Help me solve this 5=x/11-1

The value of the integral is 8π/3 - 32/3 for the first integral using polar coordinates, the integrand in terms of polar coordinates and then using the corresponding Jacobian determinant.

The region R in the first quadrant between the circles with center at the origin and radii 2 and 3 can be described in polar coordinates as follows:

2 ≤ r ≤ 3

0 ≤ θ ≤ π/2

Now, let's convert the integrand sin(x² + y²) to polar coordinates:

x = rcos(θ)

y = rsin(θ)

x² + y² = r²*(cos²(θ) + sin²(θ))

               = r²

Substituting these expressions into the integrand, we get:

sin(x² + y²) = sin(r²)

Next, we need to calculate the Jacobian determinant when changing from Cartesian coordinates (x, y) to polar coordinates (r, θ):

J = r

Now, we can rewrite the integral using polar coordinates:

∫∫_R sin(x^2 + y^2) dA = ∫∫_R sin(r^2) r dr dθ

The limits of integration for r and θ are as follows:

2 ≤ r ≤ 3

0 ≤ θ ≤ π/2

So, the integral becomes:

∫[0 to π/2] ∫[2 to 3] sin(r²) r dr dθ

To evaluate this integral, we integrate with respect to r first and then with respect to θ.

∫[2 to 3] sin(r²) r dr:

Let u = r², du = 2r dr

When r = 2, u = 4

When r = 3, u = 9

∫[4 to 9] (1/2) sin(u) du = [-1/2 cos(u)] [4 to 9]

                                    = (-1/2) (cos(9) - cos(4))

Now, we integrate this expression with respect to θ:

∫[0 to π/2] (-1/2) (cos(9) - cos(4)) dθ = (-1/2) (cos(9) - cos(4)) [0 to π/2]

= (-1/2) (cos(9) - cos(4))

Therefore, the value of the integral is (-1/2) (cos(9) - cos(4)).

Moving on to the second problem:

To evaluate the integral ∫∫_D x dA, where D is the region in the first quadrant that lies between the circles x^2 + y^2 = 16 and x^2 + y^2 = 4x, we again use polar coordinates.

The region D can be described in polar coordinates as follows:

4 ≤ r ≤ 4cos(θ)

0 ≤ θ ≤ π/2

To express x in polar coordinates, we have:

x = r*cos(θ)

The Jacobian determinant when changing from Cartesian coordinates to polar coordinates is J = r.

Now, we can rewrite the integral using polar coordinates:

∫∫_D x dA = ∫∫_D r*cos(θ) r dr dθ

The limits o integration for r and θ are as follows:

4 ≤ r ≤ 4cos(θ)

0 ≤ θ ≤ π/2

So, the integral becomes:

∫[0 to π/2] ∫[4 to 4cos(θ)] r^2*cos(θ) dr dθ

To evaluate this integral, we integrate with respect to r first and then with respect to θ.

∫[4 to 4cos(θ)] r^2cos(θ) dr:

∫[4 to 4cos(θ)] r^2cos(θ) dr = (1/3) * r^3 * cos(θ) [4 to 4cos(θ)]

= (1/3) * (4cos(θ))^3 * cos(θ) - (1/3) * 4^3 * cos(θ)

Now, we integrate this expression with respect to θ:

∫[0 to π/2] [(1/3) * (4cos(θ))^3 * cos(θ) - (1/3) * 4^3 * cos(θ)] dθ

To simplify this integral, we can use the trigonometric identity

cos^4(θ) = (3/8)cos(2θ) + (1/8)cos(4θ) + (3/8):

∫[0 to π/2] [(1/3) * (4cos(θ))^3 * cos(θ) - (1/3) * 4^3 * cos(θ)] dθ

= ∫[0 to π/2] [(1/3) * 64cos^4(θ) - (1/3) * 64cos(θ)] dθ

Now, we substitute cos^4(θ) with the trigonometric identity:

∫[0 to π/2] [(1/3) * (64 * ((3/8)cos(2θ) + (1/8)cos(4θ) + (3/8))) - (1/3) * 64cos(θ)] dθ

Simplifying the expression further:

∫[0 to π/2] [(64/8)cos(2θ) + (64/24)cos(4θ) + (64/8) - (64/3)cos(θ)] dθ

Now, we can integrate term by term:

(64/8) * (1/2)sin(2θ) + (64/24) * (1/4)sin(4θ) + (64/8) * θ - (64/3) * (1/2)sin(θ) [0 to π/2]

Simplifying and evaluating at the limits of integration:

(64/8) * (1/2)sin(π) + (64/24) * (1/4)sin(2π) + (64/8) * (π/2) - (64/3) * (1/2)sin(π/2) - (64/8) * (1/2)sin(0) - (64/24) * (1/4)sin(0) - (64/8) * (0)

= 0 + 0 + (64/8) * (π/2) - (64/3) * (1/2) - 0 - 0 - 0

= 8π/3 - 32/3

Therefore, the value of the integral is 8π/3 - 32/3.

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The y intercept is $25000, the percentage loss is 10% and the decay factor is 0.9

An equation is a mathematical expression that contains two or more numbers and variables linked together by mathematical operations such as exponents, multiplication, division, addition, subtraction and so on.

The standard form of an exponential function is:

y = abˣ

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

Let y represent the cost of a van after x years. It is given by:

y = 25000(0.9)ˣ

hence, comparing gives a = 25000, b = 0.9

a) The y intercept is $25000

b) Percentage loss = 1 - 0.9 = 0.1 = 10%

b) Decay factor = b = 0.9

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Step-by-step explanation:

Using z-score table the value is    .9793     (97.93 %)

Answer:

B. 3/8 book

Step-by-step explanation:

To find the number of books Christian reads per week, we need to simplify the given rate.

Christian reads 1/4 book every 2/3 week.

To convert this rate to a rate per week, we can divide the numerator and denominator of the fraction by 2:

1/4 ÷ 2/3 = 1/4 × 3/2 = 3/8

So Christian reads 3/8 of a book per week.

The answer is (B) 3/8 book.

Answer: B - 3/8

here is step by step please give me the crown

Step-by-step explanation: Using the proportionality concept, the number of books read by Christian per week is 3/8

The expression can be used to create a proportional equation thus :

Let the number of books read per week = b

1/4 books = 2/3 weeks

b books = 1 week

Cross multiply

1/4 = (2/3)b

1/4 = 2b/3

Cross multiply

2b × 4 = 3 × 1

8b = 3

b = 3/8

Hence, the number of books read per week is 3/8

The maximum value of the function is 10

The function is given as:

P = 2x - y

The feasible regions are given as:

(1,0), (5,5) and (5,0)

Substitute these values in P = 2x - y

P = 2(1) - 0 = 2

P = 2(5) - 5 = 5

P = 2(5) - 0 = 10

The maximum value in the above computation is 10

Hence, the maximum value of the function is 10

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Most common is 7

So

Use distributive law to verify

Verified

GCF is 7

We have the folllowing, the density population in US is:

The density population in California is:

The density in Califoria is 232.37 per mi^2

therefore, the density in California is higher than in the US.

Responder:

3,46

Explicación paso a paso:

Número de lápices comprados = 36

Costo total de los 36 lápices = 97,5

El precio unitario de cada lápiz será:

Costo total / número de lápices

97,5 / 36

= 2.708

El precio de venta por lápiz será:

Precio por lápiz + 75 céntimos

2,708 + 0,75

= 3.458

= 3,46

Por tanto, el precio de venta por lápiz será 3,46.

When the radius is 6 cm, the rate at which the radius is growing longer is approximately 0.011 cm/sec.

To find the rate at which the radius is growing when the radius is 6 cm, we need to relate the rate of change of volume to the rate of change of the radius.

The volume V of a sphere is given by the formula:

V = (4/3)πr³

Differentiating both sides of the equation with respect to time (t), we get:

dV/dt = 4πr²(dr/dt)

Given that dV/dt = 5 cm³/sec, we can plug in the value of r as 6 cm and solve for dr/dt.

5 = 4π(6)²(dr/dt)

Simplifying the equation:

5 = 144π(dr/dt)

Now, solve for dr/dt:

dr/dt = 5 / (144π)

Calculating the value:

dr/dt ≈ 0.011

Therefore, when the radius is 6 cm, the rate at which the radius is growing longer is approximately 0.011 cm/sec.

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Answer:

3

Step-by-step explanation:

Given that:

Larger square is a dilation of smaller square

Dimension of smaller square (5 - 3) units by (5 - 3) units = 2 by 2

Dimension of larger square (7 - 1) units by (7 - 1) units = 6 by 6

Hence, the scale factor used to create the larger square from the smaller square will be:

Scale factor (x) * side of smaller square = side of larger square

x * 2 = 6

2x = 6

x = 6/2

x = 3

Hence, scale factor used to generate larger square is 3

According to the question, the work done in stretching the spring from 3 ft. beyond its natural length to 7 ft. beyond its natural length is 8 lb·ft.

To calculate the work done, we need to use the formula:

\(\[ \text{Work} = \text{Force} \times \text{Distance} \]\)

Given that a force of 2 lb is required to hold the spring stretched 3 ft. beyond its natural length, we can consider this as the force applied to stretch the spring from 0 ft. to 3 ft. beyond its natural length.

Therefore, the work done in stretching the spring from 0 ft. to 3 ft. beyond its natural length is \(\(2 \, \text{lb} \times 3 \, \text{ft}\)\).

To find the work done in stretching the spring from 3 ft. beyond its natural length to 7 ft. beyond its natural length, we need to subtract the work done in stretching from 0 ft. to 3 ft. beyond its natural length.

Hence, the work done in stretching the spring from 3 ft. beyond its natural length to 7 ft. beyond its natural length is:

\(\[ \text{Work} = (2 \, \text{lb} \times 7 \, \text{ft}) - (2 \, \text{lb} \times 3 \, \text{ft}) \]\)

Simplifying the equation:

\(\[ \text{Work} = 14 \, \text{lb} \cdot \text{ft} - 6 \, \text{lb} \cdot \text{ft} \]\)

Therefore, the work done in stretching the spring from 3 ft. beyond its natural length to 7 ft. beyond its natural length is:

\(\[ \text{Work} = 8 \, \text{lb} \cdot \text{ft} \]\)

So, the answer is that the work done in stretching the spring from 3 ft. beyond its natural length to 7 ft. beyond its natural length is 8 lb·ft.

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Answer:

The question is not complete, below is the completed question

Noah built a fenced dog run that is 8 yards long and 6 yards wide. He placed posts at every corner and every yard along the length and width of the run. How many posts did he use?

Answer

There are 28 posts in total

Step-by-step explanation:

Attached to this answer is a picture showing the fenced dog run and the position of the posts.

The number of posts is determined as follows:

Number of posts for the four corners = 4 posts

Number of posts for the 8-yard side = 7 posts

N:B There are 7 posts instead of 8 posts because one post has been counted as a corner post already, hence we will not count it twice.

∴ Total number of posts for both 8-yard sides = 7 × 2 = 14 posts

Number of posts for the 6-yard sides = 5 posts (same reason as above)

Ttal number of posts for both 6 yard sides = 5 × 2 = 10 posts.

Total number of posts = 4 + 14 + 10 = 28 posts

∴ There are 28 posts in total

Answer: 52

Step-by-step explanation: it might not be it. GOD BLESS.

The answer to the given question is -4/3 or 1/2

The product of 6 and the square of a number is increased by 5 times the number, the result is 4.

Firstly, let's write the algebraic expression for the above statement and represent the number as x.

The algebraic expression can be written as:

(6 x x²) + 5x = 4

6x² + 5x = 4

The other expression can also be written as:

6x² + 5x - 4 = 0

Secondly, we must factorize the algebraic expression to solve for x.

6x² - 3x + 8x - 4 = 0

3x (2x - 1) + 4 (2x + 1) = 0

(3x + 4)(2x - 1) = 0

Thirdly, we need to solve for x.

3x + 4 = 0

3x = -4

Now, we need to divide both sides by 3.

3x/3 = -4/3

x = -4/3

or

2x - 1 = 0

2x = 1

Now, we need to divide both sides by 2.

2x/2 = 1/2

x = 1/2

Hence, the values that the number could be is -4/3 or 1/2.

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The image point of the point is (-12,8)

A dilation is a transformation that changes the size of a figure but not its shape.

In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.

In this case, the point (-3, 2) is transformed under a dilation of 4 with respect to the origin.

So the image point is (kx, ky) = (-34, 24) = (-12, 8)

So the image point of (-3,2) under a dilation of 4 with respect to the origin is (-12,8)

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Complete question

find the image point when the indicated transformation is applied to the given pre-image point

(-3,2) under a dilation of 4 with respect to the origin

Answer:

A \(1.3 - 5.6 = - 4.3\)

Step-by-step explanation:

\(1.3 - 5.6 = - 4.3\)

Hope this helps! Pwease mark me brainliest! Have a great day!

−xXheyoXx

Answer:

just answering so you can give the other person brainliest :D

Step-by-step explanation:

Answer:

189 diagonals have 21 sides.

it is called hectogan take care

The correct answer is option C) 234 days. In this case, the loan was made on March 24 and due on November 15 of the same year.

To find the exact time of the loan made on March 24 and due on November 15, we need to add up the exact days in each month between these two dates. March has 31 days, April has 30 days, May has 31 days, June has 30 days, July has 31 days, August has 31 days, September has 30 days, October has 31 days, and November has 15 days.
Adding up all the days, we get:
31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 15 = 234
Therefore, the exact time of the loan is 234 days.

To calculate the exact time between two dates, we need to count the number of days in each month and add them up.
March has 31 days, so we count from March 24 to March 31, which gives us 7 days.
Next, we move to April, which has 30 days. So we add 30 to the previous count of 7, which gives us 37 days.
In May, there are 31 days, so we add 31 to the previous count of 37, which gives us 68 days.
June has 30 days, so we add 30 to the previous count of 68, which gives us 98 days.
In July, there are 31 days, so we add 31 to the previous count of 98, which gives us 129 days.
August also has 31 days, so we add 31 to the previous count of 129, which gives us 160 days.
In September, there are 30 days, so we add 30 to the previous count of 160, which gives us 190 days.
October has 31 days, so we add 31 to the previous count of 190, which gives us 221 days.
Finally, in November, we count from November 1 to November 15, which gives us 15 days.
Adding up all the days, we get:
7 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 15 = 234
Therefore, the exact time of the loan is 234 days.

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The main criticism of differential opportunity theory is that it overlooks the fact that most delinquents become law-abiding adults (option c).

Differential opportunity theory, developed by Richard Cloward and Lloyd Ohlin, focuses on how individuals in disadvantaged communities may turn to criminal activities as a result of limited legitimate opportunities for success.

However, critics argue that the theory fails to account for the fact that many individuals who engage in delinquency during their youth go on to become law-abiding adults.

This criticism highlights the idea that delinquent behavior is not necessarily a lifelong pattern and that individuals can change their behavior and adopt prosocial lifestyles as they mature.

While differential opportunity theory provides insights into the relationship between limited opportunities and delinquency, it does not fully address the complexities of individual development and the potential for desistance from criminal behavior.

Critics suggest that factors such as personal growth, social support, rehabilitation programs, and the influence of life events play a significant role in individuals transitioning from delinquency to law-abiding adulthood.

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If the lawn measures 6m by 5. 2m, the area of the lawn is 31.2 square meters.

To find the area of the lawn, we simply need to multiply the length by the width. In this case, we have a rectangular lawn that measures 6m by 5.2m.

Area = length x width

Area = 6m x 5.2m

Area = 31.2 square meters

It's important to note that when calculating area, the units are squared, which means we are multiplying two lengths together. In this case, we multiplied meters by meters to get square meters. This is because area is a two-dimensional measurement, whereas length and width are one-dimensional measurements.

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Answer:

(2x-1)^2

Step-by-step explanation:

Explanation in the picture.

Answer:

10^2*10^2

Step-by-step explanation:

1) Write 100*100 in as powers of 10: 10^2 * 10^2

Answer:

x = 21 and y = 83

Step-by-step explanation:

Since the figures are similar, then corresponding sides and angles are congruent, that is

GE = LA

x = 21

and

∠ I = ∠ M , so

y = 83

The ordered pair of the given equation will be ( 3, 6 ) and ( -3, 18).

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

The given functions are:-

F(x) =x²-2x+3

F(x) = -2x + 12

When we plot the graph of the function we will see that the line -2x +12 cut the parabola at points ( -3, 18 ) and ( 3, 6 ) so these are the ordered pairs of the two functions. The graph of the functions is also attached with the answer.

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Answer:

a 230 metersa 230 metersa 230 metersa 230 metersa 230 metersa 230 metersa 230 meters

The ratio of John's money to Peter's money is 5/4. This means if John has a total amount of 5 then Peter will have a total of 4 as his amount.

Let's assume John has 'x' amount of  money, Peter has 'y' amount of money, The money John saved is 'p' and the money Peter saved is 'q'

So,

p = x - 80x/100                (equation 1)

q = y - 75y/100                (equation 2)

According to the given question, the amount John saved is equal to the amount Peter saved. Hence, we can equate equations 1 and 2.

p = q

x- 80x/100 = y - 75y/100

x - 0.8x = y - 0.75y

0.2x = 0.25y

x =  0.25y/0.2

x/y = 0.25/0.2

x/y = 25/20

x/y = 5/4

Hence, the ratio of John's money to Peter's money is 5/4.

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Answer:

40 cookies

Step-by-step explanation: She would bake 40 cookies in 2 hours because, if she baked 120 in 6 hours it would be like 6 + 6 = 12 but add the zero so yea

Answer:

X es igual a 3

Step-by-step explanation:

x2 - 6 = 0

(3)2 - 6 = 0

Step-by-step explanation:

he equation of a line is written as y=mx+b where m is the slope and b is the

y -intercept, Thus,m=23 And the y -intercept,b=1