A bin is constructed from sheet metal with a square base and 4 equal rectangular sides. if the bin is constructed from 48 square feet of sheet metal, then what is the largest volume of such a bin? what are its dimensions?
Answers
In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:
V = length x width x height
That is:
[tex]V = xxy = x^{2}y[/tex]
We also know that the bin is constructed from 48 square feet of sheet metal, so:
Surface area of the square base = [tex]x^{2}[/tex]
Surface area of the rectangular sides = [tex]4xy[/tex]
Therefore, the total area of the cube is:
[tex]A = 48 ft^{2} = x^{2} + 4xy[/tex]
Isolating the variable y in terms of x:
[tex]y = \frac{48- x^{2} }{4x}[/tex]
Substituting this value in V:
[tex]V = x^{2}( \frac{48- x^{2} }{x}) = 48x- x^{3} [/tex]
Getting the derivative and finding the maxima. This happens when the derivative is equal to zero:
[tex]\frac{dv}{dx} = 48-3x^{2} =0[/tex]
Solving for x:
[tex]x = \sqrt{\frac{48}{3}} = \sqrt{16} = 4[/tex]
Solving for y:
[tex]y = \frac{48- 4^{2} }{(4)(4)} = 2[/tex]
Then, the dimensions of the largest volume of such a bin is:
Length = 4 ft
Width = 4 ft
Height = 2 ft
And its volume is:
[tex]V = (4^{2} )(2) = 32 ft^{3}[/tex]
Related Questions
A box contains 3 blue and 2 red pens while another box contains 2 blue and 5 red pens. a pen drawn at random from one of the boxes turns out to be blue. what is the probability that it came from the first box
Answers
The probability of getting blue from the first box is 3/5.
Given that, a box contains 3 blue and 2 red pens while another box contains 2 blue and 5 red pens.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favourable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n.
The probability of getting blue from the first box:
The number of favourable outcomes = 3 and the number of total outcomes =5
So, P(E) = 3/5
The probability of getting blue from the second box:
The number of favourable outcomes = 2 and the number of total outcomes =7
So, P(E) = 2/7
Therefore, the probability of getting blue from the first box is 3/5.
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All at once, pandemonium broke loose. ______________ the marching band came around the corner, dogs began barking, and the horses pulling the mayor's carriage began to run!
Which word best completes the passage above? (5 points)
Anyway
Because
Following
Simultaneously
Answers
Answer:
The answer is word SIMULTANEOUSLY.
Step-by-step explanation:
The alternative that fits best is " d.Simultaneously"
All at once, pandemonium broke loose. Simultaneously, the marching band came around the corner, dogs began barking, the horses pulling the Mayors carriage began to run.
This word maintains the coherence and cohesion of the given text.
Answer:
The alternative that fits best is " d. Simultaneously"
Step-by-step explanation:
Thus, the complete sentence would read: "All at once, pandemonium broke loose. Simultaneously the marching band came around the corner, dogs began barking, and the horses pulling the mayor's carriage began to run!"
The explanation for this is that the word "Simultaneously" is the only one that fits the phrase, and maintains the coherence and cohesion of the text. The words "anyway", "because", and "following", when embedded in the phrase, change the meaning of what the author wanted to go through.
Solve the proportion. Show your work.
Answers
3*11=33 and 5*x+1= 5x+5 5x+5=33
then subtract 5 on both sides 5x+5-5=33-5
5x=28 so divide 5 on both sides
5x/5=28/5
x= 5.6
Hope I Helped
A professor uses a video camera to record the motion of an object falling from a height of 250 meters. The function f(x) = –5x2 + 250 can be used to represent the approximate height of the object off the ground after x seconds. Which is the best estimate for the amount of time elapsed when the object is 120 meters off the ground? 4 seconds 5 seconds 6 seconds 7 seconds
(The answer is 5 seconds)
Answers
Answer:
B is the answer
Step-by-step explanation:
i just took the test
1 and 2 are a linear pair, and 2 and 3 are vertical angles. m 2=(5+4 y) and m 3=(6 y-25). what is m 1
Answers
∠2 = ∠3
5 + 4y = 6y - 25
→ 30 = 2y
→ 15 = y
∠2 = 5 + 4y = 5 + 4(15) = 5 + 60 = 65
linear pairs equal 180:
∠1 + ∠2 = 180
→ ∠1 + 65 = 180
→ ∠1 = 115
The Venn diagram represents the results of a survey that asked participants whether they would want a dog or a cat as a pet.
Enter your answers in the boxes to complete the two way table based on the given data.
Dog Not dog Total
Cat ___ ___ ____
Not
Cat ___ ____ ____
Total ___ ____ ____
Answers
Arrange the numbers shown on the diagram into the correct category:
Dog Not dog Total
Cat 31 10 41
Not Cat 24 7 31
Total 55 17 72
what does 3P2 equal?
Answers
No one has mentioned, so I will. What you are looking for is the permutation of 3 things taken 2 at a time. In other words, how many different unique ways are there to arrange 3 items, say colored balls, taking 2 of them for each group. By unique, I mean that 1 red and 1 blue is the same as 1 blue and 1 red,
Must have third quartile of a data set be less than the maximum value? Explain.
Answers
The equation for the line of best fit for a data set is y = 2x + 1.5. If the point (1, 4) is in the data set, what is the residual of 1? 0.5 3.5 4.0 7.5
Answers
Answer: First option is correct.
Step-by-step explanation:
Since we have given that
[tex]y=2x+1.5[/tex]
If the point (1,4) is in the data set.
we need to find the residual of 1.
At x = 1,
[tex]y=2x+1.5\\\\y=2\times 1+1.5\\\\y=2+1.5\\\\y=3.5[/tex]
So, At x = 1, the value of y = 3.5
As we know that
[tex]Residual\ value=Estimate\ value-Actual\ value\\\\Residual\ value=4-3.5\\\\Residual\ value=0.5[/tex]
Hence, The residual of 1 is 0.5.
Thus, First option is correct.
What is the recursive formula for the sequence 3, 12, 48, 192, 768...?
Answers
The given sequence is a geometric sequence. Each term in the sequence multiplies by 4 to obtain the next. Therefore, the recursive formula for the sequence is an = 4 * an-1.
Explanation:The given sequence is: 3, 12, 48, 192, 768, and so on. Looking at the sequence, we can see that each term is multiplied by 4 to get the next term. So, the sequence is a geometric sequence. The recursive formula for a geometric sequence is given by: an = r * an-1, where an is the nth term, r is the common ratio, and an-1 is the previous term. In this case, r equals 4 (since we are multiplying each term by 4 to get the next term). Thus, "the recursive formula for this geometric sequence is: an = 4 * an-1".
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What do you call it when someone pays back a loan quickly
Answers
If someone pays back a loan quickly its called a sudden debt payoff.
Hope this helps!
ANSWER: "A Sudden Debt Pay Off"
The height of a triangular road sign is 1 inch shorter than twice its base. if the area of the sign is 60 in.2, which equation could be used to find the base (b) of the sign?
Answers
The equation that can be used to find the base of the triangular road sign is 60 = (b * (2b - 1)) / 2.
Explanation:Let's assume that the base of the triangular road sign is represented by b. According to the problem, the height of the sign is 1 inch shorter than twice its base, which can be written as:
height = 2b - 1
The area of a triangle can be calculated using the formula Area = (base * height) / 2. Substituting the given values into the formula, we get:
60 = (b * (2b - 1)) / 2
This equation can be used to find the base, b, of the sign.
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Given the three vertices F(-5, 0), G(3, -3), and H(-2, 8), what are the coordinates of I that make quadrilateral FGIH a square
Answers
18. you work a part-time job earning $6.80/hr with tips that average $2.30/hr. you work 20 hr/wk and your deductions are FICA (7.65%), federal tax withholding (8.95%), and state tax withholding (6.1%). how much are you allowed in housing expenses per month?
Im asking for help not for you to do it.
Answers
Total housing expenses per month allowed will be $168.81.
To calculate how much you are allowed in housing expenses per month, we need to first determine your after-tax income.
You earn $6.80/hr plus tips averaging $2.30/hr, resulting in an hourly wage of
$6.80 + $2.30 = $9.10
Working 20 hours a week gives you a weekly income of
20 hours × $9.10/hr = $182
Monthly, this equates
$182 4 weeks = $728
The deductions are as follows: FICA (7.65%), federal tax withholding (8.95%), and state tax withholding (6.1%). These deductions total to
7.65% + 8.95% + 6.1% = 22.7%
To get the after-tax income, we calculate
$728 - (22.7% × $728)
≈ $562.69
This is your monthly take-home pay.
Financial experts often recommend spending no more than 30% of your take-home pay on housing. Therefore
$562.69 × 30%
= $168.81 houses expenses per month
What is the IMA of the doorknob shown?
1.5
3
6
15
Answers
1. You must apply the following formula for calculate the IMA of the doorknob shown in the figure attached of the problem above:
IMA=outer radius/inner radius
outer radius=3 cm
inner radius=0.5 cm
2. When you substitute these values into the formula, you obtain:
IMA=3 cm/0.5 cm
IMA=6
Therefore, the answer is: 6
Answer:
6
Step-by-step explanation:
Seven subtracted from the quotient of a number and 2 is -6
Answers
add 7 to both sides;
n/2 -7+7 = -6+7
n/2 = 1
multiply both sides by 2 ( or divide by 1/2 ) in order to get n by itself.
n/2 * 2/1 = 1 * 2/1
n = 2
18 / n - 7 = 2
18 / n =9
18 = 9n
2 = n
18 / 2 - 7 = 2
9 - 7 = 2
2 = 2
The width of a rectangle is 4 less than half the length. if l represents the length, which equation could be used to find the width, w?
Answers
W=1/2L+4
This is the answer
point m lies between point L and N on LN
Answers
Answer:
64 units
Step-by-step explanation:
Segment addition holds, so we can write ...
LM + MN = LN
(10x +8) +(5x-4) = (12x +16)
15x + 4 = 12x + 16 . . . . . . . . collect terms
3x -12 = 0 . . . . . . . . . . . . . . subtract 12x+16
x-4 = 0 . . . . . . . . . . . . . . . . . divide by 3
x = 4 . . . . . . . add 4
LN = 12x +16 = 12·4 +16 = 48 +16 . . . . . substitute into the expression for LN
LN = 64 . . . . units
The variable z varies jointly with x and y. also, z = -75 when x = 3 and y = -5. what equation describes this variation?
Answers
zαxy
z=kxy
where k is the proportionality constant
k=z/xy
when x=3, y=-5 then z=-75
k=-75/(-5*3)=5
hence the formula will be:
z=5xy
Answer:
c
5
-10
Step-by-step explanation:
Check out the Points Scored by Lebron James during his 2012 season: 10,11.15, 18, 20, 20, 21,23, 24, 24, 26
A sport Statistics Magazine said his Median Score was 21 is that True or False?
A. True
B. False
Answers
10, 11, 15, 18, 20, 20, 21, 23, 24, 24, 26
Median is 20 (the middle of those numbers)
So,
False not 20
Mitchell and Luke record the number of deliveries they each make for their family's restaurant. The results are shown in the box plots below.
Select the true statement.
The interquartile range of Mitchell's data is greater than the interquartile range of Luke's data.
Mitchell's data and Luke's data have the same interquartile range.
The median number of deliveries made by Mitchell each week is greater than the median number of deliveries made by Luke each week.
The median number of deliveries made by Mitchell each week is equal to the median number of deliveries made by Luke each week.
Answers
The interquartile range of Mitchell's data is greater than the interquartile range of Luke's data.
Since the interquartile range (RIC) is equal to:
RIC = Q3-Q1
Of the gracifa can be observed quer for the case of Mitchell:
RIC = 34-25 = 9
While for Luke's case:
RIC = 36-28 = 8.
Therefore Mitchell's interquartile range (RIC) is greater than Luke's.
Answer:
A. The interquartile range of Mitchell's data is greater than the interquartile range of Luke's data.
Step-by-step explanation:
How many two-digit positive integers can be formed from the digits 1, 5, 6, and 8 if no digit is repeated?
Answers
We have to fill two places using the 4 digits without repeating the digits.
The first place digit can be filled in 4 ways. When first place is filled, one number is already taken, so now we can fill the second place using remaining 3 digits (3 ways)
So, the total number of ways of forming 2 digit numbers = 4 x 3 = 12 ways
Ginger wanna join a gym.she goes to the local gym and is told that there is a one-time fee of $100 to join and then a monthly fee of $30.if she belongs to the gym for one year then the 12th month is free.how much will a one year membership cost her?
Answers
100+30(11)
100+330
430 dollars, which is highway robbery..
Park rangers released 12 fish into a pond in year 0. Each year, there were twice as many fish as the year before. How many fish were there after x years? Write a function to represent this scenario.
Answers
This is probably right. I'm 99% sure. :)
Answer: The function would be,
[tex]f(x)=12(2)^x[/tex]
Step-by-step explanation:
Given,
Park rangers released 12 fish into a pond in year 0,
Thus, the initial number of fish = 12,
Also, there were twice as many fish as the year before,
⇒ After 1 year the number of fishes = 2(12) = 12(2),
Similarly,
After 2 years = 2(12(2))= 12(2)²,
After 3 years = 2(12(2)²) = 12(2)³,
................, so on,....
Thus, the number of fishes after x years would be,
[tex]12(2)^x[/tex]
Let f(x) represents the number of fish after x years,
[tex]\implies f(x) = 12(2)^x[/tex]
Which is the required function that the given scenario.
what is the largest possible product of two odd integers whose sum is 42?
Answers
You can tell this because the largest area of any rectangle is when it is a square. Even sides will always produce the greatest area. Thus, 21 and 21 would be the best numbers to use.
The largest possible product of two odd integers whose sum is 42 is 437, obtained from multiplying 19 by 23.
The question asks for the largest possible product of two odd integers whose sum is 42. To find this, we should split 42 into two odd numbers that are as close to each other as possible because the product of two numbers that are close together will be higher than the product of a pair that has a larger difference.
If we divide 42 by 2, we get 21, which is not an even integer, so we need to adjust the numbers by 1. So the two odd numbers closest to each half of 42 are 21 and 21. However, we can't have them both be the same number since we're looking for two integers, so we adjust one up and one down by 1, resulting in 20 and 22. To ensure both numbers are odd, we will subtract 1 from the first number and add 1 to the second number, giving us 19 and 23 as the two odd integers that sum to 42.
The product of 19 and 23 is 19 × 23 = 437, which is the largest possible product for two odd integers that add up to 42.
Which number is irrational? A. square root of 64 B. square root of 256 C. square root of 100 D. square root of 80
Answers
When rounding to.the nearest hundred are you to add or subtract?
Answers
Answer:
When you round to the nearest hundred:
150 or higher turns into 200, so you'd do add.
But when it's 149 or lower, you simply subtract it by 49.
Step-by-step explanation:
Antar is flying a triangular-shaped kite. it has a height of 41/2 feet and a base of 53/4 feet. what is the area of antar's kite?
Answers
A= HbxB/2 = 4.5*5.75/2= 12.94ft
Answer:
12.94
Step-by-step explanation:
john buys a new bedroom set on credit for $2760 and no interest. he pays $115 per month. what is the equation that models the money john owes?
Answers
let the amount owed by John, is y at time time,x.
the linear equation is given by:
y=mx+c
where:
m=slope
c=y-intercept
from the information:
c=$2760
m=$115
thus amount owe will be:
y=-115x+2760
i need help with number 2 please p
Answers
6b=27
b=4.5
if you plug it back in both sides equal 8