

Answer:

6

Step-by-step explanation:

The interquartile range is calculated by subtracting the first quartile from the third quartile. Box and whisker plots make it pretty easy to find the quartiles. The first quartile is the point where the box starts, and the third is where the box ends. The second is the median/line in the middle of the box.

So for that first box plot on the top, the first quartile is 7, because that's where the box begins. The third quartile is 22 because it's where the box ends.

For the second one, the first quartile is 8 and the third is 17.

To find the interquartile range of each, subtract the first quartile from the third. 22-7 = 15 and 17-8 = 9.

Now to find the difference in the interquartile ranges, subtract 9 from 15. You get 6, so that is the answer :)

solve for x. label the sides adj, opp, and/or hyp based on the part you see. show work round to the nearest 10th

Answers

Answer:

[tex]x=37.4[/tex]

Step-by-step explanation:

In an right triangle, the cosine of an angle is equal to its adjacent side divided by the hypotenuse (a/h).

Therefore, we have the following equation:

[tex]\cos 68^{\circ}=\frac{14}{x},\\x=\frac{14}{\cos 68^{\circ}}\approx\boxed{37.4}[/tex]

what is 3 x 3 x 9 x 9 x 81 x 81 x 6561 x 6561

Answers

Answer:

205891132094649

Amil has a recipe that calls for 2/3 cups of flour. Amil wants to make 4 1/2 times that recipe. How many total cups of flour does Amil need?

Answers

She will need 3 cups

:)

Answer:

she will need 3 cups

Step-by-step explanation:

the total cups of flour Amil is 3 cups

Suppose you have two rectangular prism with dimensions 2 feet by 3 feet by 5 feet. You want to join prisms together to form a larger rectangular prism. Which faces should you join if you want to make a prism with the least possible surface area?

Answers

Answer:

Below in bold.

Step-by-step explanation:

You would join the faces with the greatest area

That is the faces with dimensions 3 feet by 5 feet.

A particle moves along the x-axis with the given acceleration function a(t) = 8t - 6, initial position s(0) = 2, and initial velocity v(0). Find the position function.

Answers

Answer:

[tex]s(t) = \frac{4t^3}{3} - 3t^2 + v(0)t + 2[/tex]

Step-by-step explanation:

Relation between acceleration, velocity and position:

The velocity function is the integral of the acceleration function.

The position function is the integral of the velocity function.

Acceleration:

As given by the problem, the acceleration function is:

[tex]a(t) = 8t - 6[/tex]

Velocity:

[tex]v(t) = \int a(t) dt = \int (8t - 6) dt = \frac{8t^2}{2} - 6t + K = 4t^2 - 6t + K[/tex]

In which the constant of integration K is the initial velocity, which is v(0). So

[tex]v(t) = 4t^2 - 6t + v(0)[/tex]

Position:

[tex]s(t) = \int v(t) dt = \int (4t^2 - 6t + v(0)) dt = \frac{4t^3}{3} - \frac{6t^2}{2} + v(0)t + K = \frac{4t^3}{3} - 3t^2 + v(0)t + K[/tex]

The initial position is s(0) = 2. So

[tex]s(t) = \frac{4t^3}{3} - 3t^2 + v(0)t + 2[/tex]

Please answer both!!

Answers

27. 9x^2-24x+16=0
(3x-4)^2=0
3x-4=0
3x=4
x=4/3


28. 9x^2-30x+26=1

9x^2-30x+26-1=0

9x^2-30x+25=0
(3x-5)^2=0
3x-5=0
3x=5
x=5/3

- Solve the equation 3 + n = 12​

Answers

Answer:

n = 9

Step-by-step explanation:

Method 1(Algebra) :

3 + n = 12

3 - 3 + n = 12 - 3

n = 9

Method 2:

3 + n = 12

Move 3 to the other side of the equation.

n = 12 - 3

n = 9

I need an answer quick!!!

Answers

Answer:

0.34

Step-by-step explanation:

it is between 0.3 and 0.4 so obviously 0.3 is going to be there, but the next digit will be 4 because it moves 4 places to the right.

Answer:

The answer is .34

When you see a question like this you just go down to the next decimal place. In this example you count: .31, .32, .33, .34... and so on.

What would this One be??

Answers

Answer:

the pre-image and the image are congruent

Step-by-step explanation:

Answer:

i think its c

Step-by-step explanation:

Directions: Solve for the surface area of the following figures using the formula.

no links pls. i really need it T-T​

Answers

Answer:

3^3 x 3.14

9 x 3.14 = 28.26

28.26  x 2 = 56.52

2 x 3.14 x 3 = 18.84

18.84 x 10 = 188.4

Now lets add all given areas:

56.52 + 188.4 = 244.92 m^2 for question 1

4 x 3.14 x 12^2

4 x 3.14 x 144 = 1,808.64 cm^2 is your answer for question 2

14^2 x 3.14

196 x 3.14 = 615.44

3.14 x 14 x 33 = 1450.68

1450.68 + 615.44 = 2,066.12 cm^2 is your answer for question 3 I think

If a car moves 12 km North,19 km east, and 12 km south, what is its displacement

Answers

Answer:

19 km east

Step-by-step explanation:

By going North 12 then south 12 the two cancel eachother out leaving only the eastern movement

Answer:

19 km, East

Step-by-step explanation:

I hope you get it right

the auto parts department of an automotive dealership sends out a mean of 66 special orders daily. what is the probability that, for any day, the number of special orders sent out will be no more than 33

Answers

Answer:

0% probability that, for any day, the number of special orders sent out will be no more than 33

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 66 special orders daily

This means that [tex]\mu = 66[/tex]. We have the mean during a time interval, which means that the number of special orders follow a Poisson distribution, which has [tex]\sigma = \sqrt{\mu} = \sqrt{66}[/tex]

What is the probability that, for any day, the number of special orders sent out will be no more than 33?

Since the Poisson distribution, which is discrete, is approximated to the normal(which is continuous), we have to use continuity correction, and thus, this probability is P(X < 33 - 0.5) = P(X < 32.5), which is the p-value of Z when X = 32.5.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{32.5 - 66}{\sqrt{66}}[/tex]

[tex]Z = -4.12[/tex]

[tex]Z = -4.12[/tex] has a p-value of 0.

0% probability that, for any day, the number of special orders sent out will be no more than 33

What is the simple interest on 500 for 5 years at the rate of 5% per annum

Answers

Answer:

125

Step-by-step explanation:

Formula Simple interest:

P x r x t

I = principal x rate x time
I = 500 x .05 x 5
I = 125

( time is always expressed in years and you convert rate to a decimal )

What is the degree?

6−n

2

+5n

3

Answers

Polynomial Degree:
3
3
Leading Term:
5
n
3
5
n
3
Leading Coefficient:
5

Once again, consider the data for Fred's caloric intake. 2000 2200 2100 2400 2500 1900 2200 2200 2700 2600 Find the : (enter your answers as numbers) Sample standard deviation (rounded to the nearest hundredth)

Answers

Answer:

The sample standard deviation is of 248.19.

Step-by-step explanation:

First we find the sample mean, which is needed to find the sample standard deviation.

Sample mean:

Sum of all values in the sample, divided by the number of values. So

[tex]M = \frac{2000+2200+2100+2400+2500+1900+2200+2200+2700+2600}{10} = 2280[/tex]

Sample standard deviation:

Square root of the sum of the difference squared between each value and the mean, divided by the number of values. So:

[tex]S = \sqrt{\frac{(2000-2280)^2+(2200-2280)^2+(2100-2280)^2+(2400-2280)^2+(2500-2280)^2+(1900-2280)^2+...}{10}} = 248.19[/tex]

The sample standard deviation is of 248.19.

Can someone help me or explain how to find the missing value from the simple interest?

Answers

This is the working and answers

out of 20 consecuative whole number two are chsen at random.then the probability that ther?​

Answers

Answer:

2/20

Step-by-step explanation:

since,there are 20 whole number and if u put 2 random number the,

probability(P)=favorable outcome/possible outcome

so p=2/20

Thank You

A boat's value over time is given as the function f(x) and graphed below. Use A(x) = 400(b)x + 0 as the parent function. Which graph shows the boat's value decreasing at a rate of 40% per year?

Answers

Answer: I can't really tell you the answer because you didn't show the graphs...

Step-by-step explanation:

A boat's value over time is given as the exponential function f(x) = 400(0.6)ˣ

What is an exponential function?

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

Given that the boat's value decreasing at a rate of 40% per year, hence:

b = 100% - 40% = 60% = 0.6

A boat's value over time is given as the exponential function f(x) = 400(0.6)ˣ

Find out  more on exponential function at: https://brainly.com/question/12940982

what is the slope of this graph

Answers

Answer:

1

Step-by-step explanation:

Trust

 A 20-sided die is rolled.

A) Find the probability that the die shows a number greater than 15.

B) Find the probability that the die shows an even number.

C) Find the probability that the die shows a number that is not 5, 6, 7, or 8.

D) Find the probability that the die shows a number that is Prime.

Answers

Answer:

A) .25 or 25% or 1/4

B) .50 or 50% or 1/2

C) .55 or 55% or 11/20

D) .4 or 40% or 2/5

10+4y=20
Help me and out the steps in please

Answers

Answer: 10+4y=20

4y= 10

y= 10/4

y= 5/2

Step-by-step explanation: above

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