A customer has asked you to design an open-top rectangular stainless steel vat. It is to have a square base and a volume of 32ft3, to be welded from quarter-inch plate, and to weigh no more than necessary.
Answers
The dimensions of the vat would be 2.08ft x 2.08ft x 8ft, and the weight
of the vat would be approximately 331.4 lbs.
To design an open-top rectangular stainless steel vat with a square base and a volume of 32ft3, we will need to use some basic geometric
formulas and calculations.
1. Determine the dimensions of the vat:
Since the vat has a square base, let's assume the length and width are
the same, and we can call them "x". Then the area of the base is:
Area of base =\(x \times x = x^2\)
To find the height of the vat, we can use the formula for the volume:
Volume = Length x Width x Height
32ft3 = \(x^2 \times Height\)
Height = \(32ft3 / x^2\)
2. Determine the material needed:
The vat is to be welded from quarter-inch plate, which is 0.25 inches
thick. Therefore, the material needed for the sides and bottom of the vat
can be calculated as follows:
Material needed = (Area of bottom) + 4 x (Area of side)
Area of bottom = \(x^2\)
Area of side = Height x Thickness
Area of side = Height x 0.25 inches
Area of side = \((32ft3 / x^2) \times 0.25 inches\)
Material needed = \((x^2) + 4 \times ((32ft3 / x^2) \times 0.25 inches)\)
3. Determine the weight of the vat:
The weight of the vat can be calculated using the density of stainless
steel, which is approximately \(0.289 lbs/in^3\). Therefore, the weight of the
vat can be calculated as follows:
Weight = Volume x Density
Weight =\((x^2 \times (32ft3 / x^2)) \times 0.289 lbs/in^3\)
Weight =\(9.216 \times x^2 lbs\)
Minimize the weight:
To minimize the weight of the vat, we can differentiate the weight
formula with respect to x, set it equal to zero, and solve for x:
d Weight/dx = 18.432 x
18.432 x = 0
x = 0
This means that the weight is minimized when x is zero, which is not
possible. Therefore, we need to find the minimum weight by using the
critical point, which is at\(x = (8ft)^{(1/3) }\)or approximately 2.08 feet.
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Related Questions
How much water will it take to fill the aquarium?
Please anawer this question. Will put as brainliest if i get an answer
Answers
Answer:
4096
Step-by-step explanation:
You multiply 32 in. by 8 in. by 8 in.
Answer:
4096
Step-by-step explanation:
to find volume you can just multiply length, width, and height together :) Hope this helps!!! ❤
How do you tell if a log function is increasing or decreasing?
Answers
If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: \(f(x) = log_b(x),\) where b is the base of the logarithm.
To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.
In the case of logarithmic functions, the derivative of \(f(x) = log_b(x)\) is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.
Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
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If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: \(f(x)=log_b(x)\). where b is the base of the logarithm.
To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.
In the case of logarithmic functions, the derivative of \(f(x)=log_b(x)\). is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.
Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
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A restaurant charges a single price for its buffet. The total bill for a table of six people having the buffet was $294. Each of the 8 people at a second table also had the buffet. What was the total bill at the second table?
Answers
So the cost for the 8 people at the other table would be $49 x 8 = $392
A cube is 8 inches on each side. What is the height of a cylinder having the same volume, if it’s radius is 4 inches? Round to the nearest tenth.
Answers
You first need to find the volume of the square. Then using that volume and the radius find the height of the cylinder.
The formula to find the volume of a square is V=s^3. The formula to find the height of a cylinder is h=V/pir^2. Hope it helps.
What is the surface area of this shape?
Answers
Answer:
SA : 253.5
Step-by-step explanation:
2(6.5)(6.5) + 2(6.5)(6.5) + 2(6.5)(6.5)
84.5 + 84.5 + 84.5 = 253.5
A sawoman cams 8% commission on at the merchandise that the sets Last month she sold $7000 worth of merchandise. How much commission (in dollars) did she warm last month?
Answers
He made $480 in commission last month
What is a Commission?This refers to the fee paid to an agent or employee for transacting a piece of business or performing a service
First, convert 8% into a decimal
8%/100
= 0.08
Multiply the decimal by his sales
0.08 * 6000
480
Therefore, he made $480 in commission last month
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A group of friends wants to go to the amusement park. They have no more than $285 to spend on parking and admission. Parking is $7.25, and tickets cost $28.50 per person, including tax. Which inequality can be used to determine x, the maximum number of people who can go to the amusement park?
Answers
7.25 + 28.50(x) = 285
285 - 7.25 = 277.75
277.75 / 28.50 = 9.745…
x = 9
The maximum amount of people who can go to the park is 9 people.
Hope this helped
how to solve equations with fractions and variables in the denominator
Answers
To solve equations with fractions and variables in the denominator, we need to eliminate it by moving it to the other side. To do this, we multiply both sides of the equation by the term in the denominator. This will cancel out the fraction and leave us with a simpler equation to solve.
For example, suppose we have the equation (3 + x) / x = 2. To get rid of the fraction, we multiply both sides by x. This gives us: x * (3 + x) / x = x * 2. The x in the numerator and denominator cancel out, leaving us with:
3 + x = 2x. Now we can solve for x by subtracting x from both sides: 3 = x
This is the solution of the equation.
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Discussion Topic You can identify sample spaces for compound events using organized lists, tables, and tree diagrams. Which of the three methods do you find easiest to use? Which method is the most helpful? Why? Use the Internet or another resource to find the definition of the Fuilidamental Counting Principle. What does this principle state? How can the principle be used to help you identify a sample space for a compound event? What are the limitations of using the Fundamental Counting Principle when determining the probability of an outcome? Support your answers with an example
Answers
I find organized lists to be the easiest method to use to identify sample spaces for compound events. This is because organized lists are the most straightforward way to list all of the possible outcomes of an event.
What is Fundamental Counting Principle?Tables and tree diagrams can be helpful as well, but they can be more difficult to create and interpret.
The Fundamental Counting Principle states that if there are n ways to do one thing, and m ways to do another thing, then there are n × m ways to do both things. This principle can be used to help identify a sample space for a compound event by multiplying the number of ways each event can occur. For example, if you are rolling a die and flipping a coin, there are 6 ways to roll the die and 2 ways to flip the coin. Therefore, there are 6 × 2 = 12 possible outcomes of the compound event.
The Fundamental Counting Principle is a useful tool for identifying sample spaces, but it does have some limitations. One limitation is that it only applies to events that are independent. Independent events are events where the outcome of one event does not affect the outcome of the other event. For example, the outcome of drawing a card from a deck does affect the outcome of drawing another card from the deck. In this case, the Fundamental Counting Principle cannot be used to determine the sample space.
Another limitation of the Fundamental Counting Principle is that it does not take into account the probability of each outcome. The probability of an outcome is the likelihood that the outcome will occur. For example, the probability of rolling a 6 on a die is 1/6. The probability of flipping a coin and getting heads is 1/2. The probability of rolling a 6 and flipping a coin and getting heads is 1/6 × 1/2 = 1/12.
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This graph represents the path of a baseball hit during practice.
Downward opening parabola with (0,0.5), (6.16, 0) and vertex (3,5)
What does the x-value of the vertex represent?
Question 1 options:
the maximum height of the baseball
ground level
the time the baseball was hit
the time the baseball reached its maximum height
Answers
Answer:
Step-by-step explanation:
x-coordinate of the vertex is the time the baseball reaches maximum height.
if a+b=34 then what is 4a-8ba+9a
Answers
Answer:
12x:12x=1:
1 TRUE
Step-by-step explanation:
Please answer this question now in two minutes
Answers
Answer: a
Step-by-step explanation: simple math
3n+1=19 so i'm learning to solve 2 step equations in pre algebra but i don't really understand.
Answers
Answer:
n = 6
Step-by-step explanation:
Simplifying
3n + 1 = 19
Reorder the terms:
1 + 3n = 19
Solving
1 + 3n = 19
Solving for variable 'n'.
Move all terms containing n to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + 3n = 19 + -1
Combine like terms: 1 + -1 = 0
0 + 3n = 19 + -1
3n = 19 + -1
Combine like terms: 19 + -1 = 18
3n = 18
Divide each side by '3'.
n = 6
Simplifying
n = 6
Answer:
n = 6
Step-by-step explanation:
3n + 1 = 19
Subtracting 1 from both sides:
3n + 1 - 1 = 19 - 1
3n = 18
Dividing both sides by 3:
3n/3 = 18/3
Simplifying:
18/3 = 6
n = 6
Hope you learned from this answer!
Solve for z: 5z + x – y = 3x + 4
Answers
z = 2/5x + 1/5y + 4/5
Step 1: Add -x to both sides
Step 2: Add y to both sides
Step 3: Divide both sides by 5
Answer:
z= \(\frac{2x}{5} + \frac{4}{5} +\frac{1y}{5}\)
Step-by-step explanation:
first get the variable z on one side by itself
5z + x – y = 3x + 4
-x -x
5z – y = 2x + 4
+y +y
5z = 2x + 4+y
divide by 5 to get the answer for the variable z
5z = 2x + 4+y
\(\frac{5z}{5} = \frac {2x + 4+y}{5}\\\)
z= \(\frac{2x}{5} + \frac{4}{5} +\frac{1y}{5}\)
HOPE THIS HELPS:)
what is the median of these numbers 17 12 54 36 71 28 31 55
Answers
Answer:
The median is 33.5
Step-by-step explanation:
In order to solve for a median it would either be the middle or it would be the average of the middle if there are even amount of numbers. First you would put them in order. 12 17 28 31 36 54 55 and 71. This would mean the the middle number would be 31 and 36. Since you can't have two medians you would find the average of the two so add 31 and 36 which would be equal to 67 then divide by 2 which would equal to 33.5.
The median of numbers 17, 12, 54, 36, 71, 28, 31, 55 is 33.5.
What is the median of a set of numbers?The median of a set of numbers is the middle value when the numbers are arranged in ascending or descending order.
If there are an even number of numbers, the median is the average of the two middle values. If there is an odd number of numbers, the median is the middle number.
To find the median of the given numbers, we first need to arrange them in ascending order:
12 17 28 31 36 54 55 71
Since there are an even number of numbers (8), the median will be the average of the two middle values, which are 31 and 36.
To find the average, we add the two numbers and divide by 2:
(31 + 36) / 2 = 67 / 2 = 33.5
Therefore, the median of the given numbers is 33.5.
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5. in an experiment that tested how adding variable quantities of sugar to flowers in a vase made the flowers last longer, the dependent variable would be the
Answers
difference between repeating & terminating decimal
Answers
Answer: If you end up with a remainder of 0, then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.
Step-by-step explanation:
I hope that this helped! :)
Coach Burke was emphasizing proper hitting mechanics during Tuesday's practice at the ball field. He was extremely impressed to see several of his players hit the ball off the outfield fence and a few over the fence during batting practice. The players increased their hitting distance by:
Answers
Coach Burke's emphasis on proper hitting mechanics during Tuesday's practice at the ball field led to impressive results among the players. By focusing on elements such as stance, grip, and swing, the players were able to improve their overall hitting performance.
Their increased hitting distance can be attributed to several factors.
First, a balanced and comfortable stance allowed the players to transfer their weight effectively and generate more power in their swings. Secondly, a firm yet relaxed grip on the bat helped maintain proper bat control, ensuring that the players were able to hit the ball with maximum force. Additionally, an efficient and smooth swing, with a proper follow-through, allowed the players to make solid contact with the ball, thus increasing the hitting distance.
As a result of Coach Burke's guidance in refining these aspects of hitting mechanics, the players were able to hit the ball off the outfield fence and even over the fence during batting practice.
This improvement in hitting distance is a testament to the importance of mastering the fundamentals of baseball and the impact of quality coaching on player performance.
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Find an equation in cylindrical coordinates for the equation given in rectangular coordinates. 25x2=25y2=6x
Answers
25r(cos^2Ф-sin^2Ф)-6cosФ=0
The equation in rectangular coordinates is 25x2=25y2=6x, we need to write in cylindrical coordinates
What is rectangular coordinate system?The rectangular coordinate system consists of two real number lines that intersect at a right angle
In cylindrical coordinate, x=rcosФ
y=rsinФ
z=z
25(rcosФ)^2=25(rsinФ)^2=6rcosФ
25r^2cos^2Ф-25r^2sin^2Ф=6rcosФ
25r^2(cos^2Ф-sin^2Ф)=6rcosФ
25r(cos^2Ф-sin^2Ф)-6cosФ=0
25r(cos^2Ф-sin^2Ф)-6cosФ=0 is the required equation in cylindrical coordinates.
Therefore 25r(cos^2Ф-sin^2Ф)-6cosФ=0 is the required cylindrical equation
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the table shown below represents a function.which of the following values could not be used to complete the table ?
Answers
Answer:
A worker bee has a mass of \,1\cdot{ 10^{-4}}1⋅10
−4
1, dot, 10, start superscript, minus, 4, end superscript \text{kg}kgstart text, k, g, end text. There are 4\cdot{ 10^4}4⋅10
4
4, dot, 10, start superscript, 4, end superscript worker bees living in one hive.
What is the mass of all the worker bees in the hive together?
Write your answer in scientific notation.
Step-by-step explanation:
A volleyball team has $800 to spend on uniforms. After coach buys the uniforms
for 15 players, the team had $20 left. How much did each uniform cost?
Answers
Answer: Each uniform was $52
Step-by-step explanation: 780 divided by 15 is 52 therefore each uniform costs $52
Select the correct answer from the drop-down menu.
Triangle ABC is shown with angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees.
In this triangle, the product of tan A and tan C is
.
Answers
In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.
The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.
We have to find the product of tan A and tan C.
In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.
So, we have, tan A = tan C
Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.
Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.
Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.
Answer: `(BC)^2/(AB)^2`.
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A STEAM tutoring center offers a robotics class and an app development class to its members. There are 280 members, all of which are registered for at least one class this spring. If 75% of members registered for a robotics class and 50% registered for an app development class, how many members registered for both robotics and app development?
Answers
The number of students who registered for both robotics and app development is 70.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Total members = 280
The number of members who registered for the robotics class.
= 75% of 280
= 3/4 x 280
= 3 x 70
= 210
The number of members who registered for the app development class
= 50% of 280
= 1/2 x 280
= 140
We see that,
210 + 140 = 350
But we have 280 members.
So,
The number of students who registered for both robotics and app development.
= 350 - 280
= 70
Thus,
The number of students who registered for both robotics and app development is 70.
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43 - u = 69
how much is u?
Answers
Answer:
69-43= 26
therefore "U" is worth 26 U=26
Step-by-step explanation:
Answer:
its 26, because whaen u subtract 43 from 69 u will get 26
use the pythagorean theorem 1) a=7 b=12
Answers
Answer:
√193
Step-by-step explanation:
7^2 = 49
12^2 = 144
144 + 49= 193
√193 because you are trying to find c not c^2
plsssssssssssssssssss
Answers
Answer: it is 8.5*10^5 (or third one)
Which equations has a solution for k = 6.5? CHOOSE TWO
Answers
The equation which has a solution of k = 6.5 is -7k = -45.5.
The correct answer choice is option C
Which equation has a solution of k = 6.5?Check all that applies:
-3k = 19.5
divide both sides by -3
k = 19.5/-3
k = -6.5
-1 + k = 7.5
Add 1 to both sides
k = 7.5 + 1
k = 8.5
-7k = -45.5
k = -45.5/-7
k = 6.5
-2 + k = -8.5
k = -8.5 + 2
k = -6.5
Therefore, -7k = -45.5 has the solution k = 6.5
Complete question:
Which equation has a solution of k = 6.5?
A. -3k = 19.5
B. -1 + k = 7.5
C. -7k = -45.5
D. -2 + k = -8.5
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what's the distance between the points (4,3) and (16,8)
Answers
Answer:
13
Step-by-step explanation:
Use the distance formula to determine the distance between two points.
===========================================
Work Shown:
The two given points are \((x_1,y_1) = (4,3)\) and \((x_2,y_2) = (16,8)\)
Use the distance formula
\(d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(4-16)^2+(3-8)^2}\\\\d = \sqrt{(-12)^2+(-5)^2}\\\\d = \sqrt{144+25}\\\\d = \sqrt{169}\\\\d = 13\\\\\)
Draw a possible net for the figure above.
Please need this done like rn
Answers
Simplify the expression:
-3(3 – 06y)
Answers
Answer:
18y−9
Step-by-step explanation:
Answer:
-9 - (-18y)
simplified more answer : -9 + 18y
if the 06 is a decimal then: answer: -9 - (-1.8y)
more simplfied answer: -9 + 1.8y
Step-by-step explanation: -3 x 3 = -9
-3 x 6y = -18 y
(if 06 a decimal: -3 x 0.6y = -1.8y)
variable answers (answers with a letter ) cannot be added together with a non variable answer