help ...........................................






thanks,,,,

Answer:

[tex]\int\limits {\int\limits_R {7(x + y)e^{x^2 - y^2}} \, dA = \frac{1}{2}e^{42} -\frac{43}{2}[/tex]

Step-by-step explanation:

Given

[tex]x - y = 0[/tex]

[tex]x - y = 7[/tex]

[tex]x + y = 0[/tex]

[tex]x + y = 6[/tex]

Required

Evaluate [tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA[/tex]

Let:

[tex]u=x+y[/tex]

[tex]v =x - y[/tex]

Add both equations

[tex]2x = u + v[/tex]

[tex]x = \frac{u+v}{2}[/tex]

Subtract both equations

[tex]2y = u-v[/tex]

[tex]y = \frac{u-v}{2}[/tex]

So:

[tex]x = \frac{u+v}{2}[/tex]

[tex]y = \frac{u-v}{2}[/tex]

R is defined by the following boundaries:

[tex]0 \le u \le 6[/tex]  ,  [tex]0 \le v \le 7[/tex]

[tex]u=x+y[/tex]

[tex]\frac{du}{dx} = 1[/tex]

[tex]\frac{du}{dy} = 1[/tex]

[tex]v =x - y[/tex]

[tex]\frac{dv}{dx} = 1[/tex]

[tex]\frac{dv}{dy} = -1[/tex]

So, we can not set up Jacobian

[tex]j(x,y) =\left[\begin{array}{cc}{\frac{du}{dx}}&{\frac{du}{dy}}\\{\frac{dv}{dx}}&{\frac{dv}{dy}}\end{array}\right][/tex]

This gives:

[tex]j(x,y) =\left[\begin{array}{cc}{1&1\\1&-1\end{array}\right][/tex]

Calculate the determinant

[tex]det\ j = 1 * -1 - 1 * -1[/tex]

[tex]det\ j = -1-1[/tex]

[tex]det\ j = -2[/tex]

Now the integral can be evaluated:

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA[/tex] becomes:

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{x^2 - y^2}} \, *\frac{1}{|det\ j|} * dv\ du[/tex]

[tex]x^2 - y^2 = (x + y)(x-y)[/tex]

[tex]x^2 - y^2 = uv[/tex]

So:

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *\frac{1}{|det\ j|}\, dv\ du[/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *|\frac{1}{-2}|\, dv\ du[/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *\frac{1}{2}\, dv\ du[/tex]

Remove constants

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 {\int\limits^7_0 {ue^{uv}} \, dv\ du[/tex]

Integrate v

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 \frac{1}{u} * {ue^{uv}} |\limits^7_0 du[/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 e^{uv} |\limits^7_0 du[/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 [e^{u*7} - e^{u*0}]du[/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 [e^{7u} - 1]du[/tex]

Integrate u

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7u} - u]|\limits^6_0[/tex]

Expand

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * ([\frac{1}{7}e^{7*6} - 6) -(\frac{1}{7}e^{7*0} - 0)][/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * ([\frac{1}{7}e^{7*6} - 6) -\frac{1}{7}][/tex]

Open bracket

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7*6} - 6 -\frac{1}{7}][/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7*6} -\frac{43}{7}][/tex]

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{42} -\frac{43}{7}][/tex]

Expand

[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{1}{2}e^{42} -\frac{43}{2}[/tex]

Answer: (I am not a maths moderator)

x=4

Step-by-step explanation:

Multiply the exponents

(2x-4)^12=(4^2)^6 (exponents multiply so)

(2x-4)^12=4^12

4^12 = 16777216

(2x-4)^12= 16777216

Take the 1/12 exponent for both sides

that will remove the ^12 exponent from the left side and will take the 12th root for the right.

2x-4=4

add 4 to both sides

2x=8

divide both sides by 2

x=4

Answer:

(3p+10q)

Step-by-step explanation:

9p^2 - 100q^2

Rewriting

(3p)^2 - (10q)^2

This is the difference of squares

a^2 - b^2 = (a-b)(a+b)

(3p-10q) (3p+10q)

Answer:

( 3p + 10 q)

Step-by-step explanation:

9 p ² - l00 q ²

(3p)² - ( 10 q) ²

( a ² - b ² = ( a + b) ( a - b) )

( 3p - 10 q) ( 3 p + 10 q)

Answer:

5.78

19

Step-by-step explanation:

Let original population be, P = x

Growth in 12 years, A = 2x

Rate be = r

Time = 12years

Find the rate :

   [tex]A = P(1 + \frac{r}{100})^t[/tex]

 [tex]2x = x(1 + \frac{r}{100})^{12}\\\\\frac{2x}{x} =(1 + \frac{r}{100})^{12}\\\\2 = (1 + \frac{r}{100})^{12}\\\\ \sqrt[12]{2} = (1 + \frac{r}{100})\\\\\sqrt[12]{2} - 1 = \frac{r}{100}\\\\2^{0.08} - 1 = \frac{r}{100}\\\\1.057 - 1 = \frac{r}{100}\\\\0.057 \times 100 = r\\\\r = 5.7 \%[/tex]

The annual rate of increase of the population of this city is approximately 5.78.

Find  time in which the population becomes 3 times.

That is A = 3x

P = x

R= 5.78%

               [tex]A = P( 1 + \frac{r}{100})^t\\\\3x = x ( 1 + \frac{5.78}{100})^t\\\\3 = (1.0578)^t\\\\log \ 3 = t \times log \ 1.0578 \\\\t = \frac{log \ 3}{ log \ 1.0578 }\\\\t = 19.55[/tex]

The population will grow to three times its current size in approximately 19years .

5.78% ,19 years are the answers.

2=(1+r)^12

r=(2)^(1÷12)−1

R=0.0578*100=5.78%

3=(1+0.0595)^t

t=log(3)÷log(1.0595)

t=19 years

Exponential growth and exponential decay are two of the most common uses of exponential functions. Systems with exponential growth follow a model of the form y = y0ekt. In exponential growth, the growth rate is proportional to the amount present. In other words, for y'= ky

exponential function, multiply a by x to produce y. The exponential graph looks like a curve that starts with a very flat slope and becomes steep over time.

The exponential model, like the sphere model, starts at the origin and operates linearly near it. However, the increasing slope of the curve is less than the slope of the spherical model.

Learn  more about exponential function here:https://brainly.com/question/2456547

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Answer:

8r6s3 – 13r5s4 + r4s5 – 5r3s6 it is D

Step-by-step explanation:

The value of the difference of the polynomials is,

⇒ 8r⁶s³ - 13r⁵s⁴ + r⁴s⁵ - 5r³s⁶

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The expression is,

⇒ (8r⁶s³ – 9r⁵s⁴ + 3r⁴s⁵) – (2r⁴s⁵ – 5r³s⁶ – 4r⁵s⁴)

Now, We can find the difference as;

⇒ (8r⁶s³ – 9r⁵s⁴ + 3r⁴s⁵) – (2r⁴s⁵ – 5r³s⁶ – 4r⁵s⁴)

⇒ (8r⁶s³ – 9r⁵s⁴ – 4r⁵s⁴ + 3r⁴s⁵ – 2r⁴s⁵ – 5r³s⁶

⇒ 8r⁶s³ - 13r⁵s⁴ + r⁴s⁵ - 5r³s⁶

Thus, The value of the difference of the polynomials is,

⇒ 8r⁶s³ - 13r⁵s⁴ + r⁴s⁵ - 5r³s⁶

Learn more about the subtraction visit:

https://brainly.com/question/17301989

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Answer:

Es ydjwj rjsbt djeiweke

Answer:

Answer:

Last option

Step-by-step explanation:

First method :

Red Line:

Take 2 coordinates through which the line passes. Let it be (0, 7) and (14, 0).

[tex]slope, m=\frac{ 0-7}{14-0} = -\frac{7}{14} = -\frac{1}{2}[/tex]

[tex]Equation : (y - 7) = -\frac{1}{2}(x)[/tex]

                [tex]2y - 14 = -x\\2y + x = 14\\4y + 2x = 28[/tex]                  [tex][ multiply \ by \ 2 \ on \ both \ sides][/tex]

Blue Line:

Take coordinates through which the line passes.

Let it be (-4, -12) and (-10, -9).

[tex]slope, m = \frac{-9 + 14}{-10} = \frac{5}{-10} = -\frac{1}{2}[/tex]

[tex]equation : (y + 12) = -\frac{1}{2} (x+4)\\[/tex]

              [tex]y = -\frac{1}{2}x - 2 - 12\\\\y = -\frac{1}{2}x -14\\\\2y = -x - 28\\\\-2y = x +28[/tex]

Second Method:

From the graph it is clear the lines are parallel. The slopes of line parallel to each other are equal. So convert each equation into standard line equation form :y = mx + b

And check for set of equation whose slope are same.

First set :

[tex]y = 10x - 15 \\\\=> slope = 10\\\\-9x + 2y = 10\\2y = 9x + 10\\\\y = \frac{9}{2}x + 5 => slope = \frac{9}{2}[/tex]

Slopes are not equal.

Second set :

[tex]2y = 2x + 5\\y = x + \frac{5}{2}\\slope = 1\\\\\\3x -4y = -5\\4y = 3x + 5\\\\\y = \frac{3}{4}x + \frac{5}{4}\\\\slope = \frac{3}{4}[/tex]

Slopes are not equal.

Third set :

[tex]y = 3x +10 \\slope = 3\\\\\\2x - 3y = -6\\3y = 2x +6\\\\y = \frac{2}{3}x + 2\\\\slope = \frac{2}{3}[/tex]

Slopes are not equal.

Fourth set :

[tex]2x + 4y = 28\\4y = -2x +28\\\\y = -\frac{1}{2}x + 7\\\\slope = -\frac{1}{2}\\\\\\-2y = x + 28\\\\y = -\frac{1}{2}x - 14\\\\slope = -\frac{1}{2}[/tex]

Slopes are same.

Answer:

gotta be  answer A

Step-by-step explanation:

you can search up f(x) = square root of x

Answer:

B. Evidence

Step-by-step explanation:

Reference: like when your drawing something and you want to make sure that you draw the hair the same way some other person did.

Cite: That’s when you give the credits to someone or something 90% sure

Hope this helps :)

The type of correlation not associated with scatterplots is an indefinite correlation

Correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data.

Correlation can only be between -1 and 1 but not outside these values.

Hence the type of correlation not associated with scatterplots is an indefinite correlation

Learn more on correlation here: https://brainly.com/question/26172866

Answer:

£72000

Step-by-step explanation:

According to the Question,

Thus, 5 ⇒ 9000 People

So, 4 ⇒ 7200 People(Men)

      1 ⇒ 1800 People(Women)

Thus, The amount of money made from tickets sold to men is 7200 total Men x £10 Per Ticket Cost ⇒ £72000.

Answer:

Two hours

Step-by-step explanation:

The Royal Flush:

$65 + $30(per hour) = $95(for one hour)

$95 + $30 = $125(for two hours

The Leaky Faucet:

$35 + $45(per hour) = $80(for one hour)

$80 + $45 = $125(for two hours)

Therefore, it would take two hours for both of the repair services to have the same total.

Step-by-step explanation:

6/20

3/10 (simplified)

do you want the percentage?

Answer:

[tex]\frac{3}{10}[/tex]

Step-by-step explanation:

The multiplies of 3 from 1-20 are:

3, 6, 9, 12, 15, 18

Since there are [tex]20-1+1=20[/tex] numbers from 1-20 inclusive, the probability that a ball is a multiple of 3 is [tex]\frac{6}{20}=\boxed{\frac{3}{10}}[/tex]

Answer:

23

Step-by-step explanation:

The absolute value of any number is just the positive version of that number. For example the absolute value of -12 is 12.

Hope this helps! :)

Answer: y = 1x + 3

Step-by-step explanation:

If you plot it, you see the slope is 1/1, and the y-intercept is at (0, 3).

Answer:

SA= 882cm^2

Step-by-step explanation:

SA=2( width*length + hight*length + hight*width )

SA=2( 9*20+ 9*20+ 9*9)

SA= 2*441

SA=882cm^2

Answer:

The sum of money deposited is approximately $22,021.74

Step-by-step explanation:

The given interest and amounts of the deposit are outlined as follows;

The simple interest per annum, R = 0.325%

The number of years the money is deposited, T = 4 years

The total amount received (Interest + Initial deposit), A = $50,650

We have;

I = P × R × T

Where;

P = The principal (initial amount deposited)

R = The (annual) interest rate = 0.325%

T = The time = 4 years

Therefore;

The total amount received, A = P + I

P + I = P + P × R × T = P × (1 + R × T)

∴ A = P + I = P × (1 + R × T)

P = A/(1 + R × T)

Plugging in the values, gives;

P = 50,650/(1 + 0.325 × 4) = 506,500/23 ≈ 22,021.74

The sum of money deposited, P = $22,021.74

Answer:

25

Step-by-step explanation:

Moving it down does not change the length.

Answer:

x - 5(x - 2) - 1

Step-by-step explanation:

Answer:

x - 5(x - 2) - 1Step-by-step explanation:

Answer:

The area of a playground is 20 square yards. The length of the playground is 5 times longer than its width. Find the length and width of the playground.

length = 1 yd, width = 20 yd

length = 2 yd, width = 10 yd

length = 10 yd, width = 2 yd

length = 20 yd, width = 1 y

We know that :

⊕  Sum of the interior angles in a Pentagon should be equal to 540°

⇒  x° + (2x)° + (2x)° + 90° + 90° = 540°

⇒  (5x)° = 540° - 180°

⇒  (5x)° = 360°

[tex]\sf{\implies x^{\circ} = \dfrac{360^{\circ}}{5}}[/tex]

⇒ x° = 72°

4x + 5 = 3x +4

4x - 3x = 4-5

x = -1

value of x is equal to -1

Answer:

x = -1

Step-by-step explanation:

4x + 5 = 3x +4 (subtract 3x from both sides)

-3x        -3x

=1x         =0

rewrite: x + 5 = 4 (subtract 5 from both sides)

                  -5  -5

                  =0  =-1

Therefore x = -1 (Please mark brainliest hope i helped :)

Step-by-step explanation:

First, given that we must use point slope form, we can define that as

y - y₁ = m (x-x₁), with m being the slope .

To find the slope, we can use the equation

[tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]. Two points on the graph are (0, 1) and (1, 3). For these points, when calculating the slope, 0 and 1 represent x₁ and y₁ respectively, while 1 and 3 represent x₂ and y₂ respectively Using this formula, we can plug our points in to get

[tex]\frac{3-1}{1-0} = 2/1 = 2[/tex]

as our slope. Therefore, our equation is

y - y₁ = 2 (x-x₁).

For our first point, (0,1), we can simply plug 0 in for x₁ and 1 in for y₁ to get

y - 1 = 2(x-0) as one equation

Next, for (1,3) we can plug 1 for x₁ and 3 for y₁ to get

y - 3 = 2 (x-1) as our other equation

Answer:

274

Step-by-step explanation:

202 + 6(9 + 3) =

PEMDAS says parentheses first

202 + 6(12) =

Then multiply

202 +72

Then add

274

Answer:

274

Step-by-step explanation:

202 + 6(9 + 3)

202 + 6(12)

202 + 72

274

Answer:

43 hours

Step-by-step explanation:

[tex]\frac{y}{1} :\frac{408}{9.5}[/tex]

y × 9.5 = 408 × 1

9.5y = 408

9.5y ÷ 9.5 = 408 ÷ 9.5

[tex]y=42\frac{18}{19}[/tex]

43 hours

Answer:

B'(2,4) & C'(1,0)

Step-by-step explanation:

According To the Question,

Given, We have an ∆ABC that has coordinates A(3, 1), B(5, 5) and C(4, 1).

Now, After a translation, the coordinates of A' are (0,0) .

Then, the coordinate of B' & C' Also changes the same as like A' .

A(3,1) ⇒ A'(0,0)      {here from x-axis it reduce 3 and from y-axis it reduce 1}

Same as Above,

B(5,5) ⇒ B'(2,4)

&, C(4,1) ⇒ C'(1,0) .