Ed is setting up the locations of the corners of a 12-foot by 5-foot rectangular deck he is going to build in his backyard To make sure he has a perfect rectangle. What should the length diagonal be?

The surface area of the part of the x2 + y2 + z2 = 8z that lies inside the paraboloid z = x2 + y2, using the cylindrical coordinates is given as below:

The integral to find the surface area in the cylindrical coordinates, we can write as,

∫∫ dS = ∫∫ r dθ dr The given surface is x2 + y2 + z2 = 8z and the paraboloid is z = x2 + y2

By substituting the value of z from the paraboloid to the first equation,

we get,x2 + y2 + (x2 + y2)2 = 8(x2 + y2) Simplify it by expanding the square term as,

x2 + y2 + x4 + 2x2y2 + y4 = 8x2 + 8y2Now,

re-write the equation as,

x2 + y2 - 8x2 - 8y2 + x4 + 2x2y2 + y4 = 0On

solving this equation, we get

x2 + y2 - 8x2 - 8y2 + x4 + 2x2y2 + y4 = (x2 - 4x + y2 - 4y + 8)(x2 + 4x + y2 + 4y - 8) = 0

The equation of the paraboloid is given as, z = x2 + y2Hence,

the integral to find the surface area of the given surface in cylindrical coordinates,

∫∫ dS = ∫∫ r dθ dr Bounds of the integral to find the surface area are 0 ≤ θ ≤ 2π and r1 ≤ r ≤ r2,

where r1 and r2 are the radii of the cylinder.

Solve this equation and get the values of r1 and r2,r2 = 2r1

On solving the quadratic equation of (x2 - 4x + y2 - 4y + 8)(x2 + 4x + y2 + 4y - 8) = 0,

we get,

x2 + y2 - 4x - 4y + 4 = 0

The equation of the circle is given as

,x2 + y2 = 4x + 4y - 4 Solve for x and y to get,

x = 2 + cos θ y = 2 + sin θ

The radius of the circle is given as,

√(42 + 42) = √32 Thus,

the limits of integration of r are r1 = 0 and r2 = √32.

Integrating over the limits,

∫0^2π ∫0^√32 r dr dθ= 1/2(32) (2π)= 16πTherefore,

the surface area of the given surface is 16π.

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Answer:

- w - 24

Step-by-step explanation:

- 4(w + 6) + 3w ← multiply each term in the parenthesis by - 4

= - 4w - 24 + 3w ← collect like terms

= (- 4w + 3w) - 24

= - w - 24

The answer to this question which is based on Trignometry is that we divide when we want to calculate Trignometric Ratios

How many Trignometric ratios are available?

There are six basic trigonometric ratios: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These ratios are used to calculate angles and sides of a right triangle.

Whenever we need to calculate Trignometric ratios we have to divide the length of 2 sides of a triangle and one more the Trignometric ratios can be only found in Right Angled triangle

Hence we can just find the Trignometric ratios for any Triangle we can only do it for right Triangles

The values of Trignometric ratios can be negative also and it depends on the angle for which we want to find the Trignometric ratios.

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To find the area we have to calculate the radius first. Here the radius is 6m. So the area will be 36π m². Option C is the correct one.

Diameter is the straight line connecting two points on the edge of the circle, that passes through the Centre of the circle. It will be equal to two times the radius.

D = 2r

r = D/2 = 12/2 = 6m

Area of a circle can be calculated using the equation πr².

Area = π × 6² = 36π m²

So the area of the given circle with diameter will be 36π m².

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To calculate the probability of selecting a boy or a red-haired person as a homeroom representative to student council, we need to find the probability of each event and then use the formula P(A or B) = P(A) + P(B) - P(A and B).

There are 31 students in total (16 girls + 15 boys). The probability of selecting a boy is 15/31.

There are 5 red-haired students (3 girls + 2 boys). The probability of selecting a red-haired person is 5/31.

However, we need to account for the overlap between boys and red-haired students. There are 2 red-haired boys, so the probability of selecting a red-haired boy is 2/31.

Now we can use the formula: P(boy or red-haired) = P(boy) + P(red-haired) - P(boy and red-haired) = (15/31) + (5/31) - (2/31) = 18/31.

So, the probability of selecting a boy or a red-haired person as a homeroom representative to student council is 18/31.

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Answer:

Option A

Step-by-step explanation:

Correlation DOES NOT MEAN causation. There's weird statistics like positive correlation between the number of vanilla ice cream sold and murders committed in park, but that does not mean selling more vanilla gets more people killed.

Correlation only describe behavior of two things relative to each other. More water does not necessarily mean more grape b/c other factors like soil, climate, manure etc could result in more grapes.

Answer: X = -7

Step-by-step explanation:

the number is represented as X

6x + 10 = 4x - 4

solve your equation by subtracting 10 on both sides to make -4 -14

6x = 4x - 14

subtract 4x on both sides to get 2x

2x = -14

divide -14 by 2x

x = -7

Check it by plugging it in the equation

-42 + 10 = -28 - 4

-32 = -32

Answer:

-7

Answer:

d = 47°

Step-by-step explanation:

Image is attached

Sum of angles drawn along a straight line = 180°:

The angle drawn in pink : 180° - 112° = 68°

The angle drawn in green: 180° - 66° = 114°

The angle drawn in yellowish orange: 180° - 23° = 157°

The angle marked in purple: 180° - 102° = 78°

The figure drawn in the center is a 5-sided irregular pentagon

∴ Sum of interior angles in a 5-sided polygon = (n - 2) ×180°

                                                                            = (5 - 2) × 180°

                                                                            = 540°

The four angles calculated above will assist in calculating the fifth remaining angle of the pentagon (which is marked in light blue):

   68° + 114° + 78° + 157° + angle in light blue = 540°

Angle in light blue = 540° - 68° - 114° - 78° - 157°

                               = 123°

Sum of angles drawn along a straight line = 180°:

Angle marked in dark blue = 180° - 123°

                                                = 57°

Now focus on the angles present inside the triangle

Sum of interior angles of a triangle = 180°

= d + 76° + 57° = 180°

d has to be isolated and made the subject of the equation:

d = 180° - 76° - 57°

d = 47°

The period of the pendulum is approximately 1.57 seconds.

The period of a simple pendulum can be calculated using the formula: T = 2π√(L/g), where T is the period of the pendulum, L is the length of the pendulum, and g is the acceleration due to gravity. To calculate the period of the pendulum,

we need to first calculate the value of g. The acceleration due to gravity at the surface of the Earth is approximately 9.81 m/s^2. Substituting the values, we get:

T = 2π√(0.255/9.81) = 1.57 seconds

Therefore, the period of the pendulum is approximately 1.57 seconds.

It is important to note that this calculation assumes that the angle through which the pendulum is pulled and released is small. If the angle is too large, the pendulum will not follow a simple harmonic motion and the period calculated using this formula may not be accurate.

Additionally, other factors such as air resistance and friction may affect the motion of the pendulum and cause the period to deviate from the calculated value.

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                                  "Complete question"

t: You pull a simple pendulum of length 0.255 m to the side through an angle of 3.50 degree and release it. How much time does it take the pendulum bob to reach its highest speed? Take free fall acceleration to be 9.80 m/s^2. t = _____ s How much time does it take if the pendulum is released at an angle of 1.75 degree instead of 3.50 degree? t = _____ s

Answer: Circle, vertical axis, 5

Step-by-step explanation:

Answer:

  A.  m^2+7m+10=0

Step-by-step explanation:

This is a problem in pattern matching, and in substituting a variable for a pattern.

  (x^2+3)^2 +7x^2 +21 = -10 . . . . . . given

  (x^2 +3)^2 +7(x^2 +3) = -10 . . . . . factor the last two terms

  m^2 +7m = -10 . . . . . . . . . . . . subsitute m for x^2 +3

  m^2 +7m +10 = 0 . . . . . . . . add 10 to both sides; matches A

The total dollar change in labor expense from this 15% increase in productivity is [calculated value]. The percent change in labor expense is [calculated value].

Part I: Effective cost per hour per employee

To calculate the effective cost per hour per employee, we need to consider various factors such as base wage, fringe benefits, paid time off, and the number of working hours per year.

Base hourly wage: $12.30 per hour

Number of working hours per day: 8 (1 shift)

Number of holidays: 5

Number of vacation days: 7

First, let's calculate the total fringe benefits per hour:

Fringe benefits = 37% of base wage = 0.37 * $12.30 = $4.551

Next, let's calculate the paid time off per hour:

Paid time off = (Number of holidays + Number of vacation days) * 8 hours = (5 + 7) * 8 = 96 hours

Now, let's calculate the effective cost per hour per employee:

Effective cost per hour = Base hourly wage + Fringe benefits + (Paid time off * Base hourly wage)

Effective cost per hour = $12.30 + $4.551 + (96 * $12.30)

Part II: Reduction in labor cost

To calculate the reduction in labor cost due to a 15% increase in productivity, we need to consider the total number of working hours needed and the change in productivity.

Number of working hours needed every year: 306,050

Productivity increase from 70% to 85%: 85% - 70% = 15%

First, let's calculate the initial number of workers needed:

Initial number of workers = Number of working hours needed / (Productivity rate / 100)

Initial number of workers = 306,050 / (70 / 100)

Next, let's calculate the new number of workers needed after the productivity increase:

New number of workers = Number of working hours needed / (New productivity rate / 100)

New number of workers = 306,050 / (85 / 100)

Finally, let's calculate the total dollar change in labor expense:

Total dollar change in labor expense = (Initial number of workers - New number of workers) * Effective cost per hour * Number of working hours per year

To calculate the percent change in labor expense, we can use the following formula:

Percent change in labor expense = (Total dollar change in labor expense / Initial labor expense) * 100

Please provide the values for Effective cost per hour and Initial labor expense to calculate the final answers in Part I and Part II.

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Solution

- In order to find the length of the unknown sides, we simply need to look at the single and double strokes crossing the sides of the diagram.

- The sides with the same number of strokes have the same lengths.

- This implies that

Answer: 9:30 am

Step-by-step explanation:

To solve this question, add up the time that Will spent walking from his home to the mall and then the length of time he spent in the mall and then the amount of time it took him to walk from the mall to the office:

= 30 + 45 + 15

= 1 hr 30 mins

Then deduct this number from 11:00 am to find out when he left home:

= 11 am - 1 hr 30 mins

= 9:30 am

W satisfies all the three conditions of being a subspace of V. So, W is a subspace of V.

W is the set of all 3 x 2 matrices of the form [a,b; (a + b),0; 0,c]. It needs to be verified that W is a subspace of V, which has standard operations. Let us check whether W satisfies the three conditions to be a subspace of V or not:

Closure under addition: If X, Y are any two elements of W, then X + Y is also in

W.[a₁, b₁; (a₁ + b₁), 0; 0,c₁] + [a₂, b₂; (a₂ + b₂), 0; 0,c₂] = [a₁ + a₂, b₁ + b₂; (a₁ + b₁ + a₂ + b₂), 0; 0,c₁ + c₂]

The resulting matrix has the same form as W. So, W is closed under addition.

Closure under scalar multiplication: If X is any element of W and k is any scalar, then k

X is also in W.k[a, b; (a + b), 0; 0,c] = [ka, kb; k(a + b), 0; 0,kc]

This is of the same form as W. So, W is closed under scalar multiplication.

Contains zero vector: The zero vector is [0,0; 0,0; 0,0], which is of the same form as W. So, W contains the zero vector.

Therefore, W satisfies all the three conditions of being a subspace of V. So, W is a subspace of V.

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In performing back-substitution, we work with the echelon form of an augmented matrix that corresponds to a system of linear equations in x, y, and z.

Back-substitution is a method used to solve a system of linear equations by working with the echelon form of an augmented matrix.  To perform back-substitution, we start from the bottom row of the echelon form and solve for the variables one by one. We substitute the value of the variable we solved for into the equations above it, simplifying the system of equations at each step.

In the given problem, the echelon form of the augmented matrix represents a system of linear equations in x, y, and z. By performing back-substitution, we can find the values of x, y, and z that satisfy the system of equations.

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Answer:

No

Step-by-step explanation:

Dude, I'm not joking.

I started writing stuff as a joke, than developed it, and I think I'll write a book. You just gave me an incredible idea (not about fat people, about society itself and our future).

Thank you very much.

If you see any book written by a Racciatti in 10 years, contact me.

Hope this works, holy man so much ideas in my head. Thank you again.

Aggregate Demand (AD) is a macroeconomic concept that represents the total demand for goods and services in an economy. The X factor in the AD equation represents exports, which are an important part of the economy.

AD is calculated by adding up the individual components of demand, which include consumer spending (C), investment spending (I), government spending (G), and net exports (X-M). The X-M component represents the difference between exports (X) and imports (M).

The X component in the equation represents exports, which are the goods and services produced domestically and sold to foreign countries. Exports are an important part of the economy as they generate income and create jobs. The M component in the equation represents imports, which are the goods and services purchased from foreign countries and consumed domestically. Imports can have a negative impact on the economy as they represent a drain on resources and can lead to a trade deficit. The X factor in the equation is used to represent exports because it is a variable that can change over time. Factors that can affect exports include exchange rates, tariffs, and global demand for certain products. If the exchange rate between two currencies changes, it can make exports more or less expensive for foreign buyers, which can affect the level of exports. Tariffs are taxes on imports, which can make domestic products more competitive in foreign markets.

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Answer:

94 children, 64 students, and 47 adults attended the movie theater.

Step-by-step explanation:

Let; a be for adults, s for students, and c for children.

Make a system to solve for the amount of people.

c/a = 2

a + 2a + s = 205

3a + s = 205

Simplify.

s = 205 - 3a

s = 205 - 3a

c = 2a

Plug it in.

5c + 7s + 12a = 1482

10a + 7(205 -3a) + 12a = 1482

10a + 1435 - 21a + 12a = 1482

a + 1435 = 1482

a = 47

Substitute.

c = 2(47)

c = 94

Solve.

s = 205 - 3(47)

s = 64

Answer:

draw a line straight down through p

Answer:

20 cups holds less

Step-by-step explanation:

image you have 5 gallons and 20 cups you could see the diffrence between the 2.

Step-by-step explanation:

2:3

sum =5

=2/5×500

=200 books in the children's section while

=3/5×500

=300 bks in other sections

Answer:

The difference is 10.

6-(-4) = 10

Therefore, the image of the point (0, -7) after a dilation by a scale factor of 4 centered at the origin is (0, -28).

In mathematics, a scale factor is a numerical value that describes how much an object has been scaled or resized. It is the ratio of the size of the image to the size of the original object. Scale factors can be applied to two-dimensional or three-dimensional objects, and can be used to describe enlargements (scaling up) or reductions (scaling down) of the object.

Here,

To find the image of the point (0, -7) after a dilation by a scale factor of 4 centered at the origin, we can use the following formula:

(x', y') = (kx, ky)

where (x, y) is the original point, (x', y') is the image of the point after dilation, k is the scale factor, and the dilation is centered at the origin.

In this case, the original point is (0, -7), the scale factor is 4, and the origin is (0, 0). Plugging these values into the formula, we get:

(x', y') = (4 * 0, 4 * (-7))

Simplifying, we get:

(x', y') = (0, -28)

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Answer:

 point (-2,11)  does not lie on the given line

Step-by-step explanation:

To find : Which of the following points does not lie on the line ?

Solution :

To determine the point lie on line or not we have to put points in equation if it satisfy then it lie otherwise not.

a) Point (1,8)

Line  y=3x+5

Substitute x=1 and y=8

8=3(1)+5

8=8

(1,8) point lie on the line.

b) Point (4,12)

Line y=3x+5

Substitute x=4 and y=17,

17=3(4)+5

17=12+5

17=17

(4,17) point does not lie on the line.

c) point (-2,11)

Line y=3x+5

substitute x=-2 and y=11

11=3(-2)+5

11=-6+5

11 is not equal to -1

d) Point(0.5)

Line y=3x+5

Substitute x=0 and y=5

5=3(0)+5

5=5

Answer: 47,780 steps

Step-by-step explanation: For Alex's steps, we'll need to move the decimal four places to the right, and once you do that you should get 24,200. Add 24,200 and 23,580 together and you should get 47,780 steps.

Answer:

Based on the given information, we know the following:

Solid A is formed by joining one hemisphere to the frustum of a cone.

Solid B is formed by joining the other hemisphere to the small cone that was removed from the large cone.

The volume of solid A is 6 times the volume of solid B.

We can use the formulas for the volume of a hemisphere and a frustum of a cone to represent the volumes of solids A and B.

The volume of a hemisphere is (2/3)πr^3, where r is the radius of the hemisphere.

The volume of a frustum of a cone is (1/3)πh(R^2+r^2+Rr), where h is the height of the frustum, R is the radius of the larger base and r is the radius of the smaller base.

The volume of a cone is (1/3)πr^2h

Let's call the height of the frustum h, the radius of the large base R and the radius of the small base r

We can set up the equation: (2/3)πr^3 = 6((1/3)πr^2h + (1/3)πR^2h + (1/3)πRrh)

After simplifying, we get:

2h = 12r + 12Rh + 6Rr

We know k = (R/r)^(1/3)>(7)^1/3, we can substitute it into the equation:

2h = 12r + 12rk + 6rk^2

Solving for h, we get:

h = 6rk + 6rk^2

So h is expressed in terms of k and r.

Answer:

19b >= 53

Step-by-step explanation:

The total number of cubic feet should be more than 53. You cant have less sand so it is greater then or equal to 53, instead of less than or equal to.