Using a) parabolic coordinates and b) cylindrical coordinates, find the differential unit of length, ds2 = dx2 + dy2 + dz2 and the volume element dV = dxdydz.

The triangles are dilated by a scale factor of 2.

In geometry, dilation is a transformation that changes the size of a geometric figure, but not its shape. A dilation is performed by multiplying the coordinates of each point in the original figure by a fixed value called the scale factor.

In the given question,

To find the scale factor used to dilate triangle D to create triangle D', we can compare the corresponding side lengths of the two triangles.

Let x be the scale factor. Then we have:

Side length of D' / Side length of D = x

Using this relationship for each corresponding side length of the two triangles, we have:

12 / 6 = x (for the side of length 6 in triangle D)

16 / 8 = x (for the side of length 8 in triangle D)

20 / 10 = x (for the side of length 10 in triangle D)

Simplifying each equation, we get:

2 = x (from 12 / 6 = x)

2 = x (from 16 / 8 = x)

2 = x (from 20 / 10 = x)

Since all three equations have the same value of x, we can conclude that the scale factor used to dilate triangle D to create triangle D' is x = 2.

Therefore, the triangles are dilated by a scale factor of 2.

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Answer:

58.2677

Step-by-step explanation:

148 divide the length value by 2.54

Answer:

1 inch = 2.54 cm

148 / 2.54 = 58.2677165354 inches

Step-by-step explanation:

1. The equations for Sand, Clay, and Humus, we get: x = (12 - 3y)/4, x = (12 - 6y)/5, x = (10 - 12y)/5 2. The feasible region is the shaded region above the line Sand = 3 and to the left of the line Clay = 2.

What is linear programming?

Linear programming is a mathematical method used to optimize a linear objective function subject to linear constraints.

1. Formulating the problem as a linear programming:

Let x and y be the number of cubic feet of compost and topsoil, respectively, used to make one bag of potting soil.

We want to minimize the cost of the potting soil, which is given by:

Cost = 0.12x + 0.2y

We want to ensure that each bag of potting soil contains at least 12 pounds of sand, 12 pounds of clay, and 10 pounds of humus. The amount of each ingredient in one bag of potting soil can be calculated as follows:

Sand = 4x + 3y

Clay = 5x + 6y

Humus = 5x + 12y

We can now formulate the constraints as follows:

Sand ≥ 12

Clay ≥ 12

Humus ≥ 10

Solving for x and y in the equations for Sand, Clay, and Humus, we get:

x = (12 - 3y)/4

x = (12 - 6y)/5

x = (10 - 12y)/5

We also have the non-negativity constraints:

x ≥ 0

y ≥ 0

2. Plotting the constraints and showing the feasible region:

We can graph the constraints by plotting the equations for Sand, Clay, and Humus, and shading the region that satisfies all the constraints. The resulting feasible region is shown below:

The feasible region is the shaded region above the line Sand = 3 and to the left of the line Clay = 2.

3. Identifying the optimal solution:

We can find the optimal solution by finding the point in the feasible region that minimizes the cost of the potting soil. This point occurs where the cost function is minimized.

Cost = 0.12x + 0.2y

Substituting x = (12 - 3y)/4 and x = (12 - 6y)/5, we get:

Cost = 0.12[(12 - 3y)/4] + 0.2y

Cost = 0.12[(12 - 6y)/5] + 0.2y

Simplifying, we get:

Cost = 0.6 - 0.09y

Cost = 0.72 - 0.044y

We can now find the minimum value of Cost by setting its derivative to zero:

dCost/dy = -0.09 + 0.044 = 0

Solving for y, we get:

y = 2

Substituting y = 2 into x = (12 - 3y)/4 and x = (12 - 6y)/5, we get:

x = 3/4

x = 6/5

Therefore, the optimal solution occurs at x = 3/4 and y = 2, and the minimum cost of the potting soil is:

Cost = 0.12x + 0.2y = 0.12(3/4) + 0.2(2) = 0.39 dollars.

4. Interpreting the optimal solution:

The optimal solution indicates that the Queen City Nursery should use 3/4 cubic feet of compost and 2 cubic feet of topsoil to make one bag of potting soil, which will cost 39 cents. This solution satisfies all the constraints and minimizes the cost of the potting soil. The optimal solution also indicates that the potting soil should contain 3 cubic feet of sand, 12 cubic feet of clay, and 11 cubic feet of humus, which satisfies the minimum requirements for each ingredient.

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To approximate the binomial distribution using the normal distribution, we must first determine if the binomial distribution satisfies the criteria of the normal distribution.

Using the above normal distribution, we can find the probability of x as follows:

P(75 ≤ x ≤ 105) = P((75 – 90)/sqrt(63) ≤ z ≤ (105 – 90)/sqrt(63))

Here, z is the standard normal variable.To find the above probability, we can use the standard normal distribution table or calculator to find the values of the above z-score limits.

Using the standard normal distribution table, we get the following values:

z1 = (75 – 90)/sqrt(63) = -2.21z2 = (105 – 90)/sqrt(63) = 2.21

Using these values, we get:P(75 ≤ x ≤ 105) = P(-2.21 ≤ z ≤ 2.21) = 0.9851 – 0.0150 = 0.9701

Thus, the approximate probability of P(75 ≤ x ≤ 105) is 0.9701.

The normal distribution can be used to approximate the binomial distribution in this case. The exact probability is greater than the approximated probability by 0.0111. Therefore, the correct choice is A.

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The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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Therefore, the long-run aggregate supply curve is a vertical line that is not influenced by changes in aggregate demand or short-run economic conditions.

The long-run aggregate supply curve is represented by the vertical line at the potential output level, which indicates that in the long run, the economy will produce at its full capacity without any increase in inflation or decrease in unemployment.

In other words, the long-run aggregate supply curve is not affected by temporary fluctuations in prices or output levels, and instead represents the economy's natural rate of output in the absence of any short-term disturbances. Therefore, the long-run aggregate supply curve is a vertical line that is not influenced by changes in aggregate demand or short-run economic conditions.

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Answer:

Sin^2 x

Step-by-step explanation:

Here, we want to evaluate;

1 - sin^2x

Mathematically ;

sin^2 x + cos^2 x = 1

Thus;

sin^2 x = 1 - cos^2 x

The Nyquist sampling rate for x(t) is 1800 Hz.

Nyquist sampling theorem states that in order to accurately reconstruct a signal without aliasing, the sampling rate must be at least twice the highest frequency component in the signal.

For the given signal x(t), we need to determine the highest frequency component.

The first term in x(t) is 2 times the sinc function of 800pit. The sinc function has zeros at integer multiples of pi, and its first zero after the origin occurs at pi. Therefore, the highest frequency component in the first term of x(t) is 400 Hz (corresponding to the frequency at which the sinc function crosses zero after the origin).

The second term in x(t) is the square of the sinc function of 1800*t. The sinc function has zeros at integer multiples of pi, and its first zero after the origin occurs at pi/1800. Therefore, the highest frequency component in the second term of x(t) is 900 Hz (corresponding to twice the frequency at which the sinc function crosses zero after the origin).

Thus, the highest frequency component in x(t) is 900 Hz. According to the Nyquist theorem, the sampling rate must be at least twice this frequency, or 1800 Hz, in order to accurately reconstruct the signal without aliasing. Therefore, the Nyquist sampling rate for x(t) is 1800 Hz.

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To calculate the percent change in renewable energy investment in the US from 2005 to 2018, you can use the following formula:

Percent change = ((Final value - Initial value) / Initial value) * 100%

In this case, the initial value is $11.4 billion in 2005 and the final value is $46.5 billion in 2018. Plugging these values into the formula, we get:

Percent change = (($46.5 billion - $11.4 billion) / $11.4 billion) * 100%

= ($35.1 billion / $11.4 billion) * 100%

= 3.085 * 100%

= 308.5%

So, the percent change in renewable energy investment in the US from 2005 to 2018 was 308.5%, a substantial increase over the 13-year period.

Answer:

B

Step-by-step explanation:

B is the only case where the desired fraction is multiplied by de facto 1 (3/3 = 1) and remains unchanged.

all other answer options multiply or divide by something that is different to 1. and so, they change the original fraction.

Answer:

I'm sorry but I need some numbers to solve. we just learned this in class so I'm new though

Step-by-step explanation:

Needs numbers

Answer:

Jesse has the largest range between the two players. The difference between their ranges is 2.

Step-by-step explanation:

Jesse's range: 14

Barbara's range: 10

Range is determined by using the largest number and the smallest number in a set of integers and subtracting them. Jesse's highest number was 24, and his lowest would be 10. 24-10=14.

Barbara's highest score was 22, while her lowest was 12. 22-12=10.

subtracting Jesse's range from Barbara's range would equal 2.  

(please don't cook me if this is incorrect but i'm 97% sure i'm right)

The rate at which the distance between the tips of the hands are changing at one o'clock is 16.3 mm/h

The rate of change of a function is the rate at which the output variable changes with respect to the input variable.

Let m represent the minute hand, let h represent the hour hand, and let s represent the distance between the minute hand and the hour hand, we get

s² = m² + h² - 2·m·h·cos(S)

The angle, ∠S = 2·π/(12) = π/6

Therefore;

s² = 6² + 5² - 2×6×5×cos(π/6) = 61 + 60·(√3/2)

s = √(61 + 60·(√3/2))

s² = m² + h² - 2·m·h·cos(S)

\(\dfrac{d}{dt} (s^2)= \dfrac{d}{dt} \left(m^2+ h^2-2\cdot m \cdot h\cdot cos(\theta)\right)\)

\(\dfrac{d}{dt} (s^2)= 2\cdot s\cdot \dfrac{ds}{dt}= -2\cdot m \cdot h\times (-sin(\theta)\right))\dfrac{d\theta}{dt}\)

Which indicates that we have;

\(2\cdot s\cdot \dfrac{ds}{dt}= -2\cdot m \cdot h\times (-sin(\theta)\right))\dfrac{d\theta}{dt}\)

\(\dfrac{ds}{dt}=\dfrac{ -2\cdot m \cdot h\times \left(-sin(\theta)\right))\dfrac{d\theta}{dt}} {2\cdot s}\)

\(\dfrac{d\theta}{dt}=-\dfrac{11\cdot \pi}{6}\)

Therefore;

\(\dfrac{ds}{dt}=\dfrac{ -2\cdot m \cdot h\times \left(-sin(\theta)\right))\dfrac{d\theta}{dt}} {2\cdot s}\)

\(\dfrac{ds}{dt}=\dfrac{ 2\times 6 \times 5 \times 0.5)\dfrac{-11\cdot \pi }{6}} {2\times \sqrt{61 + 60\times \dfrac{\sqrt{3}}{2}} } \approx -16.3\)

The rate at which the hour hand is changing is approximately 16.3 mm/h

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Answer:

Step-by-step explanation:

d=-10--1=-10+1=-9

a(n) = a +(n-1)d

a(n) = -1 +(n-1)-9

a(204) = -1 +(204-1)-9

           =-1828

hope this help

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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Answer:

£177.92

Step-by-step explanation:

To increase something by 28% would be to multiply the original value by 1.28:

So to increase £139 by 28%, we do:

£139 × 1.28 = £177.92

So this is our final answer

The length of the hip on a hip roof rises 1.5 feet vertically.

The hip roof has a slope of 6 inches per foot ( hip slope factor = 1.5) and a hip run of 14 feet

Length of hip = (square root of (hip run squared + (hip slope factor x roof span squared)))
Plugging in the given values, we get:
Length of hip = (square root of (14 squared + (1.5 x 14 squared)))
Length of hip = (square root of (196 + 294))
Length of hip = (square root of 490)
Length of hip = 22 feet (rounded to the nearest whole number)
Therefore, the correct answer is C. 22.
It's important to note that the hip slope factor is a value used to calculate the actual slope of the hip, which is typically steeper than the pitch of the roof. In this case, the hip slope factor of 1.5 means that for every foot of horizontal run, the hip rises 1.5 feet vertically.

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we need to multiply this number by 100 to get the  as a percentage:

0.1806 * 100 = 18.06%

The probability of choosing a senior can be calculated using the formula:

P(senior) = (102/562) * 100

P(senior) = 18.06%

This means that there is an 18.06% chance of choosing a senior if a student is randomly selected from the school.

First, we need to calculate the total number of students in the school by adding together the number of students in each class:

Total = 165 + 145 + 114 + 102 = 562

Next, we need to calculate the probability of choosing a senior by taking the number of seniors enrolled in the school (102) and dividing it by the total number of students in the school (562).

102/562 = 0.1806

Finally, we need to multiply this number by 100 to get the probability as a percentage:

0.1806 * 100 = 18.06%

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Answer:

the height is 6 meters

Step-by-step explanation:

v = \(\pi r^{2} h\)

471 = 3.14(25)h

471 = 78.5h  Divide both sides by 78.5

\(\frac{471}{78.5}\) = \(\frac{78.5h}{78.5}\)

6 = h

Helping in the name of Jesus.

The 1st statement is true about the graph. Here the graph is a function with domain {0≤x≤5} and the range {-6≤y≤0}.

An organised representation of the data is all that the graph is. It facilitates our understanding of the facts.

The Latin term datum, which means "something delivered," is where the word data originated.

The development of a research question is followed by the ongoing observational collection of data.

Here in the question,

The graph is a function with domain {0≤x≤5} and the range {-6≤y≤0}.

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Answer:

53 degrees

Step-by-step explanation:

Angle N = angle E

because angle made by joining end points of same chord on circumference are always equal.

so angle E = 37

Angle D = 90 ( because angle made by diameter on circumference is 90 degrees)

Now in Triangle DEC. Sum if all the angles of triangle us 180

Angle D + angle E + ? = 180

37 + 90 + ? = 180

127 + ? = 180

? = 180 - 127

? = 53 degrees

The completed terms are (3 x 10¹)+(2 × 10¹⁹) + (2 × 10¹⁹) = 3 x 10¹ + 4 x 10¹⁹ = 4 x 10¹⁹, as the 10¹⁹ terms add up to 7 x 10²⁰.

To complete the terms you have to first performing the multiplication within each set of parentheses, which gave me (3 x 10¹⁹) + (4 x 10¹⁹). Then, I added these two terms together to get a final answer of 7 x 10²⁰.

In mathematics, a term is defined as the values of an algebraic expression on which mathematical operations occur. Let's look at an example of a word. This algebraic statement has terms 8x and 9.

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Only (d) 1 equation can you write to represent a single line using a point-slope equations

From the question, we have the following parameters that can be used in our computation:

Equation = Linear equation

A linear equation can only be represented with one equation

When it is represented with multiple equations, the equations are equivalent equations

This means that the equations can be converted to one another

Hence, the solution is (d) 1 equation

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Answer:

7 is 48b-4 and 8 is mn+4m

Step-by-step explanation:

Answer:

It will take Esther 200 minutes to read all 100 pages.

Step-by-step explanation:

The question is a little off, so this is how I'm interpreting it: If Esther has 100 pages to read, and she can read 20 pages in 40 minutes, how long will it take Esther to read all 100 pages?

Based on the two-tangent theorem, the value of x is calculated in the circle as: x = 2.

Based on the two-tangent theorem, if two tangents are drawn from a circle to meet each other at any point outside the circle, then the lengths of the tangents are congruent to each other, that is, they are equal.

Therefore, we would create the following equation based on the two-tangent theorem:

20x + 6 = 10x + 26

Combine like terms:

20x - 10x = -6 + 26

10x = 20

Divide both sides by 10:

10x/10 = 20/10

x = 2

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Answer:

8

Step-by-step explanation: