Given that a is rational and √2 is irrational and a is not equal to 2, show that. √2-1 is irrational​

The flux is 9.

Flux is the presence of a force field in a specified physical medium, or the flow of energy through a surface.

Given:

2x+2y+z= 1

F = 2i+2j + 2k

Now,

r = xi + yj + z( 1-2x-2y) K

dr/dx= i - 2k

dr/dy = j-2k

dr/dx* dr/dy

= ( i - 2k) * (j-2k)

= 2i + 2j + k

F(x)= 2i+2j + 2k

F(x). da = 4 +4 +2 = 10 dxdy

Hence, flux

= [tex]\int\limits^1_0 {\int\limits^{1-2y}_0 {10 } \, dx dy } \,[/tex]

=  [tex]\int\limits^1_0[/tex]  10(1-2y) dx

= [tex]\int\limits^1_0[/tex] 10-2y

= 10(1) - (1)²

=9

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The plane has intercepts (1/2, 0, 0), (0, 1/2, 0), and (0, 0, 1). Parameterize [tex]S[/tex] by the vector function

[tex]\vec s(u,v) = \dfrac{(1-u)(1-v)}2 \, \vec\imath + \dfrac{u(1-v)}2 \, \vec\jmath + v \,\vec k[/tex]

with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. (More explicitly, we have the parameterization

[tex]\vec s(u,v) = (1-v)((1-u) p_1 + u p_2) + v p_3[/tex]

where [tex]p_i[/tex] denote the given points.)

The normal vector to [tex]S[/tex] is

[tex]\vec n = \dfrac{\partial\vec s}{\partial u} \times \dfrac{\partial\vec s}{\partial v} = \dfrac{1-v}2\,\vec\imath + \dfrac{1-v}2\,\vec\jmath + \dfrac{1-v}4\,\vec k[/tex]

Then the flux of [tex]\vec F = 2\,\vec\imath+2\,\vec\jmath+2\,\vec k[/tex] across [tex]S[/tex] is given by the surface integral,

[tex]\displaystyle \iint_S \vec F \cdot d\vec\sigma = \iint_S \vec F \cdot \vec n \, dA[/tex]

[tex]\displaystyle = \int_0^1 \int_0^1 \left(2\,\vec\imath+2\,\vec\jmath+2\,\vec k) \cdot \left(\frac{1-v}2\,\vec\imath + \frac{1-v}2\,\vec\jmath + \frac{1-v}4\,\vec k\right) \, du \, dv[/tex]

[tex]\displaystyle = \frac52 \int_0^1 \int_0^1 (1-v) \, du \, dv[/tex]

[tex]\displaystyle  = \frac52 \int_0^1 (1-v) \, dv = \boxed{\frac54}[/tex]

Answer:

Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.

Step-by-step explanation:

The graph of function f(x) is the parent function.

(Parent functions are the simplest form of a given family of functions).

The graph of g(x) is related to the graph of f(x) by a series of transformations.  To determine the series of transformations, work out the steps of how to go from f(x) to g(x).

Transformations

For a > 0

[tex]\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of }\:a \\& \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\& \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a \end{aligned}[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

[tex]y=f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

Parent function:

[tex]f(x)=x^3[/tex]

Step 1

Multiply the parent function by 6:

[tex]\implies 6f(x)=6x^3[/tex]

Therefore, this is a vertical stretch by a factor of 6.

Step 2

Now make the function negative:

[tex]\implies -6f(x)=-6x^3[/tex]

Therefore, this is a reflection in the x-axis.

Step 3

Finally, add 2 to the function:

[tex]\implies -6f(x)+2=-6x^3+2[/tex]

Therefore, the function has been translated 2 units up.

Conclusion

Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.

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distance = speed * time

the first bus speed = x

second bus = x - 12

the sum of distance = 765 miles

first distance = 6x

second distance = 6 (x -12)

6x + 6(x-12) = 765

x + x -12 = 127.5

2x = 139.5

x = 69.75 mi/h which is the faster bus

the second bus speed = 57.75 mi/h

Answer:

the answer is 4gn Puig IT in

Answer: 180 degrees

Step-by-step explanation:

Angles on a line add to 180 degrees since they form a straight angle.

We can subtract the function that represents the cost in 2000 from the function that represents the cost in 1990.

Doing this gives us [tex](-20t^{2}+1000)-(-10t^{2}+1500)=\boxed{-10t^{2}-500}[/tex]

The probability that exactly 4 are cured from 7 dolphins is 0.0128

Probability is the likeliness of an event to occur and it has a range of 0 to 1, where 0 means unlikely and 1 indicates certainty of the event to happen.

It is given that the 92% of all the dolphins are cured of an ear infection ,When treated with an antibiotic

If there are total dolphins given as 7

On the basis of given data

The dolphin that cannot be cured is given by

1 - p = 1 - (92/100) = 0.08 = 8/100

q = (8/100)
n= 7

r = 4

Therefore by Binomial Distribution

[tex]P = ^nC_r p^r q^{n-r}[/tex]

Putting the values

[tex]P = ^7C_4 (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}[/tex]

[tex]P = \dfrac{7!}{4! \;3!} (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}[/tex]

P =  0.0128

Therefore the probability is 0.0128.

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Step-by-step explanation:

(4²-x²)³/²

or,(4+X) (4-X)

Substitute [tex]x = 4 \sin(y)[/tex], so that [tex]dx = 4\cos(y)\,dy[/tex]. Part of the integrand reduces to

[tex]16 - x^2 = 16 - (4\sin(y))^2 = 16 - 16 \sin^2(y) = 16 (1 - \sin^2(y)) = 16 \cos^2(y)[/tex]

Note that we want this substitution to be reversible, so we tacitly assume [tex]-\frac\pi2\le y\le \frac\pi2[/tex]. Then [tex]\cos(y)\ge0[/tex], and

[tex](16-x^2)^{3/2} = 16^{3/2} \left(\cos^2(y)\right)^{3/2} = 64 |\cos(y)|^3 = 64 \cos^3(y)[/tex]

(since [tex]\sqrt{x^2} = |x|[/tex] for all real [tex]x[/tex])

So, the integral we want transforms to

[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx = 64 \int \cos^3(y) \times 4\cos(y) \, dy = 256 \int \cos^4(y) \, dy[/tex]

Expand the integrand using the identity

[tex]\cos^2(x) = \dfrac{1+\cos(2x)}2[/tex]

to write

[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx = 256 \int \left(\frac{1 + \cos(2y)}2\right)^2 \, dy \\\\ = 64 \int (1 + 2 \cos(2y) + \cos^2(2y)) \, dy \\\\ = 64 \int (1 + 2 \cos(2y) + \frac{1 + \cos(4y)}2\right) \, dy \\\\ = 32 \int (3 + 4 \cos(2y) + \cos(4y)) \, dy[/tex]

Now integrate to get

[tex]\displaystyle 32 \int (3 + 4 \cos(2y) + \cos(4y)) \, dy = 32 \left(3y + 2 \sin(2y) + \frac14 \sin(4y)\right) + C \\\\ = 96 y + 64 \sin(2y) + 8 \sin(4y) + C[/tex]

Recall the double angle identity,

[tex]\sin(2y) = 2 \sin(y) \cos(y)[/tex]

[tex]\implies \sin(4y) = 2 \sin(2y) \cos(2y) = 4 \sin(y) \cos(y) (\cos^2(y) - \sin^2(y))[/tex]

By the Pythagorean identity,

[tex]\cos(y) = \sqrt{1 - \sin^2(y)} = \sqrt{1 - \dfrac{x^2}{16}} = \dfrac{\sqrt{16-x^2}}4[/tex]

Finally, put the result back in terms of [tex]x[/tex].

[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx \\\\ = 96 \sin^{-1}\left(\frac x4\right) + 128 \frac x4 \frac{\sqrt{16-x^2}}4 + 32 \frac x4 \frac{\sqrt{16-x^2}}4 \left(\frac{16-x^2}{16} - \frac{x^2}{16}\right) + C \\\\ = 96 \sin^{-1}\left(\frac x4\right) + 8 x \sqrt{16 - x^2} + \frac14 x \sqrt{16 - x^2} (8 - x^2) + C \\\\ = \boxed{96 \sin^{-1}\left(\frac x4\right) + \frac14 x \sqrt{16 - x^2} \left(40 - x^2\right) + C}[/tex]

Answer:

C=55m + 30

Step-by-step explanation:

You would multiply 55 by the number of months so you'd get 55m, and since 30 is a one time fee you would just add 30 to your monthly payment.

Answer:

approximately $23,655.91 (rounded to the nearest hundredths place)

Step-by-step explanation:

[tex]22,000=0.93x\\x=23,655.91[/tex]

Answer:

Step-by-step explanation:

let the list price=x

93% of x=22,000

x=22,000 ×100/93

≈23,655.91 $

Answer:

Step-by-step explanation:

(xm , ym )  = x1 + x2 / 2               and            y1 + y2 / 2

               = 9 +3 / 2                                      = 10 -10 / 2

               = 12/2                                            = 0/2

                = 6                                                  = 0

                So midpoints are (6 , 0)

Answer:

midpoint =  [tex](9\frac{1}{2} , -3\frac{1}{2} )[/tex]

Step-by-step explanation:

To find the midpoint of a line segment, you have to find the average of the x and y-values of the end-points, i.e., add the x-coordinate values and divide the answer by 2, and do the same for the y-coordinate values.

• midpoint = [tex](\frac{x_{2} + x_1}{2}, \frac{y_2 + y_1}{2} )[/tex]

                 = [tex](\frac{9 + 10}{2}, \frac{3 + (-10)}{2} )[/tex]

                 = [tex](\frac{19}{2}, \frac{-7}{2} )[/tex]

                 = [tex](9\frac{1}{2} , -3\frac{1}{2} )[/tex]

Answer: [tex]y=x-9[/tex]

Step-by-step explanation:

To find the inverse of a function you must first swap the places of x and y

[tex]x=y+9[/tex]

Now solve for y

Step 1: Flip the equation.

[tex]y+9=x[/tex]

Step 2: Subtract 9 from both sides.

[tex]y+9-9=x-9\\y=x-9[/tex]

Answer:

-6/11 goes with -1/2

-7/9 goes with -3/4

-3/13 goes with -1/4

Step-by-step explanation:

6/11 is close to 6/12 which is the same as 1/2, so -6/11 goes with -1/2

7/9 is close to 6.75/9 which is 3/4, so -7/9 is close to -3/4

3/13 is close to 3/12 which is the same as 1/4, so -3/13 goes with -1/4

Answer:

In standard form thats 4.4024

In standard form, 4+0.4+0.0024 can be written as 4.4024

Concept: Any number we can write as a decimal number, between 1.0 and 10.0, multiplied by 10, is said to be in the normal range. 1.23 × 108;

If you look closely, 1.23 is a decimal number between 1.0 and 10.0 so we have a standard form 123,000,000 as 1.23 × 108.

Given: 4+0.4+0.0024

In this case,4 is the integral value and 0.4 is at the first decimal place followed by 0.0024 at the third and 4th decimal place so combining them all together and writing them in standard form we get,4.4024

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Answer:

D.

Step-by-step explanation:

It is the only one that contains all the x-values of the points. (Domain is the set of x-values).

Answer:

First find the x and y intercepts. Recall that intercepts intersect the x and y axis of a graph, therefore either the x or y value of a coordinate point must be 0 in order for it to be an intercept.

After you find the intercept, plot the them on the cartesian coordinate system and draw a straight line (it’s a linear equation) going through the two intercepts.

Side note: Not sure how credentials work on Quora yet. I meant to say I am a student

The equation of the lines can be plotted on the graph after calculating the coordinates on each line.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two linear equation:

x = 4y  

x + y = 7.0

To plot the linear equation first we will find the few coordinates to plot on the coordinate plane.

For the equation of line:

x = 4y

x 0 1 2 3 -1 -2 -3

y 0 4 8 12 -4 -8 -12

For the equation of line:

x + y = 7.0

x 0 1 2 3 -1 -2 -3

y 7 6 5 4 8 9 10

Thus, the equation of the lines can be plotted on the graph after calculating the coordinates on each line.

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Answer:

2+3+4 = 9

Add the three numbers of the three school districts that project to lose.

In solving minimum and maximum problems, result we are looking for would be the constant, k.

When looking for the minimum functional value, we are looking for the constant, k because it can be thought of as the absolute minimum value.

An open parabola would then have k as the maximum functional value which means that the constant k is the value being sought.

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Answer:

false

Step-by-step explanation:

the answer is x=70

Answer:

the measure of line AD is 8

Step-by-step explanation:

lines AD and BC are equal, due to the markings on the lines
this means that if line BC is 8, than line AD is also 8

The solution for the system of equations is: (99/13, 150/13)

Given the two expression 2/3x+3/5y=12 and 5/2y-3x=6

We have to find solution of two given expression.

To find the value of x, we have to eliminate y by making y the subject of formula in any of the equations.

Multiply equation A by 5/3 t.o get,

5/3(2/3x) + 5/3(3/5y) = 5/3(12)

10/9x + y = 20

y = 20 - 10/9x

substituting for y into equation b, we have:

5/2(20 - 10/9x) - 3x = 6

50 - 25/9x - 3x = 6

52/9x = 44

52x = 396

The expression that gives the value of x is: 52x = 396

Hence, x = 396/52 = 99/13

y = 20 - 10/9(99/13) = 20 - 110/13 = 150/13

Hence The solution for the system of equations is: (99/13, 150/13)

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Answer:

0.339

Step-by-step explanation:

Hope it helped!

Hii!

___________________________________________________________

Answer: 0.339

Explanation:

There are two rounding rules that will help us whenever we need to round a number! These are the rules.

---

Now that we know the rules, let's get down to solving our problem! ^^

The nearest thousandth is 3 decimal places.

_._ _ _ <==== Nearest thousandth

The third number after the decimal point is 9. After it is a digit that is less than 5. According to the rounding rules, we should round down.

[tex]\boldsymbol{0.3391=== > 0.339}[/tex]

--

Hope that this helped! Best wishes.

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Th equation that can be used to find the umber of minutes Teri ran is m + 2 = 28 minutes.

Addition is a mathematical operation that is used to determine the sum of two or more numbers.

The total minutes run by Julie = minutes ran by Teri + 2

28 = m + 2

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The difference in price between the two companies is $81-$79.56 = $1.44

Fire side Shop

Price of Chimney cap =$120

First Discount = 25% of(120)=$30

Price after 1st Discount = $120-$30=$90

Second Discount = 10% of 90=$9

Price after 2nd Discount = $90-$9=$81

Builders' Supply

Price of Chimney Cap= $111

First Discount= 25% of 111 = $27.75

Price after 1st Discount = $111 - $27.75 = $83.75

Second Discount = 5% of $83.75 = $ 4.1875

Price after 2nd Discount = $83.75 - $4.1875 = $79.5625 ≈ $79.56

Therefore,

a) Builders supply offers the lower price.

b) Difference in price = $81-$79.56 = $1.44

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The probability of failure for Luis will be 0.18.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The probability of passing is = 0.82

We know that the maximum probability of happening any event is 1 or 100 per cent if the probability of passing of the person is 0.82 then the probability of failure will be calculated as:-

Probability of failing = 1 - probability of passing

Probability of failing = 1 - 0.82

Probability of failing = 0.18

Therefore the probability of failure for Luis will be 0.18.

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|2x + 5| ≤ 11

x = 3

2(3) + 5

6 + 5

11 ≤ 11

The solution for the x in the inequality |2x + 5| ≤ 11 is {-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3}

Inequality shows relation between two expression which are not equal to each others.

The given inequality is,

|2x + 5| ≤ 11

To find the solution for the x, solve the inequality,

|2x + 5| ≤ 11

-11 ≤ 2x + 5 ≤ 11

Subtract 5 from whole the expression,

-11 - 5 ≤ 2x + 5 - 5 ≤ 11 - 5

-16 ≤ 2x ≤ 6

-8 ≤ x ≤ 3

The value of x for the given inequality varies from -8 to 3.

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Answer:

One solution

Step-by-step explanation:

The equation can be rewrite as 3x - 6 = 22 - x

so we try to get all the x on one side so we add x and 6 to both sides so we get 4x = 28 then we divide by 4 both side and get x=7

Answer:

Inequality:  x + 6 ≤ 24

Solution:  x ≤ 18

Step-by-step explanation:

Plus:  "+" →  to add something to something else

Less than or equal to:  "≤" → the expression on the left side of the inequality sign is smaller than the expression on the right side of the sign.

Let x be the unknown number.

A number plus 6 is less than or equal to twenty-four:

x + 6 ≤ 24

To solve the found inequality, subtract 6 from both sides:

⇒ x + 6 - 6 ≤ 24 - 6

⇒ x ≤ 18

Therefore, the solution to the inequality is x ≤ 18.  The unknown number x can be any real number equal to or less than 18.

No be n

Solve

Solution set

Answer:

Step-by-step explanation: