P. 1. Evaluate the double integral

Answers

Answer 1

The given double integral results [tex]\frac{e^8-1}{4e^8}=0.25[/tex]

Integration

The integrals are the opposite of derivatives. They are used in several applications, like: calculations of areas, volumes and others.

For solving an integration, you should know its rules. For this question will be necessary to apply the following integration rules:

For constant function - ∫b dx = b ∫ dx= bx+CFor integration by parts - ∫u v dx = uv -∫v duFor exponential function - [tex]\int\ e^x \, dx[/tex] =[tex]e^x+C[/tex]

Changing the order integration

[tex]\int _0^2\int _0^xe^{-2x^2}dydx[/tex]

[tex]\int _0^2xe^{-2x^2}dx[/tex]

[tex]\frac{e^8-1}{4e^8}=0.25[/tex]

Related Questions

What is the radius of the circle?

Answers

Answer:

13cm

Step-by-step explanation:

In this case you have to use the Pythagorean theorem.

cy = 24/2

cy=12 cm ( a perpendicular drawn to a chord from the center bisects the chord..

ac=5 cm (given)

now,

ay^2= 25cm + 144 cm

ay^2 = 169 cm

√169 = 13 cm

Answer:

13 cm

Step-by-step explanation:

Since AC is perpendicular to XY , and XA and AY are both radii of the same circle, you can say that AC is a perpendicular bisector.

From there, we can say that XC is 1/2 of 24 cm, or 12 cm.

We can then form triangle ACX use the Pythagorean theorem to find the length of AX.

The square root of 12^2 + 5^2 is 13.

Therefore, the radius of the circle is 13 cm

What are the vertices of A'B'C if ABC is dilated by a scale factor of 1/6?

Answers

The coordinates of the vertices A'B'C when ABC is dilated by a scale factor of 1/6 are 1/6(x,y)

How to determine the vertices?

The rule of transformation is given as:

Dilation by a scale factor of 1/6

Mathematically, this is represented as:

(x,y) => 1/6(x,y)

This means that the coordinates of the vertices ABC are multiplied by 1/6 to get the coordinates of the vertices A'B'C

Answers

Answer:

x = 41

Step-by-step explanation:

x = 180 - 97 - 42

x = 41

Sum of the triangle = 180

I hope my answer helps you.

Answer:

x° = 41°

Step-by-step explanation:

x° = (180-42- 97)° = 41°

Hope this helps

Define a rational number and show that no rational number x belongs to Q satisfies x² = 2

Answers

Answer:

A rational number is a number that can be expressed as a fraction of two integers.

if x²=2 then x=√2, but √2 is an irrational number (not rational), so there is no rational number x that satisfies x² = 2.

Step-by-step explanation:

Which circle will have the largest radius?
O OAC = 16 cm
OOD.r=20 cm
OOC.r= 21 cm
O OB. C = 18 cm

Answers

Answer:

c-21cm

Step-by-step explanation:

21 is the biggest one(unless the options are the diameters..it wouldstill be option c though)

step by step
short answer please

Answers

The appropriate value for the median is less than 25. In the positively skewed distribution, if the data is bent on the lower side( which means the median is less than 25), then the average(mean) will be more than the middle value(median)

A city has 15 stations, including 6 hip hop stations. What is the possibility that a randomly chosen radio station in the city was a hip-hop station? Write your answer as a fraction or whole number.

Answers

Answer:

I'm pretty sure the answer is 6½

Hallar M=64(n+2)=141(5)
Ayuda en este ejercicio porfa :,(

Answers

Answer:

n≈9

n=9.015625

Step-by-step explanation:

64(n+2)=141(5)

Break up the parenthesis.

64n+128=705

Subtract 128 from both sides.
64n=577

Divide 64 from both sides.

577/64

Then you get your answer.

n≈9

The length of a rectangle is 4FT less than three times the width, and the area of the rectangle is 55FT. Find the dimensions of the rectangle.

Answers

Answer:

The required dimensions of rectangle are 11 feet and 5 feet.

Step-by-step explanation:

Given, The length of a rectangle is 4 ft less than three times the width, and the area of the rectangle is 55 ft².

Let's assume width of rectangle be x feet and length be 3x - 4 feet. Using the formula of Area of rectangle we'll find the value of length and width.

[tex] \\ \dashrightarrow{ \red{ \underline{ \underline {\sf\: \:Area _{(rectangle)} = Length \times width}}}} \\ \\ [/tex]

Substituting the required values:

[tex]\dashrightarrow\: \: (3x - 4)(x) = 55 \\ [/tex]

[tex]\dashrightarrow\: \: 3x^2 - 4x = 55 \\ [/tex]

[tex]\dashrightarrow\: \: 3x^2 - 4x - 55 = 0 \\ [/tex]

[tex]\dashrightarrow\: \: 3x^2 + 11x - 15x - 55 = 0 \\ [/tex]

[tex]\dashrightarrow\: \: x(3x+11) -5(3x+11) = 0 \\ [/tex]

[tex]\dashrightarrow\: \: (x-5)(3x+11) = 0 \\ [/tex]

[tex] { \red{ \dashrightarrow\: \: { \underline{ \underline{ {x = 5 \: or \: \dfrac{-11}{3}}}}}}} \\ \\ [/tex]

Hence,

Length of rectangle = 3x - 4 = 3(5) -4 = 11 feet Breadth of rectangle= x = 5 feet

[tex]\therefore[/tex] The required dimensions of rectangle are 11 feet and 5 feet.

100 points! Please help find the direction!

Answers

The direction will be resultant

A=11iB=20i+9√3j

Now

R=√A²+B²+2ABcos60R=√(11i)²+(20i+9√3j)²+2(11i)(20+9√3j)(1/2)R=√1155.5R≈33.98°

PLEASE ANSWER FOR EXTRA POINTS ⭐️⭐️⭐️!

Answers

Answer:

the answer is B.(3,6)

because y>2

so,the answer is 3&6.

A multiple-choice test has five possible answers for each question. If a student guesses at the answer, what is the probability that he or she selects the correct answer for one particular question?

Answers

Answer:

20% chance of getting the right answer

Step-by-step explanation:

he has a 1/5 chance, translated into 20 percent

⭐ Question
I have 30 red marbles, 28 blue marbles, 13 green marbles, and 6 magenta marbles.
What is the probability I pull 3 blue marbles? Write as a fraction, no need to simplify.

Answers

Answer:

im thinking that is 3/74 because i count them

Step-by-step explanation:

3/74 rhe answer but 3/77 are wrong he just thinking

Answer:

3 over 77, 3/77

Step-by-step explanation:

You add up all of the marbles. (including the blue ones)

30+28+13+6 = 77.

So. You have a 3/77 chance of pulling a blue marble.

12x +15x² - 18x³
Factorise the expression

Answers

Answer:

-3x(2x+1)(3x-4)

Step-by-step explanation:

Add and subtract the second term to the expression and factor by grouping.

Anser and Explanation:

First, factor out an x to get:

[tex]x(-18x^2 + 15x + 12)[/tex]

Then, factor out a -3:

[tex]-3x(6x^2 - 5x - 4)[/tex]

Finally, factor by grouping:

[tex]-3x(6x^2 + 3x - 8x - 4)[/tex]

[tex]-3x(3x(2x + 1) - 4(2x + 1))[/tex]

[tex]-3x(3x - 4)(2x + 1)[/tex]

so -3x(3x - 4)(2x + 1) is the factored expression.

Cameron buys a pack of pencils and a pencil sharpener for $15. The pencil sharpener costs twice as much as the pack of pencils. How much does the pack of pencils cost?
A. $2
B. $10
C. $5
D. $30

Answers

Answer:

D. $30

Step-by-step explanation:

All you have to do is multiply 15 by 2 and you'll get 30.

Answer:
Option c

Explanation:
Check out the work I’ve attach

Hope it helps, Let me know if you have any other questions!
Have a nice rest do your day :)

olivia is walking to raise money for the childrens hospital. people can choose to sponser her at two diffrent levels. the first plan pays 10 dollars up front and 50 cents per mile. the second plan pays 4 dollars then 2 dollars per mile. for how many miles will the two plans donate the same amount?

Answers

Using linear functions, it is found that the two plans will donate the same amount for 4 miles.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

In this problem, the functions for the amount donated with n miles are given by:

f1(n) = 10 + 0.5n.f2(n) = 4 + 2n.

They will donate the same amount for n miles as such:

f1(n) = f2(n).

10 + 0.5n = 4 + 2n.

1.5n = 6

n = 6/1.5

n = 4.

More can be learned about linear functions at https://brainly.com/question/24808124

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Car A travels at a rate of 45 miles per hour.
Car B travels at a rate of 80 miles in 2
hours. Find the unit rate of each car. Which
car is traveling faster?

Answers

Unit rate in this case denotes to distance traveled in miles per hour.Indirectly it denotes to speed

#Car A

Speed=45mph

#Car B

Speed=Distance/Time=80/2=40mph

As we can observe

car A is traveling faster

Choose all statements that are true.
A 15% of 15 is 1.
B 5% of 50 is 10.
C 10% of 100 is 10.
D 2% of 100 is 5.
E 3% of 200 is 6.

Answers

Answer:

C, D, E

Step-by-step explanation:

15 * .15 = 2.25

50 * .05= 2.5

100 * .10= 10

100 * .05= 5

200 * .03= 6

x^2+y^2=y is written in polar form as r = ?
r = 3sinA is written in rectangular form as x^2+y^2= ?

Answers

[tex]x^2+y^2=r^2~\hfill x=rcos(\theta )~\hfill y=rsin(\theta ) \\\\[-0.35em] ~\dotfill\\\\ r=3sin(A)\implies \stackrel{\textit{multiplying both sides by "r"}}{r^2~~ = ~~3~rsin(A)}\implies x^2+y^2=3y[/tex]

r = 3sinA is written in rectangular form as[tex]x^2+y^2 = 3y.[/tex]

What is De Moivre's theorem for exponentiation of complex numbers?

Any complex number z = a + ib can be written in polar form as:

[tex]z = r(\cos(\theta) + i\sin(\theta))[/tex]

Complex numbers are those numbers that contain the imaginary and the real part.

Raising this to nth power (n being an integer), we get:

[tex]z ^n = r^n (\cos(n\theta) + i\sin(n\theta))[/tex]

We need to find r = 3sinA is written in rectangular form as[tex]x^2+y^2[/tex].

We know that

x = r cosA

y = r sin A

We have been given ;

r = 3sinA

Multiply by r on both sides;

[tex]r^2 = 3r sin A\\\\r^2 = 3 y[/tex]

therefore,

[tex]x^2+y^2 = 3y[/tex]

Hence, r = 3sinA is written in rectangular form as [tex]x^2+y^2 = 3y[/tex].

Learn more about cube root of complex numbers here:

https://brainly.com/question/16048106

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a spinner has 8 congruent sectors: 6 yellow and 2 green. the radius of the spinner is 5cm. what is the area of the yellow sector.

Answers

Area of the yellow sector is 58.91 cm2

The spinner has a circular shape and would be solved as a circle.

Area of a circle = pi r^2

= 3.142 * 5^2

= 78.55 cm2

The circle is divided into 8

78.55 / 8 = 9.8188

Area of 6 parts = 6 * 9.8188
= 58.9128 cm2

Find the quotient: 5/8 divided by 3.

Answers

Answer:

5/24

Step-by-step explanation:

Instead of dividing 5/8 by 3/1, you could multiply by the reciprocal to get the same answer.

5/8 · 1/3

Hope that helps!

A,B,C,D are points on the circumference of a circle centre o
ed is a tangent to the circle
angle odb = 25
work out angle bad

Answers

The points A,B,C,D make up the circumference of the circle

The measure of angle BAD is 65 degrees

How to determine the measure of angle BAD?

The measure of angle ODB is given as:

ODB = 25 degrees

Considering the triangle BOD, we have:

ODB + BOD + DBO = 180

Where:

ODB = DBO = 25

So, we have:

25 + BOD + 25 = 180

Solve for BOD

BOD = 130 degrees

The angle at an arc is twice the angle at the circumference.

So, we have:

BOD = 2 * BAD

Substitute 130 for BOD

130 = 2 * BAD

Divide both sides by 2

65 = BAD

Hence, the measure of angle BAD is 65 degrees

Answers

Answer:

It will take them 5 hours to make 180 cupcakes

Step-by-step explanation:

17 + 19 = 36 x 5 = 180

Answer:

5 hours

Step-by-step explanation:

so since it al together you add 17+19 which equals 36. after that you divide 180 by 36 which equals 5. to recheck this I multipled 17 by 5 and 19 by 5. equaling 85 plus 95 equals 180 meaning it is 5

Easy math 2 pictures

Answers

Answer:

See below

Step-by-step explanation:

x = hours

Payless charges = 50 + 60x

Squad charges = 80 + 50x when are they equal ?

50 + 60x = 80 + 50x

x = 3 hours

Surface area = 2 * ( 10 *5 + 5*3 + 3*10) = 190 ft^2

Help help help help math

Answers

Answer:

Step-by-step explanation:

2x+y

=2(2)+1

=4+1

Answer:

Step-by-step explanation:

Sub x=2, y = 1

2(x) + y = 5

2(2) + 1 = 5

Solve.

-14 - (-12)
A. -26
B. -2
C. 2
D. 26

Answers

Answer:

-2

Step-by-step explanation:

Apply the rule for this:

a - (- b) = a + b

Thus, we have:

-14 - (-12) = -14 + 12

Add the number:

Since there are more negative than positive the final solution is negative

Hence, now 14 - 12 = 2

Now bring the negative down:

-2

Therefore, the answer is -2

Kavinsky

When there are two minuses beside each other

⇒ we can equate them as a '+'

so:

-14 - (-12) = -14 + 12 = -2 or Choice (B)

Hope that helps!

High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 14 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?

Answers

Using the normal distribution, it is found that a student has to score 1.08 standard deviations above the mean to be publicly recognized.

Normal Probability Distribution

In a normal distribution with mean [tex]\mu[/tex]standard deviation [tex]\sigma[/tex]z-score of a measure X is given by:

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

It 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, which is the percentile of X.

The top 14% of the scores are given by scores above the 86th percentile, which corresponds to Z = 1.08, hence, a student has to score 1.08 standard deviations above the mean to be publicly recognized.

More can be learned about the normal distribution at https://brainly.com/question/24663213

Which statement correctly maps AB to A′B′
x,y)↦(x+7,y−8)(x,y)↦(x+7,y−8)

(x,y)↦(x+8,y−7)(x,y)↦(x+8,y−7)

(x,y)↦(x−8,y+7)(x,y)↦(x−8,y+7)

(x,y)↦(x−7,y+8)

Answers

Answer: ( x + 8, y -7)
x value is moved 8 units to the left. So add 8 to x value.
Y value is moved 7 units down. So subtract 7 from y value

Answer:x+8, y-7

Step-by-step explanation:

a cart is pushed 40 meters against 45 newtons of friction = how much work done

Answers

Answer:

-1.8 kJ

Step-by-step explanation:

Given

Displacement = 40 metersForce against = 45 N

Solving

W = F x SW = - 45 x 40W = -1800 J = -1.8 kJ

Answer:

2250 J

Step-by-step explanation:

Work done is given by the formula :

work done = force × distance

Substituting values given gives us:

Work done = 45 × 40

Work done = 2250 J

Find the range of the following sets of numbers 100,90,20,40,0,76

Answers

Answer:

100

Step-by-step explanation:

Range = highest - lowest (R = H - L)

In order, the set is 0, 20, 40, 76, 90, 100

100-0 = 100

Answer:

100

Step-by-step explanation:

Range = Highest value -lowest value

100-0=100

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