Designing a Silo
As an employee of the architectural firm of Brown and Farmer, you have been asked to design a silo to stand adjacent to an existing barn on the campus of the local community college. You are charged with finding the dimensions of the least expensive silo that meets the following specifications.

The silo will be made in the form of a right circular cylinder surmounted by a hemi-spherical dome.
It will stand on a circular concrete base that has a radius 1 foot larger than that of the cylinder.
The dome is to be made of galvanized sheet metal, the cylinder of pest-resistant lumber.
The cylindrical portion of the silo must hold 1000π cubic feet of grain.
Estimates for material and construction costs are as indicated in the diagram below.

The design of a silo with the estimates for the material and the construction costs.

The ultimate proportions of the silo will be determined by your computations. In order to provide the needed capacity, a relatively short silo would need to be fairly wide. A taller silo, on the other hand, could be rather narrow and still hold the necessary amount of grain. Thus there is an inverse relationship between r, the radius, and h, the height of the cylinder.


Rewrite your estimated cost for the cylinder in terms of the single variable, r, alone. Cost of cylinder = ___________________

the solution for the initial value problem is: u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t) where λ = ± sqrt(-4n² / a), and n is a non-zero integer.

The given partial differential equation is:

au(x, t) = 4 * (d²u(x, t) / dt²) / (dx²)

a) BCs (Boundary Conditions):

We have u(0, t) = 0 and u(π, t) = 0.

IC (Initial Condition):

We have u(x, 0) = x.

To solve this initial value problem, we need to find a function f(x) that satisfies the given boundary conditions and initial condition.

The solution for f(x) can be found using the method of separation of variables. Assuming u(x, t) = X(x) * T(t), we can rewrite the equation as:

X(x) * T'(t) = 4 * X''(x) * T(t) / a

Dividing both sides by X(x) * T(t) gives:

T'(t) / T(t) = 4 * X''(x) / (a * X(x))

Since the left side only depends on t and the right side only depends on x, both sides must be equal to a constant value, which we'll call -λ².

T'(t) / T(t) = -λ²

X''(x) / X(x) = -λ² * (a / 4)

Solving the first equation gives T(t) = C1 * exp(-λ² * t), where C1 is a constant.

Solving the second equation gives X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) + C3 * cos(sqrt(-λ² * (a / 4)) * x), where C2 and C3 are constants.

Now, applying the boundary conditions:

1) u(0, t) = 0:

Plugging in x = 0 into the solution X(x) gives C3 * cos(0) = 0, which implies C3 = 0.

2) u(π, t) = 0:

Plugging in x = π into the solution X(x) gives C2 * sin(sqrt(-λ² * (a / 4)) * π) = 0. To satisfy this condition, we need the sine term to be zero, which means sqrt(-λ² * (a / 4)) * π = n * π, where n is an integer. Solving for λ, we get λ = ± sqrt(-4n² / a), where n is a non-zero integer.

Now, let's find the expression for u(x, t) using the initial condition:

u(x, 0) = X(x) * T(0) = x

Plugging in t = 0 and X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) into the equation above, we get:

C2 * sin(sqrt(-λ² * (a / 4)) * x) * C1 = x

This implies C2 * C1 = 1, so we can choose C1 = 1 and C2 = 1.

Therefore, the solution for the initial value problem is:

u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t)

where λ = ± sqrt(-4n² / a), and n is a non-zero integer.

Note: Please double-check the provided equation and ensure the values of a and the given boundary conditions are correctly represented in the equation.

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The slope of the line is -4.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

From the diagram, the graph passes through point ( 0,2) and (1,-2)

Point 1( 0.2 )

x₁ = 0

y₁ = 2

Point 2( 1,-2 )

x₂ = 1

y₂ = -2

To determine the slope of the line, plug the coordinates into the above slope formula.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( -2 - 2 )/( 1 - 0 )

Slope m = ( -4 )/( 1  )

Slope m = -4/1

Slope m = -4

Therefore, the slope of the line is -4.

Option A is the correct answer.

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Answer:

Cost of rice cooker without VAT = Rs 3600

VAT amount = Rs 468

Step-by-step explanation:

Given:

To calculate:

Calculation:

we know that:

Cost of rice cooker with 13% VAT = Cost price + Vat% of Cost of rice cooker

Rs 4,068= Cost Price*(1+Vat%)

Rs 4,068 = Cost Price*(1+0.13)

Rs 4,068 = Cost Price*(1.13)

Dividing both side by 1.13

Cost Price = \(\tt \frac{Rs\: 4,068}{1.13}\)

Cost Price of rice cooker without VAT= Rs 3,600

Note: Here Cost of rice cooker is Selling Cost of rice cooker

Now

Vat amount = Vat % of cost of rice cooker

                   =0.13*Rs 3,600

                   =Rs 468

Therefore, Vat amount is Rs 468.

Answer:

if vat 13% is added, 113% value is 4068.. So, we need 100%? That is (4068x100) / 113 = 3600. So, the original price without vat is 3600.

The question is incomplete. Here is the complete question.

Mavis is interested whether military status is related to gender in American Samoa. The data she collected about the population of American Samoa in 2010 is below.

Find the marginal distribution of military status in percentages. Round to the nearest whole percentages.

In Armed Forces:

Military-dependent:

Civilian:

Answer: In Armed Forces: 0%

              Military-dependent: 3%

              Civilian: 97%

Step-by-step explanation: Marginal Distribution is defined as the probability distribution of variables contained in a subset.

For the American Samoa's military status, marginal distribution is

1) In Armed Forces:

\(p_{1}=\frac{87}{55,519}*100\)

\(p_{1}=0.15\)

2) Military-dependent:

\(p_{2}=\frac{1709}{55,519}*100\)

\(p_{2}=3.08\)

3) Civilian:

\(p_{3}=\frac{53,723}{55,519}*100\)

\(p_{3}=96.77\)

Now round each percentage to the nearest whole percentage:

Armed forces: 0%

Military: 3%

Civilian: 97%

The marginal distributions of military status are, in nearest whole percentage:

Armed forces: 0%

Military: 3%

Civilian: 97%

The missing parts are solved using ratio and are given as follows:

15) DE is derived as 6

16) BE is derived as 4.5

17) CE is derived as: 16

The missing parts of the geometric shapes above are derived using ratio or proportion.

15)

Where AB = 12 and DB = 9 and AC = 8

Thus,

DB/AB = DE/AC

⇒ 9/12 = DE/8

First, we can simplify 9/12 by dividing the numerator and denominator by 3 to get:

3/4 = DE/8

To solve for DE, we can cross-multiply by multiplying both sides of the equation by 8:

3/4 * 8 = DE

DE = 6

Therefore, the solution to the equation is DE = 6.

16)

Since, DE =6, AC = 9, and CE = 3 ; we can say that:

AC/DE = BE/CE
⇒ 9/6 = BE/3

irst, we can simplify 9/6 by dividing the numerator and denominator by 3 to get:

3/2 = BE/3

To solve for BE, we can cross-multiply by multiplying both sides of the equation by 3:

3/2 * 3 = BE

BE = 4.5

Therefore, the solution to the equation is BE = 4.5.



17)

Where

DE = 6 AC = 8 and BE = 12

AC/DE = CE/BE

⇒ 8/6 = CE/12

First, we can simplify 8/6 by dividing the numerator and denominator by 2 to get:

4/3 = CE/12

To solve for CE, we can cross-multiply by multiplying both sides of the equation by 12:

4/3 * 12 = CE

CE = 16

Therefore, the solution to the equation is CE = 16.

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Answer:

B. HF and QR

Step-by-step explanation:

HF is the same as QR just smaller. Also you can confirm this by looking at the order in the shapes from the question:

GFHE and TRQS

FH = RQ or HF = QR

hope this helps!

Answer:

g = 2d - 8

g + d = 46

Step-by-step explanation:

It is given that the guitarist wrote eight less than twice as many songs as the drummer did, hence one would multiply by the number of songs the drummer wrote by two, and subtract eight.

It is also given that the combined total of songs that they both wrote is 46, hence one would add up the songs that they wrote, and attain a result fo 46.

Answer:

c

Step-by-step explanation:

Tim weighting this bc it said

I would say B as the answer... 81 is just to high and 19 doesn't seem right.. so I'm just gonna go with B 23%

I am very sorry if this is wrong in anyway!

Answer:

the answer is 23%

Step-by-step explanation:

i used a percent increase calc... was too lazy to do the work haha

Answer:

9.42478

Step-by-step explanation:

Answer:

 9.42 cm^3

Step-by-step explanation:

Answer:

y = 10 , x= -3

Note: I have never hears this called "combination method"

if you research this on-line it is typically called the "elimination" or the  "addition" method.

Step-by-step explanation:

5x + y = 5

10x + 3y = 20

~~~~~~~~~~~~~~~~~~~~~

multiply top equation by -2

-10x + -2y = -10

10x + 3y = 20

y = 10

x= -3

The maximum number of years a blender can last and still be in the lowest 6% of life spans is 10.2215.

The blenders produced by a company have a normally distributed life span with a mean of 8.2 years and a standard deviation of 1.3 years. The company is willing to have a warranty that replaces at most 6% of the blenders it sells. We need to calculate the maximum number of years a blender can last and still be in the lowest 6% of life spans.

The mean is equal to 8.2. The standard deviation is 1.3. The probability is 6%. We will calculate the corresponding z-score. It is a normal distribution.

P(z) = 0.06

z = 1.555

z = (x - μ)/σ

1.555 = (x - 8.2)/1.3

x - 8.2 = 1.555*1.3

x = 8.2 + 2.0215

x = 10.2215

Hence, the maximum number of years a blender can last and still be in the lowest 6% of life spans is 10.2215.

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Answer:

C. The value of z has to be greater than 1

Step-by-step explanation:

\(15 - 15z < 0 \\ - 15z < - 15 \\ 15z > 15 \\ z > 1\)

Answer: isn't it 42÷7=6?

Answer:

42 / 7 = 6

Step-by-step explanation:

Just use a multiplication table.

Shor's Algorithm Efficiency of Shor’s algorithm in the general case, when r does not divide 2, is calculated as follows:

Shor's algorithm is an effective quantum computing algorithm for factoring large integers. The algorithm calculates the prime factors of a large number, using the modular exponentiation, and quantum Fourier transform in a quantum computer.In this algorithm, the calculation of the quantum Fourier transform takes O(N2) quantum gates, where N is the number of qubits required to represent the number whose factors are being determined.

To calculate the Fourier transform efficiently, the number of qubits should be set to log2 r. The general form of Shor's algorithm is given by the following pseudocode:

1. Choose a number at random from 1 to N-1.

2. Find the greatest common divisor (GCD) of a and N. If GCD is not 1, then it is a nontrivial factor of N.

3. Use quantum Fourier transform to determine the period r of f(x) = a^x mod N. If r is odd, repeat step 2 with a different value of a.

4. If r is even and a^(r/2) mod N is not -1, then the factors of N are given by GCD(a^(r/2) + 1, N) and GCD(a^(r/2) - 1, N).

The efficiency of the algorithm is determined by the number of gates needed to execute it. Shor's algorithm has an exponential speedup over classical factoring algorithms, but the number of qubits required to represent the number whose factors are being determined is also exponentially large in the number of digits in the number.

In the general case when r does not divide 2, the efficiency of Shor's algorithm is reduced. However, the overall performance of the algorithm is still better than classical factoring algorithms.

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Answer: C. 8x2 - 6x - 3

Step-by-step explanation:

I took the test. Hope this helps

The prime polynomial is 8x^2 - 6x - 3

Polynomials are expressions that are represents using terms and coefficients

For a polynomial to be prime, then the polynomial cannot be factored into smaller expressions

From the given options, 8x^2 - 6x - 3 cannot be factorized.

Hence, the prime polynomial is 8x^2 - 6x - 3

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The area of the shaded segment of the circle is 39.27 square meter.

From the given figure, radius = 8 m.

We know that, the area of the minor segment of the circle is (θ / 360°) × πr²- (1/2) r² sin θ.

Angle of minor arc = 360°-240°

= 120°

Here, area of the segment = (120°/360°) ×3.14×8²-1/2 ×8²×sin 120°

= 1/3 ×3.14×64-1/2×64×√3/2

= 39.27 square meter

Therefore, the area of the shaded segment of the circle is 39.27 square meter.

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Answer:28°

Step-by-step explanation:

Angle O is double the size of the angle at the circumference

76x2=152

tangents are right angles from the radius

90°

90+90+152=332

360-332=28°

Option D. The faculty should use the median to make their argument. The median will be lower than the mean since the mean is influenced by the few extremely high salaries.

Mean is the average of any data set whereas the median is the middle value we get after arranging the data in ascending order.

So for example, if the salaries of any 5 faculty members are as follows:

$10,000 , $50,000 , $80,000 , $150,000 , $160,000

Mean= (10,000+50,000+80,000+150,000+160,000) / 5

Mean= $90,000

Median= (5+1) / 2

Median= 6/2

Median= 3rd value

As the data is already arranged in ascending order, Median is $80,000

Hence, if the faculty want to give the community the impression that they deserve higher salaries, they should advertise the median of their current salaries.

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Answer:

it's significant figure it have 4 significant figure

it have other value also percentage, rational and whole number

Answer:

1. Median:70, Range:12, IQR: 8

2. Median: 59, Range: 48, IQR: 31

Step-by-step explanation:

Hello, the answers I have are just approximations because I can not tell the specific number in between each mark.

The median is the middle vertical line of the box. The range is you maximum subtracted from your minimum. You can find these at the lines that extend out of the box. The interquartile range is the ends of the box subtracted from each other, meaning quartile 3 subtracted from quartile 1.

Hope this helps.

Answer:

He has 60 paper clips before giving some away.

Step-by-step explanation:

Before : 5x : 3x

After:  5x - 12 = 3x + 12

5x -  12 = 3x + 12

First, we need to take away the smallest value of x from the largest.

-3x

2x - 12 = 12

Then, we need to add +12 to get rid of -12 on the lefthand side.

2x = 24

Divide by 2 to get x on its own.

x = 12

Bert had 5x so we need to multiply x (what we found as 12) by 5. 12 x 5 = 60. Bert had 60 paper clips before he gave some away.

We can prove this answer as correct, too.

5 x 12 = 60

3 x 12 = 36

60 - 12 = 36 + 12

48 = 48

Hope this helps, have a good day. :D

The irreducible polynomials modulo 3 of degree 2 are x^2 + x + 2$ and $x^2 + 2x + 2.

In this question, we are required to list all irreducible polynomials modulo 3 of degree 2.

The set of all polynomials mod 3 of degree 2 is as follows: 0, 1, 2, x, x + 1, x + 2, 2x, 2x + 1, 2x + 2, x^2, x^2 + 1, x^2 + 2, x^2 + x, x^2 + x + 1, x^2 + x + 2, x^2 + 2x, x^2 + 2x + 1, x^2 + 2x + 2

Let's start by finding the product of all polynomials mod 3 of degree 1.

(x - 0)(x - 1)(x - 2) = x^3 - 3x^2 + 2x

Now, we will find all the possible products of polynomials of degree 1 and degree 2.

(x + 0)(x^2 + ax + b) = bx^2 + (a)x^3 + b  (x + 1)(x^2 + ax + b) = x^2(a + 1) + x(1 + a + b) + b  (x + 2)(x^2 + ax + b) = bx^2 + (a + 2)x^3 + (2a + b)x + 2b

The first polynomial, x^3 - 3x^2 + 2x, already contains $x^2$, so we will only take into consideration the coefficients of $x$ and the constant term.

Now, we will cross off all the polynomials which have coefficients that are multiples of 3 as they are reducible.

x^2 + 1, x^2 + 2, x^2 + x + 1, x^2 + x + 2

Therefore, the irreducible polynomials modulo 3 of degree 2 are $x^2 + x + 2$ and $x^2 + 2x + 2$.

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The maximum likelihood estimate for the bias of the coin is 1/3.

The maximum likelihood estimate for the bias of the coin is the proportion of times it came up heads, which is 10/30 or 1/3.

The idea behind maximum likelihood estimation is to find the value of the parameter (in this case, the bias of the coin) that makes the observed data (in this case, the number of heads and tails) the most likely to occur.

In other words, we want to find the value of the parameter that maximizes the likelihood function.

For a coin flip, the probability of getting heads is p and the probability of getting tails is 1-p. The likelihood function for observing 10 heads and 20 tails is:

\(L(p) = (p)^{10} * (1-p)^{20}\)

To find the maximum likelihood estimate, we take the derivative of the likelihood function with respect to p and set it equal to zero:

\(d/dp [L(p)] = 10*(p)^9*(1-p)^20 - 20*(p)^{10}*(1-p)^{19} = 0\)

Solving for p, we get:

p = 1/3

Therefore, the maximum likelihood estimate for the bias of the coin is 1/3.

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Answer:

5.4661089e+63

Step-by-step explanation:

The factors of the polynomial f (x) = x^5 - 7x - 22x³ + 44x² - 104x + 288 that is true for f (9) = 0 are (x - 9) and (x⁴ + 2x³ - 4x² + 8x - 32).

The factor theorem states that: if p(x) is divisible by x - a if and only if p(a)=0.

The polynomial expression x^5 - 7x - 22x³ + 44x² - 104x + 288 and f (9) = 0, then x - 9 = 0 is a factor. Applying long division as follows;

x^5 divided by x equals x⁴

x - 9 multiplied by x⁴ equals x^5 - 9x⁴

subtract x^5 - 9x⁴ from x^5 - 7x - 22x³ + 44x² - 104x + 288 will result to 2x⁴ - 22x³ + 44x² - 104x + 288

2x⁴ divided by x equals 2x³

x - 9 multiplied by 2x³ equals 2x⁴ - 18x³

subtract 2x⁴ - 18x³ from 2x⁴ - 22x³ + 44x² - 104x + 288 will result to -4x³ + 44x² - 104x + 288

-4x³ divided by x equals -4x²

x - 9 multiplied by -4x² equals -4x³ + 36x²

subtract -4x³ + 36x² from -4x³ + 44x² - 104x + 288 will result to 8x² - 104x + 288

8x² divided by x equals 8x

x - 9 multiplied by 8x equals 8x - 72x

subtract 8x - 72x from 8x² - 104x + 288 will result to - 32x + 288.

-32x divided by x equals -32

x - 9 multiplied by -32 equals -32x + 288

subtract -32x + 288 from- 32x + 288 will result to a remainder 0(zero).

We can then conclude the factors (x - 9) and (x⁴ + 2x³ - 4x² + 8x - 32) are the product of linear factors for the polynomial f (x) = x^5 - 7x - 22x³ + 44x² - 104x + 288 that makes it zero.

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Answer:

Line A

Step-by-step explanation:

The slope of 2x is a positive slope so it can't be line d(which is negative) or line c(which is horizontal).

That leaves us with lines a and b. 2x is a steep slope and line a has a steep slope while line b has a shallow slope so it is line a.

Answer:

3 acute angles with different measures and 1 right angle and 2 acute angles with same measures