Solve the problem and then click on the correct graph.



y = |x|

The double integral of f(x, y) over D is ∫∫D f(x, y) dxdy = 2π/3.

What is intergration?

Integration is a fundamental concept in calculus that involves finding the integral of a function. It is the reverse process of differentiation and is used to compute areas, accumulate quantities, and solve various mathematical problems.

To evaluate the double integral ∫∫D f(x, y) dxdy over the region D, we need to determine the limits of integration.

The region D is defined by the condition \(x^2 + y^2\) ≤ 16, which represents a disk of radius 4 centered at the origin.

In polar coordinates, we can express x and y in terms of r and θ as follows:

x = r cos(θ)

y = r sin(θ)

The limits of integration for r and θ will correspond to the region D.

For r, we have 0 ≤ r ≤ 4, as the radius of the disk is 4.

For θ, we need to determine the range of angles that cover the entire disk. Since the disk is symmetric about the origin, we can choose any range of angles that covers a full circle. A suitable range is 0 ≤ θ ≤ 2π, which represents one complete revolution.

Now, we can set up the double integral:

∫∫D f(x, y) dxdy = ∫∫D √(16 - \(x^2 - y^2\)) dxdy

Converting to polar coordinates:

∫∫D √(16 - \(r^2\)) r dr dθ

Using the limits of integration:

∫₀²π ∫₀⁴ √(16 - \(r^2\)) r dr dθ

The inner integral with respect to r can be evaluated using substitution. Let u = 16 - \(r^2\), then du = -2r dr. The limits of integration become u(0) = 16 and u(4) = 0. The integral becomes:

∫₀²π ∫₁⁰ √u (-du/2) dθ

Simplifying:

-1/2 ∫₀²π ∫₁⁰ √u du dθ

The inner integral with respect to u is a standard integral:

-1/2 ∫₀²π [2/3 \(u^{(3/2)\)]₁⁰ dθ

Applying the limits of integration:

-1/2 ∫₀²π [2/3 \((0)^{(3/2)\) - 2/3 \((1)^{(3/2)\)] dθ

Simplifying further:

-1/2 ∫₀²π [-2/3] dθ

Integrating with respect to θ:

-1/2 [-2/3 θ]₀²π

Applying the limits of integration:

-1/2 [-2/3 (2π) - (-2/3 (0))]

Simplifying:

-1/2 [-4π/3]

Final result:

2π/3

Therefore, the double integral of f(x, y) over D is ∫∫D f(x, y) dxdy = 2π/3.

To learn more about integration visit:

https://brainly.com/question/30094386

#SPJ4

Answer:

255

Step-by-step explanation:

If 422 guests were at a hotel and 170 ordered food, The percentage of food would clearly be 255.

Logarithm base b of 45 is 3.806.

To evaluate log base b of 45 using the given approximations, we can use the properties of logarithms.

We can express 45 as a product of numbers with bases for which we have the logarithm approximations:

45 = (9) * (5)

Taking the logarithm of both sides:

log b(45) = log b(9 * 5)

Now, using the property of logarithms that states log(ab) = log(a) + log(b), we can split the expression:

log b(45) = log b(9) + log b(5)

Given that log b(9) = 2.197 and log b(5) = 1.609 (approximations provided), we substitute these values:

log b(45) ≈ 2.197 + 1.609

Calculating the sum:

log b(45) ≈ 3.806

Therefore, using the given approximations, we can estimate that log base b of 45 is approximately 3.806.

To learn more about Logarithm here:

https://brainly.com/question/30226560

#SPJ4

Answer:

The slope is 1/4.

Step-by-step explanation:

M = Y2 - Y1

X2 - X1

M = 6 - 2

9 - (-7)

M = 4

16

M = 1

4

The double integral over a triangular region with vertices (0,0), (1,2), and (0,3) will be evaluated.

To evaluate the double integral over the given triangular region, we need to set up the integral in terms of the appropriate bounds.

Let's denote the double integral as ∬R f(x, y) dA, where R represents the triangular region.

The vertices of the triangle are given as (0, 0), (1, 2), and (0, 3).

To set up the bounds of integration, we can observe that the triangle is bounded by the lines x = 0, x = 1, and the line joining the points (0, 3) and (1, 2).

For the inner integral, the lower limit of integration (y) is given by the line x = 0, and the upper limit is given by the line joining the points (0, 3) and (1, 2).

Therefore, the bounds for the inner integral are y = 0 to y = 3 - x.

For the outer integral, the lower limit of integration (x) is 0, and the upper limit is 1.

We can now set up the double integral as follows:

∬R f(x, y) dA = ∫[0 to 1] ∫[0 to 3-x] f(x, y) dy dx

Please note that without specifying the function f(x, y) or providing further instructions, we cannot provide a specific numerical evaluation of the integral.

Learn more about Double integral click here :brainly.com/question/18125359

#SPJ11

The value of the missing part of the triangle given above would be = 7.5. That is option A.

To calculate the missing length of the similar triangle, the formula listed below should be used.

That is;

a/a+b = c/c+d

where a = 8

b = 10

c = 6

d = ?

That is;

8/8+10 = 6/6+d

make d the subject of formula;

8(d+6) = 6(18)

8d +48 = 108

8d = 108-48

8d = 60

d = 60/8

d = 7.5

Learn more about triangles here:

https://brainly.com/question/28470545

#SPJ1

Answer:

i think that the correct answer would be A or C

Step-by-step explanation:

hope this helps

sorry if the answers that i gave you is incorrect

Answer:

2nd option

Step-by-step explanation:

the nth term of a geometric sequence is

\(a_{n}\) = a₁ \((r)^{n-1}\)

where a₁ is the first term and r the common ratio

here a₁ = 64 and r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{32}{64}\) = \(\frac{1}{2}\) , then

\(a_{n}\) = 64 \((\frac{1}{2}) ^{n-1}\)

Answer:

D. They are the same size.

Step-by-step explanation:

Triangle A:

sin 37 = 6 / H      where H = the hy[otenuse

H = 6 / sin 37

H = 9.8698

Triangle B:

cos 53 = 6/H

H = 6 / cos 53

H = 9.9698

Answer:

1.2, 3/5, 25%, 0.17, -12

Step-by-step explanation:

In order to put these from greatest to least, you must put these in like terms.

Since there are more decimals that other terms, we're going to convert them all to decimals.

25%= 0.25

0.17= 0.17

3/5= 0.60

1.2= 1.20

-12= -12.00

Now that we see which numbers are greater, we convert them back to their original terms and place them in order from greatest to least.

1.2, 3/5, 25%, 0.17, -12

Answer:

I dont understand spanish

Step-by-step explanation:

We can use Coulomb's law to calculate the magnitude of the electric field at a distance r away from a point charge Q:

E = k * Q / r^2

where k is Coulomb's constant, Q is the charge of the point charge, and r is the distance from the point charge.

In this problem, we have a point charge Q of -10 nC located at (1.2 cm, 0 cm), and we want to find the x-component of the electric field at a distance r = 5.3 cm away at position (-4.1 cm, 0 cm).

To find the x-component of the electric field, we need to use the cosine of the angle between the electric field vector and the x-axis, which is cos(180°) = -1.

So, the x-component of the electric field at position (-4.1 cm, 0 cm) is:

E_x = - E * cos(180°) = - (k * Q / r^2) * (-1)

where k = 9 x 10^9 N*m^2/C^2 is Coulomb's constant.

Substituting the given values, we get:

E_x = - (9 x 10^9 N*m^2/C^2) * (-10 x 10^-9 C) / (0.053 m)^2

E_x ≈ -30,566.04 N/C

Rounding this to two significant figures and including the appropriate units, we get:

The x-component of the electric field is about -3.1 x 10^4 N/C (to the left).

The area of the given trapezoidal site is 250,000 sq. ft.

The area of the trapezoidal with the dimensions of both bases and the height is given by the formula,

Area = 1/2 × height × (base1 + base2)

Units: square units

The given trapezoidal site has a base of 150 feet, i.e., base1 = 150 ft; a height of 2000 ft, i.e., height = 2000 ft and a parallel base of 100 feet, i.e., base2 = 100 ft.

Then, the area of the trapezoidal is

= 1/2 × 2000 × (150 + 100)

= 1/2 × 2000 × 250

= 250,000 sq. ft

Learn more about the area of the trapezoidal here:

https://brainly.com/question/1463152

#SPJ4

Answer:

Multiply the bottom equation by -3/2 then add the equations.

Multiply the top equation by-3. then add the equations

Step-by-step explanation:

Given the simultaneous equation

2x- 6y=6  ... 1

6x - 4y = 2 ... 2

To eliminate a variable, we have to make the coefficient of one of the variable to be the same.

Multiply equastion 1 by -3

-6x+18y= -18  

6x - 4y = 2

Add the result:

-6x + 6x + 18y-4y = -18+2

18y-4y = -18+2

14y = -18

y = -9/7

Another way is to Multiply the bottom equation by -3/2 then add the equations.

Multiplying equation 2 by -3/2 will give;

6x(-3/2) - 4y(-3/2) = 2(-3/2)

-9x + 6y = -3

Add to equation 1;

2x- 6y=6

-9x + 2x + 0 = -3+6

-7x = 3

x = -3/7

Hence the correct two options are;

Multiply the bottom equation by -3/2 then add the equations.

Multiply the top equation by-3. then add the equations

Answer:

A

Step-by-step explanation:

The opposite sides of a parallelogram are congruent, then

WT = VU = 21.3 → A

Answer:

Parallelogram, Rhombus or a regular trapezium.

Step-by-step explanation:

Since all the units add up to 10 units, which is a factor of 180 degrees, all quadrilaterials work in this case as all quadrilaterals must have angles summing up to 180 degrees.

I might be wrong though. :(

Answer:

n = 2

Step-by-step explanation:

Given

\(\frac{1}{2}\)(n - 4) - 3 = 3 - (2n + 3)

Multiply through by 2 to clear the fraction

n - 4 - 6 = 6 - 2(2n + 3) ← distribute

n - 10 = 6 - 4n - 6 ( add 4n to both sides )

5n - 10 = 0 ( add 10 to both sides )

5n = 10 ( divide both sides by 5 )

n = 2

Using cosine rule, The length of BC is approximately x = 66.73 units

What is the cosine rule?

The cosine rule, also known as the law of cosines, is a mathematical formula used to calculate the length of a side or the measure of an angle in a triangle. It is called the cosine rule because it involves the cosine of an angle.

The formula for the cosine rule is:

\(c^2 = a^2 + b^2 - 2ab\times cos(C)\)

To solve this problem, we can use the Law of Cosines, which relates the length of a side of a triangle to the cosine of one of its angles and the lengths of the other two sides.

The formula for the Law of Cosines is:

\(c^2 = a^2 + b^2 - 2ab\times cos(C)\)

where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

In this case, we want to find the length of side BC, so we'll use the Law of Cosines with angle A, which is opposite side BC:

\(BC^2 = AC^2 + AB^2 - 2AC \times AB\times cos(A)\)

We know that AC = 45 and A = 36 degrees, so we can substitute those values in:

\(BC^2 = 45^2 + AB^2 - 245 AB \times cos(36)\)

To solve for BC, we need to find the length of AB. We can use the fact that the angles in a triangle add up to 180 degrees:

\(A + B + C = 180\\36 + B + 90 = 180\\B = 54 degrees\)

Now we can use the Law of Sines to find the length of AB:

\(AB/sin(B) = AC/sin(A)\\AB/sin(54) = 45/sin(36)\\\\AB = 45 \times sin(54)/sin(36)\\AB \approx 57.35\)

Substituting this value into our Law of Cosines equation:

\(BC^2 = 45^2 + 57.35^2 - 24557.35 \times cos(36)BC \approx 66.73\)

Therefore, the length of BC is approximately x = 66.73 units.

To learn more about the cosine rule, visit:

https://brainly.com/question/30766161

#SPJ1

Answer:

105.6 ft

Step-by-step explanation:

1 acre = 43,560 ft²

2/3(43,560) = 29,040

x = width of the lot

Area = (275 ft)(x) = 29,040 ft²

x = 29040/275 = 105.6 ft

The three solutions of the equation y = -2x - 1 are (–2, 3), (1, –3), and (2, –4).

To find the solutions, we substitute different values of x into the equation and solve for y.

For the first solution, when x is –2, we have y = -2(-2) - 1 = 3. Therefore, the first solution is (-2, 3).

For the second solution, when x is 1, we have y = -2(1) - 1 = -3. Thus, the second solution is (1, -3).

For the third solution, when x is 2, we have y = -2(2) - 1 = -4. Hence, the third solution is (2, -4).

These three points satisfy the equation y = -2x - 1, and therefore, they are the solutions of the equation. They represent coordinate pairs (x, y) where the equation holds true.

For more such answers on equation

https://brainly.com/question/17145398

#SPJ8

By factoring out this common factor, we obtain the simplified expression 0.006(25c - 12).

We can start by determining the common factor between the two terms in order to factor the phrase 0.15c - 0.072. The common factor in this situation is 0.006, which we may factor out to obtain:

0.15c - 0.072 = 0.006(25c - 12) (25c - 12)

As a result, factoring the expression 0.15c - 0.072 gives 0.006 (25c - 12).

It is possible to utilise this factored form to further simplify calculations or to resolve equations that contain this statement. If we needed to find c in the equation 0.15c - 0.072 = 0, for instance, we could use the factored form to obtain:

0.006(25c - 12) = 0

25c - 12 = 0

c = 12/25

In conclusion, factoring the expression 0.15c - 0.072 involves finding the common factor between the two terms, which is 0.006. By factoring out this common factor, we obtain the simplified expression 0.006(25c - 12).

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ4

Answer:

Translate A, 5 to the right and then 5 downwards.

Translate B, 6 downwards and then 5 to the right.

If you move then in this way it will make it so that A is in the exact same spot as A' or overlapping showing that they are congruent. The same can be said with B and B'.

The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

Learn more about compound interest here:

https://brainly.com/question/14295570

#SPJ1

To find the height of the trapezoid-shaped tabletop, we can use the formula for the area of a trapezoid.

Given that the area is 5,994 square centimeters, the longer base is 131 centimeters, and the shorter base is 85 centimeters, we can calculate the height of the trapezoid.

The formula for the area of a trapezoid is given by A = (1/2) × (b1 + b2) × h, where A is the area, b1 and b2 are the lengths of the bases, and h is the height.

We are given that the area is 5,994 square centimeters, the longer base is 131 centimeters, and the shorter base is 85 centimeters.

Substituting these values into the formula, we can solve for the height:

5,994 = (1/2) × (131 + 85) × h

Simplifying the equation:

5,994 = (1/2) × 216 × h

5,994 = 108h

Dividing both sides by 108:

h = 5,994 / 108

h = 55.5

Therefore, the height of the tabletop is 55.5 centimeters.

Learn more about trapezoid here: brainly.com/question/31380175

#SPJ11

Using the concepts of probability, we got 0.5 is the probability of drawing the sum $20 or more when  two bills are drawn randomly without replacement.

We have an envelope contains 8 bills;

Two of $1 bills, Two of $5 bills, Two of $10 bills, Two of $20 bills.

When two bills are drawn randomly without replacement, we have to find the probability that their sum is $20 or more.

Total  outcomes = 2 x 2 x 2 x 2 = 16

Total possible outcomes, more than 20;

(1, 20), (20, 1), (5, 20), (20, 5), (10, 10), (20, 10), (10, 20), (20, 20) = 8 cases

That is,

The total possible outcomes is 8.

Now,

The probability of bill to be $20 or more = Possible outcome / Total outcome

Probability = 8/16 = 1/2=0.5

Hence, When two bills are drawn randomly without replacement,  the probability that their sum is $20 or more is 0.5.

To Learn more about probability, visit  here;

brainly.com/question/16673337

#SPJ4

(Complete question)

an envelope contains eight bills: 2 ones, 2 fives, 2 tens, and 2 twenties. two bills are drawn at random without replacement. what is  the probability that their sum is $20 or more?

The laplace transform of f(t) is \(F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}\) and it's values exists for \(s=w\pm\sqrt{3}wi\).

Given,

\(f(t)=sin^2(wt)\\\\\therefore sin^2x=\frac{1-cos2x}{2}\\\\f(t)=\frac{1-cos2wt}{2}\)

applying laplace transform on both sides,

\(L[f(t)]=L[\frac{1-cos2wt}{2}]\\\\F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}\)

The range for values of s for which F(s) exists is when F(s)≥0

\(\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)} \geq0\\\\\frac{1}{2s} \geq\frac{2w}{2(s^2+4w^2)}\\\\2(s^2+4w^2) \geq 2sw\\\\s^2-2sw+4w^2 \geq0\)

using formula to find roots,

\(s=\frac{-(-2w)\pm\sqrt{(-2w^2)-4(4w^2)}}{2}\\\\s=\frac{-(-2w)\pm\sqrt{(12w^2}}{2}\\\\s=w\pm\sqrt{3}wi\)

Thus,  the laplace transform of f(t) is \(F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}\) and it's values exists for \(s=w\pm\sqrt{3}wi\).

To learn more about laplace transform refer here

https://brainly.com/question/13077895

#SPJ4

The volume of the right cone is 7 units.

The radius of a cone can be found as follows:

The volume of the right cone is 245π unit³. The height of the right cone is 15 units.

Therefore,

volume of a right cone = 1 / 3 πr²h

where

Hence,

volume of the right cone = 245π

h = 15 units

Hence,

245π = 1 / 3 × π × r²  × 15

divide both sides by π

245 = 15 / 3 r²

245 = 5r²

r² = 245 / 5

r = √49

r = 7 units

Therefore,

radius of the cone = 7 units

learn more on volume here:https://brainly.com/question/20420173

#SPJ1

Step-by-step explanation:

18+3=x+3

21=x+3

x=21-3

x=18

A 3x3 matrix's must first be calculated in order to determine the eigenvectors and eigenvalues of the matrix, using the quadratic formula, get the eigenvalues, determine the associated eigenvectors.

A 3x3 matrix's determinant must first be calculated in order to determine the eigenvectors and eigenvalues of the matrix. This may be accomplished by applying the expansion on eigenvalues may then be determined by using the quadratic formula to the eigenvalue equation. , the newly obtained eigenvalues may be used to solve the system of equations derived from the eigenvalue equation in order to get the associated eigenvectors. After the eigenvectors have been identified, they may be to the matrix's eigenvalues. You may eigenvalues and eigenvectors. To the matrix's structure and identify its distinctive equation, eigenvectors and eigenvalues. The solutions to a system of equations as well as the stability of the system may be found using eigenvectors and eigenvalues.

Learn more about matrix here

https://brainly.com/question/28180105

#SPJ4

Answer:

4

Step-by-step explanation:

The passage is using persuasive language to encourage readers to purchase the Weav-eo Bracelet kit. It is emphasizing the popularity of the craft and the vibrant colors of the bracelets in order to entice readers to buy the kit.

Persuasive writing is a form of writing in which the author uses words and phrases to convince the reader to believe in a particular point of view. It is often used in advertising, speeches, and political campaigns. It is used to convince the reader to take a certain action, or to agree with a particular idea or opinion. The main goal of persuasive writing is to influence the reader’s opinion in some way. To achieve this, writers must use strong arguments, clear language, and emotional appeals. The writer must also make sure that the argument is logical and supported by evidence.

To learn more about persuasive
https://brainly.com/question/30130345
#SPJ1