Sam has sheets of metal which are 36 cm by 36 cm square. He wants to cut out identical squares which are x cm by I cm from the corners of each sheet. He will then bend the sheets along the dashed lines to form an open container. a Show that the volume of the container is given by V(2) = x(36 – 2x)2 cm? . b What sized squares should be cut out to produce the container of greatest capacity? 36 cm 36 cm
Answers
Four squares with size of 6 centimeters should be cut to produce the container of greatest capacity.
How to model and analyse an open boxa) The volume of the box ([tex]V[/tex]), in cubic centimeters, is equal to the area of the base ([tex]A[/tex]), in square centimeters, multiplied by the height of the box ([tex]h[/tex]), in centimeters. The area of the surface is the product of the width ([tex]w[/tex]) and length (l), both in centimeters:
[tex]V = w\cdot l\cdot h[/tex]
[tex]V = (36-2\cdot x)^{2}\cdot x[/tex] (1)
The volume of the container is [tex]V = (36-2\cdot x)\cdot x[/tex] cubic centimeters. [tex]\blacksquare[/tex]
b) We need to apply first derivative analysis and second derivative analysis to determine the dimensions of the maximum squares to be cut:
FDT[tex]-4\cdot (36-2\cdot x)\cdot x+(36-2\cdot x)^{2} = 0[/tex]
[tex]-4\cdot x + 36-2\cdot x = 0[/tex]
[tex]6\cdot x = 36[/tex]
[tex]x = 6[/tex]
SDT[tex]V'' (x) = -4\cdot [(-2)\cdot x+(36-2\cdot x)]-4\cdot (36-2\cdot x)\cdot x + (36-2\cdot x)^{2}[/tex]
[tex]V''(x) = 8\cdot x-4\cdot (36-2\cdot x)-4\cdot (36\cdot x-2\cdot x^{2})+(36-2\cdot x)^{2}[/tex]
[tex]V'' (6) = -48[/tex]
Since [tex]V''(6) < 0[/tex], the critical value of [tex]x[/tex] leads to a maximum.
Four squares with size of 6 centimeters should be cut to produce the container of greatest capacity. [tex]\blacksquare[/tex]
To learn more on optimization, we kindly invite to check this verified question: https://brainly.com/question/5425085
Related Questions
10. Find the value of the function () = 15x2 - 4 if x = 6.
a. 180
116
b. 2/19
C.
d. 4
Answers
Answer:
your question is not clear
Step-by-step explanation:
because of option not correct arrange
A scientist measures the velocity of a major river at various depths. After collecting and analyzing the data, the scientist determines that the equation y=−0.114x+1.658, where x represents the depth, in feet, and y represents the velocity of the river, in feet per second, can be used to model the data. The linear model has a correlation coefficient of 0.964.
Answers
Answer:
If you translate that in romanian i will do it.
The velocity of a major river at various depths has no relation.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
We are given that;
Equation y=−0.114x+1.658
Now,
In this case, the equation y = -0.114x + 1.658 represents a linear relationship between x (depth) and y (velocity) of the river. The correlation coefficient is 0.964, which means there is a very strong positive correlation between these two variables. This means that as depth increases, velocity also tends to increase proportionally.
| x | y |
| 0 | 1.658 |
| 5 | 1.098 |
|10 | 0.538 |
|15 |-0.022 |
The calculator gives us a p-value of approximately 0.0002, which is much smaller than 0.05. This means that we can reject the null hypothesis that there is no correlation between depth and velocity of the river and conclude that there is a statistically significant positive correlation between them.
Therefore, by the given equation there will be no relation.
Learn more about linear equations;
https://brainly.com/question/10413253
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Write the equation of a line through point (-5,1) and perpendicular to 2x – 3y = 6?
Answers
Answer:
B. Slope = -5/4, no, not perpendicular
Step-by-step explanation:
approximately how many times did taryn gaslight and manipulate cam??
A. never!!
B. once or twice
C. we’re gonna bump it up a little and say a good 10-20 times
D. too many to count this mf crazy.
Answers
do this for brainliest!!
Answers
Answer:
125 is the answer
Step-by-step explanation:
Find the measure of angle r
Answers
Answer:
75 degrees
Step-by-step explanation:
75+r+30=180
105+r=180
r=75
The probability of making a type i error is denoted by.
Answers
The probability of making a type i error is the likelihood of type i error, and it is denoted by α
How to determine the symbolThe type-i error involves rejecting a good prediction or value indicated by the null hypothesis.
In other words, the probability of wrongly rejecting the null hypothesis is the probability of the type-i error.
And it is represented by the alpha symbol.
Hence, the probability of making a type i error is α
Read more about probability at:
https://brainly.com/question/25870256
ASAP!!!!!!!!! PLS!!!!!
Answers
Answer:
[tex]\huge\boxed{\text{6 by 10 inches}}[/tex]
Step-by-step explanation:
In order to solve for this, we can make two equations, where a is the length of the first side and b is the length of the second side.
[tex]ab=60[/tex] (Area)[tex]2a+2b=32[/tex] (Perimeter)We can now solve this systems of equations by using substitution.
Let's change the equation [tex]ab=60[/tex] into the form [tex]a= mb+c[/tex].
We can divide both sides by b.
[tex]a = \frac{60}{b}[/tex]
We can now plug [tex]\frac{60}{b}[/tex] in as a into [tex]2a+2b=32[/tex].
[tex]2(\frac{60}{b}) + 2b = 32[/tex]
Let's simplify this equation:
[tex]\frac{120}{b} + 2b = 32[/tex] [tex]2b^2 + 120 = 32b[/tex] [tex]2b^2 - 32b + 120 = 0[/tex] [tex]b^2 - 16b + 60 = 0[/tex] [tex]-10 \cdot -6 = 60\\-10 + -6 = -16[/tex] (Quadratic factoring, [tex]x_1 \cdot x_2=c, x_1 + x_2 = b[/tex]) [tex](b-10)(b+6)[/tex] [tex]b = 10\ \text{or}\ 6[/tex]Now, since we have both roots of this quadratic, we know that the two sides will be 10 and 6 inches long.
Hope this helped!
Which of the following is a factor of 2x2-2
Answers
Answer:
2(x-1)
Step-by-step explanation:
Multiply 2 by the terms inside.
Answer:
this is both factors
2(x+1), (x−1)
Step-by-step explanation:
need answers, please explain asap! need the answer for 2 and 3!
Answers
Volume of a cube formula: [tex]V=a^3[/tex]
Surface area of a cube formula: [tex]SA=6a^2[/tex]
[tex]a[/tex] is the side lengthArea of a TrapezoidArea of a trapezoid formula: [tex]A=\dfrac{1}{2}(a+b)h[/tex]
[tex]a[/tex] is the length of the top side[tex]b[/tex] is the length of the bottom side[tex]h[/tex] is the height (forms a right angle with the bottom of the trapezoid)Solving the QuestionQuestion 2We're given:
Volume of the cube = 343 cm³We must solve for the surface areaFirst, use the volume formula to solve for the side length:
[tex]V=a^3[/tex]
⇒ Plug in the known volume:
[tex]343=a^3\\\sqrt[3]{343}=\sqrt[3]{a^3}\\a=7[/tex]
Therefore, [tex]a=7[/tex].
Now, plug this value into the formula for surface area:
[tex]SA=6a^2\\SA=6(7)^2\\SA=294[/tex]
Therefore, the surface area of the cube is 294 cm².
Question 2We're given:
One can of paint covers 72 ft²[tex]a=14[/tex][tex]b=24[/tex][tex]h=16.5[/tex]For this question, we must solve for the area of the trapezoid, then divide its double by 72 to find how many cans of paint we need for two coats.
Solve for the area of the trapezoid:
[tex]A=\dfrac{1}{2}(a+b)h[/tex]
⇒ Plug in the given information:
[tex]A=\dfrac{1}{2}(14+24)(16.5)\\\\A=\dfrac{1}{2}(38)(16.5)\\\\A=(19)(16.5)\\A=313.5[/tex]
Therefore, the area of the trapezoid is 313.5 ft²
Multiply it by 2:
[tex]313.5*2\\=627[/tex]
Divide this by 72:
[tex]\dfrac{627}{72}\\\\=8.7[/tex]
Therefore, we need 9 cans of paint to paint two coats over the deck.
Peiling and John saved the same amount of money. After Peiling lent $28 to John, John had 5 times as much money as Peiling. How much did John have in the end?
Answers
Answer:
140$
Step-by-step explanation:
so if peilling lent 28$ and then john has 5x as much that means john had 4x as much before getting the 28$ which would mean that john had 112$ dollars so now with that knowledge just add the 28$ to get 140$ or just do 5 x 28 to get 140
Richard owned n cows.
Ellis had exactly 4 times as many cows as Richard.
Richard buys 13 extra cows.
Ellis sells 9 of his cows.
Ellis still has more cows than Richard.
Form an inequality, in terms of n.
Solve the inequality to find the least value of n.
You must show all your working.
Answers
Ellis has (4n)
Richard now has (n+13)
Ellis now has (4n-9)
Ellis has more cows that Richard
That means
4n-9 > n+ 13
3n > 22
n > 22/3
Hope this helps.
Alice makes a scale drawing of her bedroom. She uses a scale of 3 cm to represent 5 m. What ratio is Alice using?
Answers
Answer:
[tex]\frac{3}{500}[/tex]
Step-by-step explanation:
1m is 100 cm, so we have [tex]\frac{3}{500}[/tex]
A rectangle has a height 3 times the length of its base. If the base increases by 3 cm and the height by 5 cm then the area is 319 2. What are the dimensions of the rectangle?
Answers
Answer:
The length of a rectangle is 3 times the width.The area is 75 cm^2.
if I had 9 bucks to spend on the book fair, how much money would I have if I bought 2 posters, a comic, and an Invisible ink pen? Would I have enough?
__________________
l poster: $2 l
l Comic: $3 l
l Invisible ink pen: $3 l
l_________________l
Answers
3. Henry's banks said they will putin 20% interest annually if he keeps at least $5,000 in his savings account. How much money. in interest will the bank put in Henry's
All changes saved
account?
STO
$10,000
O $100
$1,000
Answers
Hey there!
Option answer: $1,000
Calculate the percentage
=> 5000 × 20/100
=> 5000/1 × 20/100
=> 50/1 × 20/1
=> 1000/1
=> 1000
Therefore, 20% of $5000 is $1000
(Multiple Choice Worth 1 points) What should be added to -5 to make the sum 0?
Answers
Answer:
5
Step-by-step explanation:
-5+5=0
Your cafeteria line requires 8 minutes on the average for each customer to proceed through the line and pay the cashier. The average time space between each customer is 30 seconds. If the line is open for 1 1/2 hours for lunch, how many customers can you serve for lunch?
Answers
Answer:
You can serve 81 customers for lunch during the 11,5 hours opening.
Step-by-step explanation:
11,5 hours is 690 minutes.
Each customer takes 8,5 minutes (8 + 0,5)
690 / 8,5 = 81,17
As we can't serve "part" of customer:
81,17 ≈ 81 customers
PLEASE HELP ASAP I WOULD RLY APPRECIATE IT
Answers
Answer:
The measurement of 7 is equal to 47 because it is congruent to 5.
The equation that could be is is: (2x-5) + 47 = 180
x is equal to 69.
Step-by-step explanation:
69 times 2 = 138 -5 = 133
133 + 47 = 180
help please asap so much appreciated
Charmaine watered 3 plants.
Every plant got
gallons of water.
How much water did she use in all?
Write your answer in simplest form.
Answers
Because she used 5/9 gallons for each three plants you multiply the amount she used by three. 5/9 * 3 which equals to 15/9. That simplifies to 1 and 2/3.
For 30 points
The pattern 2, 5, 17, ________, ________ follows the rule multiply by 4, then subtract 3. What are the next two terms?
Answers
Answer:
the next two are 65, and 257
Answer:
65 and 257
Step-by-step explanation:
17x4=68 68-3=65. 65x4=260 260-3=257
The sum of two numbers is 87. The difference of the same to numbers is negative 111. Find the numbers.
Answers
Answer:
99 and - 12
Step-by-step explanation:
let x and y be the 2 numbers, then
x + y = 87 → (1)
x - y = - 111 → (2)
Adding the 2 equations term by term eliminates the y- term
2x = - 24 ( divide both sides by 2 )
x = - 12
Substitute x = - 12 into (1)
- 12 + y = 87 ( add 12 to both sides )
y = 99
The 2 numbers are 99 and - 12
Calculate.
(2017 x 0.2018 x 2018 x 20.18)/(20.17 x 201.8 x 2.018)
Answers
Answer is:
2018
Have a good day :D
does anyone know the answer to this? i need it asap
Answers
SHOW WORK AND I WILL GIVE BRAINIEST
Ethan is a 5 ft 4 inches tall. How tall is he in cm, if 1 in is about 2.54 cm?
Answers
Answer:
he is 162.56
Step-by-step explanation:
Answer:
162.56 cm
Step-by-step explanation:
Convert 5 ft 4 inches to inches (5 x 12) +4
Then convert to cm
64in 2.54cm
--------- x --------------- = 162.56cm
1 1 in
Cancel the term inches and multiply 64 by 2.54cm
Please help fast!!!! A spinner has 3 sections
Answers
Answer:
9/20
Step-by-step explanation:
36/80
orrrr just
9/20
Plsssss help me to answer this question I will mark you brainlist.
The solution the inequality 4(3x + 2) - 6 > 8 + 2(x - 8) is a x > n. What is the value of n?
n=?
Answers
Answer:
-1
Step-by-step explanation:
First you simplify your parenthesis, then subtract 2x from both sides. Then subtract both sides by 2, then finally divide both sides by 10. x > -1 So n = -1
Hope I helped! :)
Math help!
Imagine a 10 by 10 by 10 cube made up of 1000 unit cubes and floating in space. What is
the greatest number of unit cubes that can be seen by an observer at any moment in time?
Answers
That would be 300 unit cubes, bc each side has 100 unit cubes (10 x 10)
If you want more explanation lmk!
Does AN time E equal to ABN if A=1, B=5, E=3 & N=0?
Answers
Answer:
Yes, AN time E equal to ABN if A=1, B=5, E=3 & N=0.
Step-by-step explanation:
Given;
Does AN time E equal to ABN if A=1, B=5, E=3 & N=0?
A = 1
B = 5
E = 3
N = 0
Note;
0 multiply everything is 0.
Solve;
So If A=1, B=5, E = 3, N=0
AN times E = (1 x 0) x 3 = 0
ABN = (1 x 5 x 0) = 0
Therefore, the question would be true.
~Learn with Lenvy~
100 POINTS!!!
What is the meaning of the initial value in this table?
A. How much he purchased the computer for.
B. How much he spent.
C. How much it goes down.
D. How much he pays per month
EXPLAIN
Answers
Answer:
A
Step-by-step explanation:
Since he is paying the computer off, the first value is considered the initial value, and in this case it is the amount he purchased the computer for.