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.
Combine the results to yield a formula for the total cost of the silo project. Total project cost C(r)= ______________
Answers
The cost of the cylinder in terms of the single variable, r, alone is 2000π + πr⁴
How to calculate the costThe volume of a cylinder is given by πr²h. We know that the volume of the cylinder must be 1000π cubic feet, so we can set up the following equation:
πr²h = 1000π
h = 1000/r²
The cost of the cylinder is given by 2πr²h + πr² = 2πr²(1000/r²) + πr² = 2000π + πr⁴
The cost of the cylinder in terms of the single variable, r, alone is:
Cost of cylinder = 2000π + πr⁴
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Related Questions
please help, I'm stuck
Answers
Answer:
Step-by-step explanation:
4
help help help help help help help help help help
Answers
Answer:
1/4
GO GOOD LUCK
Step-by-step explanation:
U doing IXL? LOL
make me brainliest please
Answer:
The probability is 2/11
Step-by-step explanation:
If you look at the table it says that there are 2. Add up all of the possibilities which are 11, and then put it into a probability.
Five times a number is 30. Find that number.
Answers
Answer:
The number is 6
Step-by-step explanation:
Let x be the number
five times means multiply
5x
is 30 means equals 30
5x= 30
Divide each side by 5
5x/5 = 30/3
x = 6
Answer:6
Step-by-step explanation:
5 times 6 is 30
for a regression analysis, the value of r is 0.42. what is the value of the coefficient of nondetermination?
Answers
For a Regression Analysis that the value of R is 0.42, the value of the Coefficient of Non-Determination is 0.8236.
What is the Coefficient of Non-Determination?Coefficient of non-determination is the variation recorded in the dependent variable which is not counted by the changes in the explanatory variable. This is calculated by subtracting Coefficient of Determination from 1.
Coefficient of Non-Determination explains the amount of unexplained, or unaccounted for, variance among two variables, or among a set of variables (predictors) in an outcome variable.
The formula for the Coefficient of Non-Determination is 1 – R².
So, in this case:
1 – R²
= 1 – (0.42)²
= 1 – 0.1764
= 0.8236
Hence, the value of the Coefficient of Non-Determination is 0.8236.
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What is the correct height of the triangle ??
Answers
Answer:
9 units
Step-by-step explanation:
The dotted line, which is the height, is labeled as 9, so it is 9 units.
Hope that helps!
Answer: 9 units
Step-by-step explanation: If you look at the question on the photo you see a dotted line with a 9 on it. On a triangle when you something like that you know it the actual height of the triangle
Identify the characters of series below. nvž enn |||-) En=12 100 1-) Σπίο 3* 2"-1 ||-) En=2 n A) I Convergent, II Divergent, III Convergent B) I Convergent, Il Convergent, III Divergent C) I Convergent, II Convergent, III Convergent D) I Divergent, Il Divergent, III Divergent E) I Divergent, II Divergent, III Convergent
Answers
Based on the information, we can determine convergence or divergence of series.The given options do not provide a clear representation of potential outcomes.It is not possible to select correct option.
The given series is "nvž enn |||-) En=12 100 1-) Σπίο 3* 2"-1 ||-) En=2 n". In the series, we have the characters "nvž enn |||-)" which indicate the series notation. The characters "En=12 100 1-" suggest that there is a summation of terms starting from n = 12, with 100 as the first term and a common difference of 1. The characters "Σπίο 3* 2"-1 ||-) En=2 n" indicate another summation, starting from n = 2, with a pattern involving the operation of multiplying the previous term by 3 and subtracting 1.
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Which of the following functions has the greatest y-intercept? (1 point) f(x) x y −3 9 −2 4 −1 1 0 0 1 1 2 4 g(x) = 5 cos(3x) − 5 f(x) g(x) Not enough information f(x) and g(x) have the same y-intercept
Answer : they have the same y-intercept
Answers
Both function have same y - intercept.
The two given functions are;
x: -3 -2 -1 0 1 2
f(x): 9 4 -1 0 1 4
And, g(x) = 5 cos (3x) - 5
Since, We know that;
The y-intercept occurs when x=0.
Therefore,
⇒ f(x) has a y-intercept of 0
(from given tabular data).
And, g(x) has a y-intercept of at x = 0
g(0) = 5 cos (0) - 5
= 5 - 5
= 0
Hence, Both function have same y - intercept.
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If 15 people start a race, in how many different ways can the top 3 finishers be determined?
Answers
Hence, 15 people out of 3 people can be chosen in 35 ways.
Combinations:It is a method that helps us to determine the number of possible ways an item can be chosen given that the order of selection does not matter. Hence we are free to select the items in any order.Combinations are often confused with permutations. Permutations are the number of ways the given items can be arranged. Here the order is important.The formula for combinations:If we have 'n' items and we are required to choose 'r' items, the number of ways in which it can be done is calculated as:\(^{n}C_{r} }\) = \(\frac{n!}{(n-r)!r!}\)It is given that:
The total number of people in a race, n = 15
The number of finalists, r = 3.
Hence, the number of ways in which 3 people out of the 15 people can be finishers are:
\(^{15}C_{3} }\) = \(\frac{15!}{(15-3)!3!}\) = \(\frac{15!}{12!3!}\) = 35.
Hence, 15 people out of 3 people can be chosen in 35 ways.
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Which equation represents a line which is perpendicular to the line y = -4x - 5
A) x + 4y = -32
B) 4x - y = -4
C) 4x + y = 3
D) 4y - x = 4
Answers
Explanation
To find an equation perpendicular to another, the product of the slopes of both equations must equal -1
In y= -4x-5, the slope is -4. To obtain a line perpendicular to this line, -4(x)= -1, where the slope of the new line, x, must equal 1/4.
D must be the answer since it is the only equation that could be manipulated back to y= 1/4x
1) 4y - x = 4
2) 4y = 4 + x
3) y = 1 + 1/4x
This corresponds correctly with the new slope that we found, therefore correct.
Hope this helped :)
The length of a rectangle is 4 centimeters less than its width. What are the dimensions of the rectangle if its area is 45 square centimeters?
Answers
Answer: 34
Step-by-step explanation:
When given the picture using what you know find the answer. What is m
Answers
Answer:
40 degrees
Step-by-step explanation:
Answer:
Angle E = 25 deg because of reflective
Angle C = 115 degree because 180 - 65
Since triangle = 180 deg
Angle D = 180 - 115 - 25
= 40 deg
Step-by-step explanation:
if my avg is a 96 and my final exam is a 75 which is 25% of my whole grade what will my final grade be
Answers
Step-by-step explanation:
That means the 96 is 75% of your grade
96 (.75) + 75 (.25) = 90.75 final grade
Lisa worked 26 hours last month and earn seven dollars per hour she spent $17 on her earring since then how much money does she have left?
Answers
After spending $17 the amount of money left with Lisa is $165.
What is equation?
Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
Lisa worked 26 hours last month.
For each hour she earns $7.
Total earnings of Lisa in last month is equated as -
Earning = 26 × 7
Earning = $182
She spent $17 dollars on earring.
The amount of money left with her is equated as -
Total Earning - Money spent
Money Left = 182 -17
Money Left = $165
Therefore, the money left with Lisa is $165.
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I will brainlist who can answer this 5 Questions!
A b c Choices!
Answers
2.A
3.c
4.a
5.d
Hope this helped
Solve the following inequality using the algebraic approach:
x + 2 greater-than 3 x minus 8
a.
x greater-than negative 5
b.
x less-than negative 5
c.
x less-than 5
d.
x greater-than 5
Answers
To solve the given inequality, the solution is: x < 5. So, the correct answer is option C.
Here, we can solve the inequality x + 2 > 3x - 8 as follows :
We get 2 on both sides of an inequality by the process of subtraction
or, x + 2 - 2 > 3x - 8 -2
or, x > 3x -10
We get 10 on both sides of an inequality by the process of addition
or, x +10 > 3x -10 + 10
or, x + 10 > 3x
We get x on both sides of an inequality by the process of subtraction
or, x + 10 -x > 3x -x
or, 10 > 2x
We get 2 into both sides of an inequality by the process of division
or, 5 > x
Therefore, x < 5.
To solve the given inequality, the solution is: x < 5. So, the correct answer is option C.
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The graph of y = 4x? - 4x - 1 is shown.
Use the graph to find estimates for
the solutions of
i) 4x2 - 4x - 1 = 0
1%C
ii) 4x2 - 4x - 1 = 2
Answers
Then the two solutions are: x = (4 + 5.66) / 8 = 11.2075 and x = (4 - 5.66) / 8 = -0.2075
What is meant by Bhaskara's equation?The sine approximation formula of Bhaskara I is a rational equation in one variable for computing the approximations of the trigonometric sines found by Bhaskara I (c. 600–c. 680), an Indian mathematician of the seventh century.
Indian astronomer and mathematician Bhaskara II lived in the 12th century. He created a number of the same foundations and findings that are entirely attributable to Europeans and are still very helpful in modern science and forecasts, such as a basic form of calculus.
Here we have the equation:
y = 4 × x² - 4 × x - 1
And the graph should be available (you can see it below this answer)
Now, we're seeking answers to:
4 × x²- 4 × x - 1 = 0
The two x values at which the graph of our function intersects the y = 0 line, or the x-axis, will be these solutions.
The next step is to identify the two x values where our graph crosses the x-axis.
We can estimate the solutions in the graph as follows:
x = -0.2
x = 1.2
The Bhaskara's equation can be used to determine the precise solutions, and we will discover that the solutions are provided by:
\($x=\frac{-(-4)+-\sqrt{(-4)^2-4 * 4 *(-1)}}{2 * 4}=\frac{4+-\sqrt{32}}{8}=\frac{4+-5.66}{8}\)
Then the two solutions are:
x = (4 + 5.66) / 8 = 11.2075
x = (4 - 5.66) / 8 = -0.2075
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Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage. Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In last five years, the market value of the house has increased by 4.8% per year 6. If she wants to sell the house today, the total transaction cost will be 5% of selling price Given the above information, please calculate the internal rate of return (IRR) of this investment in house
Can you show the math as far as formulas go?
Answers
Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.
Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.
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data collected at an airport suggests that an exponential distribution with mean value 2.675 hours is a good model for rainfall duration. (a) what is the probability that the duration of a particular rainfall event at this location is at least 2 hours? at most 3 hours? between 2 and 3 hours? (round your answers to four decimal places.) at least 2 hours at most 3 hours between 2 and 3 hours
Answers
The probabilities are approximately:
(a) Probability of at least 2 hours: 0.5266
(b) Probability of at most 3 hours: 0.6349
(c) Probability between 2 and 3 hours: 0.1083
To find the probabilities, we can use the cumulative distribution function (CDF) of the exponential distribution.
For an exponential distribution with mean value λ, the CDF is given by:
CDF(x) = 1 - e^(-λx)
In this case, the mean value is given as 2.675 hours. So, λ = 1/2.675 = 0.3738 (rounded to four decimal places).
(a) To find the probability that the duration of a particular rainfall event is at least 2 hours, we need to find CDF(2).
CDF(2) = 1 - e^(-0.3738 * 2) = 1 - e^(-0.7476) ≈ 0.5266 (rounded to four decimal places).
(b) To find the probability that the duration of a particular rainfall event is at most 3 hours, we need to find CDF(3).
CDF(3) = 1 - e^(-0.3738 * 3) = 1 - e^(-1.1214) ≈ 0.6349 (rounded to four decimal places).
(c) To find the probability that the duration of a particular rainfall event is between 2 and 3 hours, we subtract the probability of it being at most 2 hours from the probability of it being at most 3 hours.
Probability = CDF(3) - CDF(2) ≈ 0.6349 - 0.5266 ≈ 0.1083 (rounded to four decimal places).
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A lounge chair manufacturing company's daily production costs, (y), is dependent on the number of lounge chairs (x) produced daily. Use the graph below to answer the question.
Graph of function p of x equals 25 x squared minus 200 x plus 500. The graph has the x-axis labeled as number of items produced, and the y-axis labeled as cost. The curve begins at (0, 500), decreases to (4, 100), and then increases to infinity.
What is the approximate number of items that should be produced to minimize production costs?
0
4
100
500
Answers
Answer:
(b) 4
Step-by-step explanation:
You want the approximate number of items that should be produced to minimize production costs.
GraphThe graph shows cost is lowest when the number of items produced is 4.
4 items should be produced to minimize production cost.
The wholesale price for a necklace is $10.the mark up percent is 200%.what is the mark up
Answers
The mark up is $30.
What is markup?As stated, markup is the distinction between a product's selling price and its cost price. Retail minus Cost is markup. The term "markup" describes the discrepancy between a product's selling price and its actual cost. It is specified as a percentage over the price. In other words, the seller makes a profit when the price of the commodity or service is higher than the overall cost. A unit's gross profit, which is the sales price less the cost to create or buy it for resale, is divided by its cost to determine the markup %. The markup percentage is computed as (12 - 8) / 8 and is equal to 50% if an item costs the business $8 to produce but is sold for $12.
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How is the pattern changing to get from one term to the next?
1, 3, 9, 27,...
A. multiplying by 3
B. adding 2
C. subtracting 2
D. dividing by 3
Answers
Explanation: this is just something u can eye ball
the variables r and s are inversely proportional, and r=7 when s=6. determine s when r=10.
Answers
If the variables "r" and "s" are inversely proportional and r=7 when s=6 , then when r = 10 , value of "s" will be 4.2 .
When the two variables are inversely proportional, their product is constant. That means, for two variables "r" and "s" , the it is represented in equation as :
⇒ r × s = k, where k is a constant ;
the value of variable "r" = 7 when s = 6,
First , we have to find the value of k:
⇒ k = r × s = 7 × 6 = 42 ;
So, for any value of r and s, the product "rs" will always be equal to 42.
When r = 10, we can use the equation to find s:
⇒ s = k/r = 42/10 = 4.2
Therefore , when r = 10 , the variable "s" is 4.2.
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The price of shirts in a store is $20 and the price of ties in the same store is $15. A customer buys 2 shirts and 3 ties during a sale when the price of shirts is discounted 15% and the price of ties is discounted 10%. How much did the customer save due to the sale?
Answers
Let's calculate the savings for each item separately and then find the total savings.
Original price of 2 shirts = 2 * $20 = $40
Discount on shirts = 15% of $40 = $40 * 0.15 = $6
Price of 2 shirts after discount = $40 - $6 = $34
Original price of 3 ties = 3 * $15 = $45
Discount on ties = 10% of $45 = $45 * 0.10 = $4.50
Price of 3 ties after discount = $45 - $4.50 = $40.50
Total savings = Savings on shirts + Savings on ties
Total savings = $6 + $4.50 = $10.50
Therefore, the customer saved $10.50 due to the sale.
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is 4.680 rational or irrational
Answers
Answer:
I believe ... yes
Step-by-step explanation:
help wanted can someone help me and give me a short understanding of this
Answers
z = 24
Angle y° and (5z - 44)° are linear pairs, meaning that the two measures together will add up to 180°.
To solve for z, know that (5z - 44)° and 76° are vertical angles, meaning that both angles are the same.
So simply set them equal to each other to find z:
5z - 44 = 76
5z = 76 + 44
5z = 120
z = 24
Now to solve for y, remember that since (5z - 44)° and 76° are vertical angles, they are the same, meaning you can denote (5z - 44)° as simply 76°. Like I said earlier, y and 76° are a linear pair so simply subtract 76 from 180 to find y:
180 - 76 = 104°
Find the value of x
12x
6x+28
Your answer
Answers
Step-by-step explanation:
Hey there!
By looking at the figure, the given "2x" and "6x + 28" are co-interior angle.
So,
2x + 6x + 28 = 180°. ( sum of co-interior angle is 180°)
8x + 28°=180°
8x = 180° - 28°
8x = 152°
\(x = \frac{152}{8} \)
X = 19°
Therefore, X = 19°.
Hope it helps...
Answer:
x=19
Step-by-step explanation:
These are same-side interior angles. The Same-Side Interior Angles Theorem states that if two parallel lines are cut by a transversal, then the same side interior angles are supplementary. This means that the sum of the two angles is equal to 180°.
2x+6x+28=180°
8x=180-28
8x=152
x=19
Brianna has a bag of marbles that are all the same size. Of all the marbles in the bag, there are 6 red, 7 white, 3 black, and 4 green marbles. Find the probability of each below. Use the probability to predict how many times Brianna would pick a green marble if she chose a marble 50 times. Give the probabilities as simplified fractions.
Answers
Answer:
4 out of 20 marbles
construct a 45-45-90 degree triangle with leg equal to AB
Answers
The required 45-45-90 degree triangle is shown, where each of the two acute angles is 45 degrees and the length of the hypotenuse is equal to the length of each leg multiplied by the square root of 2.
What is the right-angle triangle?A right-angled triangle, also known as a right triangle, is a triangle in which one of its interior angles measures exactly 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.
Here,
o construct a 45-45-90 degree triangle with leg AB, we can follow these steps:
The resulting triangle will have sides AB, BC, and AC, where AB and BC are equal in length and AC is the hypotenuse.
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A cylinder has a base diameter of 20 meters and a height of 17 meters. What is its volume in cubic meters, to the nearest tenths place?
Answers
Answer:
5338 \(m^{3}\)
Step-by-step explanation:
The volume for a cylinder is solved by using this equation;
\(V= \pi \times r^2\times h\)
Where we would use 3.14 in place of \(\pi\).
10 would be the radius because the radius is half of your diameter which is 20.
So, Volume will be,
\(V=(3.14)\times (10)^{2} \times(17)\\V=3.14\times 100\times 17=5338 \quad {m^3}\)
So volume will be 5338 \(m^{3}\).
A competency test has scores with a mean of 82 and a standard deviation of 2. A histogram of the data shows that the distribution is normal. Between what two values do about 99.7 of the values lie?
Answers
Answer:
Between 76 and 88