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 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.

Part A
Suppose the cylinder has a radius of r. What would be the surface area of the hemi-spherical dome? The construction cost for the metal dome is estimated at $30 per square foot. Write an expression for the estimated cost of the dome.

Surface area of dome = ____________________

Cost of dome = ____________________

Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

Answer:

angle 2 is 104

angle 9 is 66

angle 10 is 114

angle 7 is 76

Step-by-step explanation:

The Greek mathematicians started using the symbol pi (π) for as long as 4000 years in mathematical world.

A Short History of Pi

Even if we counted the number of seconds in those 4000 years and round the value of pi (π) to so many places, we would still only be estimating the true value of pi. Pi has been known for over 4000 years. Below is a quick summary of the discovery of.

By multiplying the radius of a circle by three, the ancient Babylonians determined its area, yielding the number pi = three. About 1900–1680 BC Babylonian tablets show a value of 3.125 for, which is a more accurate estimate.

The Rhind Papyrus, which dates to around 1650 BC, sheds light on ancient Egyptian mathematics. The calculation used by the Egyptians to determine a circle's area yielded a result that was around 3.1605 for.

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Answer:

5x+6= 10x-8

14= 5x

x= 2.8

Step-by-step explanation:

The probability that more boys than girls are chosen is 0.4731. So option b is correct.

Combination:

The act of combining or the state of being combined. A number of things combined: a combination of ideas. something formed by combining: A chord is a combination of notes. an alliance of persons or parties: a combination in restraint of trade.

Here it is given that there are 18 boys and 19 girls and 5 students are chosen.

We have to find the probability that more boys than girls are chosen.

Probability = \(C^{5} _{18}\) + \(C^{4}_{18} C^{1} _{19}\) + \(C^{3} _{18} C^{2} _{19}\) / \(C^{5}x_{37}\)

                  = 8568 + 58140 + 139536 / 435897

                  ≈ 0.4731

Therefore the probability is 0.4731.

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Answer:

They are all equal sides so divide 180 by 3

Step-by-step explanation:

Answer: D the final mean is higher than the original

Step-by-step explanation:

90+85+98+60+84+78/6= 82.5 as the original mean

dropping 60 which is the lowest grade means 90+85+98+84+78/5=87 which means the new mean is 87 which is greater than the original mean of 82.5

So the answer is D

The domain and range need to be determined for a given relation, and it will be determined whether the relation represents a function.

To determine the domain and range of a relation, we need to examine the set of inputs (domain) and the set of corresponding outputs (range). The domain is the set of all possible input values for which the relation is defined, while the range is the set of all possible output values that result from the given inputs.

In the context of determining whether the relation represents a function, we need to ensure that each input value from the domain corresponds to a unique output value. If there is any input value that produces multiple output values, the relation is not a function.

To determine the domain, we examine the set of all valid input values. This can be based on restrictions or limitations stated in the problem or the nature of the relation itself. The range, on the other hand, is determined by observing the set of all output values that result from the given inputs.

Once the domain and range are determined, we can check if each input in the domain corresponds to a unique output in the range. If every input has a unique output, the relation represents a function. If there is any input that maps to multiple outputs, the relation does not represent a function.

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As we can see, the line is continuous, and the area is below the line, therefore, we can conclude that the inequality is given by:

Answer:

100

0

Step-by-step explanation:

Answer:

Step-by-step explanation:

A simple way to calculate the distance between numbers on a number line is to count every number between them. A faster way is to find the distance by taking the absolute value of the difference of those numbers. Absolute value of a number on a number line is its distance from 0 on the number line .

Answer:

y = -2x - 18

Step-by-step explanation:

The left turn departure sight distances for a passenger car taking a left turn from the minor road to the major road is 121.275

Here we given that a 2 lane highway with a grade of 6% has a posted speed limit of 50 mph and a design speed of 55mph. the minor road approach grade is -1.5%.

And we need to find the left turn departure sight distances for a passenger car taking a left turn from the minor road to the major road.

While we looking into the given question we have identified that the following are the values given in the problem,

=> Speed limit = 50 mph

=> design speed = 55mph

=> grade = -1.5%

As per the length of the sight triangle leg or ISD along the major road is

determined using the following equation:

=> ISD = 1.47 V t

=> ISD = 0.278 V t

Where:

ISD refers length of sight triangle leg along major road, ft (m)

V refers design speed of major road, mph (km/h)

t refers time gap for minor road to enter the major road, sec

When we apply the value, then we get,

=> ISD = 1.47 x 55 x  -1.5

=> ISD = -121.275

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Answer:

1 = 2x      2= -3    4 =3

Step-by-step explanation:

Answer:

1. 5x-3=-15

2. -15/5=-3

3. -15/-3=5

Step-by-step explanation:

Hope this helps :)

So there are 152 machines. After 24 hours of operation they make 1.47x\(10^{7} \)

So we know that 1.47x\(10^{7} \) = 14,700,000.


Now we just divide this by 24.

14700000/24=612,500

Now thats the total, we need to divide by 152 since there are that many machines that make up that number.

612,500/152 about 4029


So your rate is 4029 per hour per machine.

The value of logm 4/m is 1.139 - 2 logm m. This means that we can express logm 4/m in terms of other logarithmic values without finding the exact value of m.

Given that logm 3 = 0.903, logm 4 = 1.139, and logm 7 = 1.599. We are to find logm 4/m.

Using the properties of logarithm, we have,

logm 4/m = logm 4 - logm m

               =1.139 - logm m               .....................................(1)

Again, using the properties of logarithm, we know that:

logm 4 = logm (2 × 2)  

        = logm 2 + logm 2

         = 1.139 = 2logm 2                    ..................................(2)

Substituting equation (2) into (1) gives:

logm 4/m = 2logm 2 - logm

           m = 2logm (2/m)          ..................................................(3)

Using the property of logarithm once again, we know that:

loga b = logc b / logc a                     ............................................(4)

Substituting equation (4) into equation (3), we have:

logm 4/m = 2 logm 2 - logm

m= logm [(2/m)² / m]                       .............................................(5)

Now, we are to find logm 4/m by substituting the given values.

Using equation (2), we have:

logm 2 = (1.139)/2

     = 0.5695

Using equation (5), we get:

logm 4/m = logm [(2/m)² / m]

logm 4/m = logm [4/m²m]

 logm 4/m = logm 4 - logm

logm 4/m = 1.139 - 2 logm m

Therefore, by using the properties of logarithm, we have found that logm 4/m = 1.139 - 2 logm m. This means that we can express logm 4/m in terms of other logarithmic values without finding the exact value of m.

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The volume of the square pyramid-shaped roof with a height of 5 feet and a side length of 6 feet is 60 cubic feet.

A square pyramid has a square base and four triangular sides that come together to form a single point. To calculate the volume of a square pyramid, you can use the formula: 1/3 x Base x Height, where the base is the area of the square base and the height is the height of the pyramid.

In the given scenario, the rooftops of the village are shaped like square pyramids. The height of the roof is 5 feet and the length of the sides is 6 feet. Let us calculate the volume of the roof using the formula mentioned above:

The base of the square pyramid = side * side= 6 * 6= 36 sq. ft, Height of the square pyramid = 5 ft. Volume of the square pyramid= 1/3 * Base * Height= 1/3 * 36 sq. ft * 5 ft= 60 cubic feet. Therefore, the volume of the roof is 60 cubic feet.

Summary: A square pyramid has a square base and four triangular sides that come together to form a single point. The formula to calculate the volume of a square pyramid is 1/3 x Base x Height. The rooftops of the village are shaped as square pyramids with a height of 5 feet and the length of the sides is 6 feet. To calculate the volume of the roof, we can use the formula and find the volume of the roof. The volume of the roof is 60 cubic feet.

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Answer:

True

Step-by-step explanation:

If the natural numbers other than one is squared, it should be either a multiple of 3 or exceeds a multiple of 3 by 1

Answer:

1 - 4

2 - 2

3 - 5

4 - 3

5 - 1

Step-by-step explanation:

Hope this helps

Step-by-step explanation:

Hey there!

Given;

4(X+1) -3 and 4x+1.

No, they are equivalent.

Reason:

Solving 1st expression.

4(x+1) = 4x + 4 - 3

Now, next expression is: 4x+1.

So, 4x + 4 = 4x+1

So, they are equivalent to eachother.

Hope it helps...

is 4(x+1) - 3 and 4x + 1 equivalent and why?

Step-by-step explanation:

Hey there!

Given;

4(X+1) -3 and 4x+1.

No, they are equivalent.

Reason:

Solving 1st expression.

4(x+1) = 4x + 4 - 3

Now, next expression is: 4x+1.

So, 4x + 4 = 4x+1

So, they are equivalent to eachother.

Hope it helps...

The determinant of the given matrix a is: det(a) = b2c2 + a2c2 + a2b2 - 2a2b2 - 2a2c2 + 2abc.

The determinant of a 3x3 matrix can be found using the formula:

det(A) = a11(a22a33 - a32a23) - a12(a21a33 - a31a23) + a13(a21a32 - a31a22)

Substituting the given matrix values, we get:

det(a) = 1(b2c2 - c(b2) + a2(c2) - c(a2) + a(b2) - a(b2)) - a(1c2 - c1 + a2c - c(a2) + a - a(a2)) + a(1b2 - b1 + a(b2) - b(a2) + a - a(b2))

Simplifying this expression, we get:

det(a) = b2c2 + a2c2 + a2b2 - a2b2 - b2c - a2c - a2b + a2c + abc - abc - a2c + ac2 + ab2 - ab2 - abc

Simplifying further, we get:

det(a) = b2c2 + a2c2 + a2b2 - 2a2b2 - 2a2c2 + 2abc

Thus, the determinant of the given matrix a is:

det(a) = b2c2 + a2c2 + a2b2 - 2a2b2 - 2a2c2 + 2abc.

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Answer:

B

Step-by-step explanation:

The lengths of the two boards (234 inches and 246 inches) and adding them together, we find that the combined length of the boards is 480 inches.

To find the total length of the two boards, you need to add their individual lengths together.

Step 1: Identify the length of each board. The first board is 234 inches long, and the second board is 246 inches long.

Step 2: Add the lengths of the boards together.

234 (length of first board) + 246 (length of second board) = 480

So, the total length of the two boards on the shelf is 480 inches. This means that if you were to place the two boards end-to-end, they would cover a distance of 480 inches.

In summary, by identifying the lengths of the two boards (234 inches and 246 inches) and adding them together, we find that the combined length of the boards is 480 inches. This calculation helps us understand the total amount of space the boards would occupy if placed side by side.

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The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

Given the equation x^2 = 2y.

The coordinates of the point are (4,1).We have to find the abscissa on the curve that is nearest to this point.So, let's solve this question:

To find the abscissa on the curve x2 = 2y which is nearest to the point (4,1), we need to apply the distance formula.In terms of x, the formula for the distance between a point on the curve and (4,1) can be written as:√[(x - 4)^2 + (y - 1)^2]But since x^2 = 2y, we can substitute 2x^2 for y:√[(x - 4)^2 + (2x^2 - 1)^2].

Now we need to find the value of x that will minimize this expression.

We can do this by finding the critical point of the function: f(x) = √[(x - 4)^2 + (2x^2 - 1)^2]To do this, we take the derivative of f(x) and set it equal to zero: f '(x) = (x - 4) / √[(x - 4)^2 + (2x^2 - 1)^2] + 4x(2x^2 - 1) / √[(x - 4)^2 + (2x^2 - 1)^2] = 0.

Now we can solve for x by simplifying this equation: (x - 4) + 4x(2x^2 - 1) = 0x - 4 + 8x^3 - 4x = 0x (8x^2 - 3) = 4x = √(3/8)The abscissa on the curve x^2 = 2y that is nearest to the point (4,1) is x = √(3/8).T

he main answer is that the abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

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The equation that describes the relationship of full boxes and half-boxes of fruit is x = (100 - 2y) / 5

To create an equation that represents this relationship, we first need to define our variables. Let's let x be the number of full boxes Kiran sells, and y be the number of half-boxes he sells.

Since Kiran earns $5 for each full box and $2 for each half-box, we can express his total earnings in terms of x and y as follows:

Total earnings = (number of full boxes sold x $5) + (number of half-boxes sold x $2)

Substituting x and y into this equation, we get:

Total earnings = 5x + 2y

Since we know that Kiran earned $100, we can set this equation equal to 100 and solve for either x or y. Let's solve for x:

5x + 2y = 100

Solving for x, we get:

x = (100 - 2y) / 5

This equation tells us that the number of full boxes Kiran sells is equal to 100 minus 2 times the number of half-boxes he sells, divided by 5.

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             - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

\(\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond\)

         Find the slope of the line that passes through (6, 9) and (9, 5).

\(\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}\diamond\)

\(\boxed{\\\begin{minipage}{3cm}\xrightarrow {slope\:formula\:below} \\ $\displaystyle\frac{y_2-y_1}{x_2-x_1}$ \\ \end{minipage}}}\)

Substitute 5 for y₂, 9 for y₁, 9 for x₂ and 6 for x₁:-

\(\boxed{\frac{5-9}{9-6}}\)

On simplification,

↬ \(\boxed{\frac{-4}{3}}\)

   ►So we conclude that the slope of the line is

 ►\(\boxed{-\frac{4}{3}}\) ◀︎

              - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Answer:

d

Step-by-step explanation:answer is d on edg

The parametric equations for the motion of the particle in the xy plane that traces the counterclockwise ellipse are x = 6cos(t) and y = 4sin(t), where t is the parameter. The parameter interval for the motion is 0 ≤ t ≤ 2π.

To find the parametric equations for the counterclockwise motion of the particle along the given ellipse, we can start by parameterizing the ellipse equation  \(16x^2 + 9y^2 =\) 144. We divide both sides of the equation by 144 to normalize it, giving us  \((x^2/9) + (y^2/16\)) = 1. By comparing this equation with the standard form of an ellipse, we can see that a = 3 and b = 4.

We can then use the trigonometric parametrization of an ellipse to obtain the parametric equations. Letting x = acos(t) and y = bsin(t), where t is the parameter, we substitute the values for a and b, resulting in x = 6cos(t) and y = 4sin(t). These equations represent the motion of the particle along the ellipse.

Since we want the particle to trace the ellipse counterclockwise, we need to cover the full circumference of the ellipse. This corresponds to a parameter interval of 0 ≤ t ≤ 2π, which completes one full revolution around the unit circle. Therefore, the parametric equations for the motion of the particle are x = 6cos(t) and y = 4sin(t), with a parameter interval of 0 ≤ t ≤ 2π.

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Answer:

40%

Step-by-step explanation:

The proof of trigonometric identity (sin(x) + tan(x))/sin(x) = 1 +secx is given below.

The given trigonometric identity is,

(sin(x) + tan(x))/sin(x).

We know that tan(x) = sin(x)/cos(x), so we can substitute that in:

sin(x)/ sin(x) + sin(x)/cos(x) / sin(x)

We can simplify the fraction in the numerator:

sin(x)/ sin(x) + sin(x)/sin(x)cos(x)

We know that sin(x)/sin(x) = 1, so we can simplify further:

1+ 1/cos(x)

We know that 1/cos(x) = sec(x), so we can substitute that in:

1 + sec(x).

Now we have the same expression as the right-hand side of the identity, so we have proven that:

sin(x) + tan(x)/sin(x) = 1 + sec(x)

Therefore, (sin(x) + tan(x))/sin(x) = 1 +secx.

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