Use the Divergence Theorem to calculate the surface integral S F · dS; that is, calculate the flux of F across S. F(x, y, z) = (cos(z) + xy2) i + xe−z j + (sin(y) + x2z) k, S is the surface of the solid bounded by the paraboloid z = x2 + y2 and the plane z = 4.

The answer is:

The radius of the circle is 29.21 units.

To solve the problem, we need to remember that the radius of a circle is the distance from its center to any point of the circle.

We can use the following equation to calculate the distance between the center and the given point:

[tex]distance=radius=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }[/tex]

So, we are given the information:

[tex]Center(12,5)\\Point(-6,-18)[/tex]

Where,

[tex]x_1=12\\y_1=5\\x_2=-6\\y_2=-18[/tex]

Now, substituting and calculating, we have:

[tex]radius=\sqrt{((-6)-(12))^{2}+((-18)-(5)^{2}}\\\\radius=\sqrt{(-18)^{2}+(-23)^{2}}=\sqrt{324+529}=\sqrt{853}=29.21units[/tex]

Hence, we have that the radius of the circle is 29.21 units.

Have a nice day!

Answer:

AB =  29.23

Step-by-step explanation:

Points to remember

Distance formula

Distance between two points (x₁, y₁) and (x₂, y₂) is given by

Distance = √[(x₂- x₁)² + (y₂ - y₁)²]

To find the radius

Center = (12, 5) and point on the circle = (-6, -18)

Radius = √[(x₂- x₁)² + (y₂ - y₁)²]

  =  √[(12 - - 6)² + (5 -  -18)²]

  = √[(12 + 6)² + (5 +18)²]

  =√[18² + 23²] = √[324 +529 ]  =  29.23

Answer:

C, the two rounded rectangles

Step-by-step explanation:

Isometry can be divided into two words: iso = same and metry = measure

So, isometry means "same measure".

In this case, that means the transformation didn't change the measures of the object.

In A and B, you can see the figure has been transformed, while in C, it's the same shape and size, just a different color.

Answer:

C, the two rounded rectangles

Step-by-step explanation:

Isometry can be divided into two words: iso = same and metry = measure

So, isometry means "same measure".

In this case, that means the transformation didn't change the measures of the object.

In A and B, you can see the figure has been transformed, while in C, it's the same shape and size, just a different color.

Read more on Brainly.com - https://brainly.com/question/12600222#readmore

Answer:

The third one (QRP)

Step-by-step explanation:

it indicates that the angle is at point R, which it isn't! The letter in the middle shows where the angle is

Option C is not a correct way to name the angle. This is obtained by understanding the correct ways of naming an angle.

The correct ways of naming an angle are,

In the given question,

Hence option C is not a correct way to name the angle.

Learn more about naming a triangle here:

brainly.com/question/26038114

#SPJ2

Answer:

$ 555

Step-by-step explanation:

Salary for a 40-hour work week = $380

Total income for the week will be = Salary of regular 40 hours + Salary of 14 hours overtime

Salary per hour for the overtime work = $ 12.50

So,

The salary for 14 hours of overtime will be = $ 12.50 x 14 = $ 175

Therefore,

Total income for the week will be = $ 380 + $175 = $ 555

Thus, for a 40 hour work week and 14 hours of overtime the total income of the week will be $ 555

Answer:

  see attached

Step-by-step explanation:

The function that tells you the number of dollars you spend on a given number of pounds creates graphs with the coordinates (pounds, dollars).

If you want 1 pound to correspond to G dollars, then a point on the graph will be ...

  (1, G)

Answer:

(1,g)

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

It is x=24

Answer:

(C) [tex]x=12[/tex]

Step-by-step explanation:

Given: It is given that OP is parallel to NQ and ON=7, NM=21. PQ=x, QM=36.

To find: The value of x.

Solution: It is given that OP is parallel to NQ and ON=7, NM=21. PQ=x, QM=36, thus using the proportionality theorem, we get

[tex]\frac{ON}{OM}=\frac{PQ}{PM}[/tex]

Substituting the given values, we have

[tex]\frac{7}{7+21}=\frac{x}{x+36}[/tex]

Upon solving the above equation, we get

[tex]\frac{7}{28}=\frac{x}{x+36}[/tex]

[tex]\frac{1}{4}=\frac{x}{x+36}[/tex]

[tex]x+36=4x[/tex]

[tex]x=12[/tex]

Hence, the value of x is 12 and option C is correct.

Answer:

The length is 21 meters

Step-by-step explanation:

* Lets use variable to represent the dimensions of the rectangle

- The length of the rectangle is 6 meters longer than its width

# Let the width of the rectangle = x meters

∴ The length of the rectangle = x + 6 meters

- The area of the rectangle = Length × width

∵ The area of the rectangle = 315 meters²

∵ The length of the rectangle = x + 6

∵ The width of the rectangle = x

∴ x(x + 6) = 315 ⇒ open the brackets to solve the equation

∴ x² + 6x = 315 ⇒ subtract 315 from both sides

∴ x² + 6x - 315 = 0

- Lets factorize the quadratic equation to find the value of x

∵ The last term of the quadratic is negative

∴ The brackets have different sign

# x² = x × x ⇒ 1st terms in the two brackets

# -315 = -15 × 21 ⇒ 2nd terms in the two brackets

# x × -15 = -15x ⇒ 1st term in the first bracket and 2nd term in

  the second bracket

# x × 21 = 21x ⇒ 1st term in the second bracket and 2nd term

  in the first bracket

# 21x - 15 x = 6x ⇒ the middle term of the quadratic equation

∴ The factoriz of x² + 6x - 315 = 0 is

  (x + 21)(x - 15) = 0

∴ x + 21 = 0 OR x - 15 = 0

# x + 21 = 0 ⇒ subtract 21 from both sides

∴ x = -21 ⇒ neglect this answer because there is no negative

  value for the dimensions

# x - 15 = 0 ⇒ add 15 to both sides

∴ x = 15

- The value of the width is x

∴ The width = 15 meters

- The value of the length is x + 6

∴ The length = 15 + 6 = 21 meters

Answer:

• lateral area: 36√3 square units

• total surface area: (36 +36√3) square units

Step-by-step explanation:

The area of an equilateral triangle of side length s is given by ...

A = (√3)/4·s^2

Your pyramid has four (4) such faces of side length 6 units, so the total (lateral) area of the triangular faces is ...

LA = √3·(6 units)^2 = 36√3 square units

___

Of course the area of the square base is simply the square of its edge length, so is ...

A = (6 units)^2 = 36 square units

That means the total surface area, the lateral area plus the base area, is ...

(36 +36√3) square units

Answer:

Option B

Step-by-step explanation:

Given

f(x)=  (x^2+x-2)/(x^3-1)

For vertical asymptotes we have to put the denominator of the function equal to zero:

x^3-1=0

x^3=1

So,

x=1

As the degree of denominator is greater than the degree of numerator, there will be only horizontal asymptote which will be y=0 because all the y values will be dragged down to the x-axis.  

So the horizontal asymptote: y=0

And Vertical asymptote: x =1

Answer:

b

Step-by-step explanation:

Answer:

  (x^2 -2x +1) -16/(5x+10)

Step-by-step explanation:

The quotient and remainder can be found by polynomial long division or by synthetic division.

___

For synthetic division, it is recommended to divide the dividend and divisor by the leading coefficient of the divisor (5), so the divisor coefficient is 1. This results in a divisor of (x+2) and a remainder of -16/5. The simplified remainder becomes ...

  (-16/5)/(x+2) = -16/(5x +10)

See the attachments for the various methods of computing the quotient.

For this case we must find the difference of the following expressions:

[tex]0.00067\\2.3 * 10 ^ {- 5}[/tex]

For the second expression we must run the decimal 5 times to the left, because the exponent is negative, that is:

[tex]0.000023[/tex]

We subtract:

[tex]0.00067-0.000023 = 0.000647[/tex]

Represented in scientific notation we have:

[tex]6.47 * 10 ^ {- 4}[/tex]

Answer:

Option A

Answer:

6.47 x 10^(-4)

Step-by-step explanation:

already did it mate

Answer:

C

Step-by-step explanation:

g(x) = f(x - π/3), so g(x) is f(x) shifted to the right π/3 units.

Answer C.

Answer:

86.25

Step-by-step explanation:

97+84+78+86=345 then u divide by 4 which is 86.25

Answer:

75 yd

Step-by-step explanation:

Given in the question a right angle triangle.

Base of right angle triangle = x

Height of right angle triangle = 40yd

To find x we will use trigonometry identity

here Ф = 62°

opposite = base

adjacent = height

Plug values in the formula to find x

Tan(62) = x / 40

   x        = (40)(Tan(62))

             = 75.229 yd

             ≈ 75 yd

The value of x is:

              x=75.2 yard.

We are given a right triangle with base 40 yard.

Also, the perpendicular length of the triangle corresponding to angle 62° is: x

Now we find the value of x using the trignometric formula as:

[tex]\tan 62\degree=\dfrac{x}{40}[/tex]

We know that the value of tan 62°=1.88073

Hence, we have:

[tex]1.88073=\dfrac{x}{40}\\\\\\x=40\times 1.88073\\\\\\x=75.2292[/tex]

         Hence, we have: x=75.2 yard

Answer:

73 markers

Step-by-step explanation:

let b = blue markers

black markers = b+5

red markers = 4* black markers

                     = 4 * (b+5)

                      = 4b+20

The total markers is blue + black + red

                           b + b+5 + 4b+20 = 6b+25

We know she has 8 blue markers

black markers = b+5 = 8+5 = 13

red markers = 4b +20 = 4*8 +20 = 32+20 = 52

The total markers =6b+25= 6(8) + 25 = 48+25 = 73

Answer:

3/b^4

Step-by-step explanation:

b^0 = 1

3b^(-4) / b^0 = 3b^(-4) / 1 = 3b^-4

Since you are instructed to write only positive exponents, the answer is 3/b^4

Answer:

  c.  8 units

Step-by-step explanation:

You are to find the y-intercepts of the two functions given, then report the difference between them. The y-intercept is the y-value when x=0.

For f(x), we have ...

  f(0) = 3·2^0 = 3·1 = 3

__

For the table, we can see that x=0 is halfway between x=-2 and x=2, so the y-intercept can be expected to be halfway between y=3 and y=-13. That value for y is ...

  g(0) = (3 + (-13))/2 = -10/2 = -5

That is, the y-intercept of g(x) is -5.

__

The difference between f(0) and g(0) is ...

  f(0) -g(0) = 3 -(-5) = 8 . . . . units

35 cubic in.

7/2=3.5

10*4=20/2=10

10*3.5=35

The answer to the problem is Undefined slope .

Answer:

x = ±5

Step-by-step explanation:

x^2-25=0

Add 25 to each side

x^2-25+25=0+25

x^2 = 25

Take the square root of each side

sqrt(x^2) = sqrt(25)

x = ±5

If [tex]z=1-i[/tex], then [tex]|z|=\sqrt{1^2+(-1)^2}=\sqrt2[/tex] and [tex]\arg z=-\dfrac\pi4[/tex] because [tex]z[/tex] lies in the fourth quadrant.

By DeMoivre's theorem,

[tex]z=|z|e^{i\arg z}\implies z^{10}=(\sqrt2)^{10}e^{-i10\pi/4}=32e^{-i5\pi/2}=32e^{-i\pi/2}=-32i[/tex]

so the answer is B.

Answer:

B

Step-by-step explanation:

edge 2020

Answer:

The area of cylinder 949.536 in²

Step-by-step explanation:

Points to remember

Curved surface area of cylinder = 2πrh

Where r - radius of cylinder

h - Height of cylinder

To find the area of cylinder

Here r = diameter/2 = 6.3/2 = 3.15 in

h = 48 in

Area =  2πrh

 = 2 * 3.14 * 3.15 * 48

= 949.536 in²

Therefore area of cylinder 949.536 in²

Answer:

Step-by-step explanation:

You can compute the slope from two of the points, then write the point-slope form of the equation of the line.

  slope = (change in y)/(change in x)

  = (15 -20)/(3 -1) = -5/2

Then the equation of the line, using the first point) is ...

  y = m(x -h) +k . . . . . . for slope m through point (h, k)

  y = -5/2(x -1) +20

The x-intercept is the value of x where y=0:

  0 = -5/2(x -1) +20 . . .put 0 where y is in the equation, then solve for x

  0 = (x -1) -8 . . . . . . . . multiply by -2/5 (the inverse of the x-coefficient)

  9 = x . . . . . . . . . . . . . simplify, add 9

The x-intercept is (9, 0).

__

The y-intercept is the value of y where x=0:

  y = -5/2(0 -1) +20 . . . . . . put 0 where x is in the equation, then solve for y.

  y = -2.5 +20 = 17.5

The y-intercept is (0, 17.5).

_____

Comment on the problem

Your question page seems to offer both lesson and video help. Either or both may be better than the written solution here.

Answer:

c. 1,000,000 plate numbers

Step-by-step explanation:

Each of the 6 digits of a Delaware plate can take on any of 10 values, so there are ...

10×10×10×10×10×10 = 1,000,000

possible plate numbers.

Delaware can assign 1,000,000 license plate numbers under its six-digit numbering system, as each of the six places can have any digit from 0 to 9 giving 10^6 or one million possible combinations.

The question asks how many license plate numbers Delaware can assign under their six-digit numbering system. To find the number of possible combinations for a six-digit number where each digit can be any number from 0 to 9, we need to calculate 10 possibilities for each position (including the leading zero) multiplied together.

Therefore, the calculation follows this pattern: 10  imes 10  imes 10  imes 10  imes 10  imes 10, which equals 1,000,000 possible combinations. This is because each of the six places in the license plate number can have any of the ten digits from 0 to 9. So the answer to how many license plate numbers Delaware can assign under their system is 1,000,000 plate numbers.

Answer:

-x² -2x -5 -12/(x-2)

Step-by-step explanation:

The attachment shows the synthetic division. You can find the remainder by evaluating the dividend for x=2:

-2³ -2 -2 = -12 . . . . matches the above answer, not [A] or [C] shown

_____

You can always multiply out your answer to see if it matches the problem.

(-x^2 -2x +3)(x -2) +3 = -x^3 +7x -3 . . . . not the dividend you started with

1. a Early Pay: y = 45

 b. Deposit Plus: y = 12.00 + 4.00x

 c. Daily Pay: y = 6.00x

2.  Early pay = $25

   Deposit Plus = 12.00 + 4.00(4) =  12.00 + 16.00 = $28.00

 Daily Pay = 6.00(4) = $24.00

Daily Pay is the cheapest one.

3. Early Pay = $45

 Deposit Plus = 12.00 + 4.00(8) = 12.00 + 32.00 = $44.00

 Daily Pay = 6.00(8) = $48.00

Deposit Plus is the cheapest one.

4. Early Pay = $45

Deposit Plus = 12.00 + 4.00(12) = 12.00 + 48.00 = $60.00

Daily Pay = 6.00(12) = $72.00

Early Pay is the cheapest one.

5.  Since Jane likes to swim most days, it would be cheaper for her to do the Early pay option, because the price is a one time fee and she can swim every day.

Since Suzy doesn't really like to go swimming and might only go a couple times, it would be best for her to do the daily pay, that way she didn't spend any money up front if she doesn't swim at all.

Answer:

(-5,1)

(-2,4)

Step-by-step explanation:

y = x + 6

y = x^2 + 8x + 16

Since both equations are equal to y, we can set them equal to each other

x + 6  = x^2 + 8x + 16

Subtract x from each side

x -x + 6

= x^2 + 8x-x + 16

6 = x^2 +7x +16

Subtract 6 from each side

6-6 = x^2 +7x +16-6

0 = x^2 +7x +10

Factor

What 2 numbers multiply together to give us 10 and add together to give us 7?

5*2 = 10

5+2 =7

0 = (x+5) (x+2)

Using the zero product property

x+5 = 0  x+2 = 0

x = -5   x=-2

Now we need to find the y's that go with the x's

x=-5

y= x+6

y =-5+6

y=-1

(-5,1)

x=-2

y = -2+6

y=4

(-2,4)

1. 9/12 because all of them added together is 12 but cinnamon raisin is 3 so 12-3 gives u 9 and the total is 12 so 9/12

1b. Plain(2) wheat(1) poppy(4) 2+1+4=7. The total is again 12 so 7/12

Answer:

degree

Step-by-step explanation:

The degree is the unit of measurement for angles; it is equal to 1/360th of a complete revolution.

Step 1: Find the area of the living room on the blueprint with the formula Area = length x height

A = 4 x 8

A = 32

Step 2: We now know that the area of the living room on the blueprint is 32 inches, but we have to convert it into the actual answer. To do this multiply 32 by 40 (you have to do this because 1 inch is 40 inch in reality meaning that each inch in  the 32 inches is times 40 <<< Does that make sense?), so...

40 x 32 = 1,280

Hope this helped!

Answer:

The measurements for the actual room are, in inches, 160 x 320

Step-by-step explanation:

If you want the computed area, then multiply those numbers together since A=bh.  I assumed you were just looking for the measurements of the actual room.  Set up a ratio for the scale first, the model info in the numerator and the actual room info in the denominator:

[tex]\frac{m}{a}: \frac{1}{40}[/tex]

Here, the m is the model on paper and the a is the actual room.  So if the length of the room on paper is 4 inches, that will go on top with the model stuff and we will solve for the missing equivalent length of the actual room:

[tex]\frac{m}{a} :\frac{1}{40} =\frac{4}{x}[/tex]

Cross multiply to get that the length of the actual room is 160 inches long. Divide by 12 if you need that number in feet.

Doing the same with the width:

[tex]\frac{m}{a} :\frac{1}{40}=\frac{8}{y}[/tex]

Cross multiply to get that the width of the actual room is 320 inches.  Again, if you need that in feet, divide by 12.