An open box is to be made from a square piece of cardboard, 36 inches by 36 inches, by removing a small square from each corner and folding up the flaps to form the sides. What are the dimensions of the box of greatest volume that can be constructed in this way?
Answers
9514 1404 393
Answer:
24 in square by 6 in deep
Step-by-step explanation:
Let x represent the side of the square cut from each corner. Then the dimensions of the base of the box are 36-2x in each direction. The total volume of the box is ...
V = LWH = (36 -2x)(36 -2x)x = x(4x² -144x +1296)
The volume will be a maximum where dV/dx = 0.
dV/dx = 12x^2 -288x +1296 = 0
x² -24x +108 = 0 . . . . divide by 12
(x -6)(x -18) = 0 . . . . . factor
x = 6 or 18 . . . . . . x = 18 gives a minimum volume; we want x = 6
Then the dimensions are 36 -2(6) = 24 inches square by 6 inches deep.
Related Questions
KBL Ltd. entered into an agreement to lease a vehicle from Morgan Ltd.: Cash price of the vehicle Kshs 20.000 Lease payments: 5 instalments of Kshs 5.142 paid in arrears Required: How much of this finance charge will appear in each year's profit and loss expense in the lessee's books using the actuarial method? (10 Marks)
Answers
Finance charge is the amount it costs of borrowing money
The finance charge that will appear in each year's profit and loss expense in the lessee's books are;
[tex]\begin{array}{|c|cc|}\mathbf{Year}&&\mathbf{Finance \ Charge \ (Kshs)}\\&&\\First&&1.8\\&&\\Second&&1.499\\&&\\Third&&1.171\\&&\\Fourth&&0.814\\&&\\Fifth&&0.424\end{array}\right][/tex]
The total financial charge = 5 × 5.142 - 20.000 = 5.71
The annual percentage rate, APR, of an instalment payment is given as follows;
[tex]\dfrac{(1 - (1 + r)^{-5}}{r} \times 5.142 = 20.000[/tex]
Solving using a graphing calculator gives;
r = APR ≈ 0.09 = 9%
The calculation for charges each year is as follows:
Payment interest for the first instalment = 20 × 9% = 1.8
The principal of the first payment = 5.142 - 1.8 = 3.342
The loan balance = 20 - 3.342 = 16.658
Payment interest for the second instalment = 16.658 × 9% = 1.49922
Second payment principal = 5.142 - 1.49922 = 3.64278
Loan balance = 16.658 - 3.64278 = 13.01522
Payment interest for the third instalment = 13.01522 × 9% = 1.1713698
Third payment principal = 5.142 - 1.1713698 = 3.9706302
Loan balance = 13.01522 - 3.9706302 = 9.0445898
Interest for the fourth payment = 9.0445898 × 9% = 0.814013082
Fourth payment principal = 5.142 - 0.814013082 ≈ 4.327986918
Loan balance = 9.0445898 - 4.327986918 = 4.716602882
Fifth payment interest = 4.716602882 × 9% = 0.42449425938
Fifth payment principal = 5.142 - 0.42449425938 ≈ 4.718
Therefore, we have;
[tex]\begin{array}{|c|cc|}\mathbf{Year}&&\mathbf{Finance \ Charge \ (Kshs)}\\&&\\First&&1.8\\&&\\Second&&1.499\\&&\\Third&&1.171\\&&\\Fourth&&0.814\\&&\\Fifth&&0.424\end{array}\right][/tex]
Learn more about the actuarial method here:
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In math how can you tell if something is a function.
Answers
Answer:
if the line dosent have the same x's
Step-by-step explanation:
Which expressions are equivalent to the expression 7(5 + m) - 8?
Answers
Answer:
27 + 7m
Step-by-step explanation:
[tex]7(5 + m) - 8[/tex]
open the bracket:
[tex] = 35 + 7m - 8 \\ = 27 + 7m[/tex]
Analyze the diagram below and complete the instructions that follow.
Identify the cross section of the solid shown in the diagram.
A. tetrahedron
B. quadrilateral
C. rectangle
Dsquare
Answers
JT has two jobs. He mows yards and washes cars in his neighborhood. Let X represent the amount of weekly
earnings for mowing yards, and let y represent the amount of weekly earnings for washing cars. The mean of X is
$60, and the mean of Y is $35. Which answer choice correctly calculates and interprets the mean of the sum, S= X
+ Y?
Ps = 47.5; next week, JT will earn $47.5.
Hs = 47.5; JT can expect to earn $47.5, on average, in a typical week.
Hs = 95; next week, JT will earn $95.
Ps = 95: JT can expect to earn $95, on average, in a typical week.
Answers
Answer is D) 95; JT can expect blah blahh
smallest to largest. 14/5, 2.4, 2 1/3, 1.41
Answers
Answer:
1.41, 2 1/3, 2.4, 14/5
Step-by-step explanation:
Change everything to decimal points first
If a car is traveling at 45 km/h, what is its speed in meters per second?
Answers
Answer:
4.5 meters
Step-by-step explanation:
Which expression has a value that is 6 times the value of the expression 63 - 3y?
ОА. 6x 63 – Зу
O B. 63 – 3y = 6
Ос. 63 = (6 x Зу)
OD. 6 X (63 – 3y)
Answers
Determine a series of transformation that would map figure h onto Figure I
Answers
Answer:
isnt it figure h???
Step-by-step explanation:
Answer:
A translation right 8 units followed by a reflection over the x-axis
Step-by-step explanation:
An elevator was on the 23rd floor. It
then went down 7 floors and then
another 4 floors. What floor was the
elevator on now?
Answers
Answer:
The 12th floor
Answer:
12th floor
Step-by-step explanation:
4+7 = 11
23-11 = 12
Can you explain what a stem and leaf plot is?
Answers
Answer:
A stem and leaf plot, or stem plot, is a technique used to classify either discrete or continuous variables. A stem and leaf plot is used to organize data as they are collected. ... Each number in the data is broken down into a stem and a leaf, thus the name. The stem of the number includes all but the last digit
hope it helped!
if 2x + 8 = 16, what is the vaule of x + 4?
Answers
Answer:
your answer
Step-by-step explanation:
mark me a brainlist
Hello!
✥ Answer: ✥
Value of x + 4 is 8.
❀ Step-by-step explanation: ❀
1. If 2x + 8 = 16, what is the value of x + 4?
2x + 8 = 16
2x = 16 - 8
2x = 8
x = 8 ÷ 2
x = 4
x + 4 => 4 + 4 = 8
Good luck!
GENTE PORFAVOR ME AJUDA
Answers
You have asked for help without actually providing what you need help on.
How do you solve by undoing for 4-2x-x=12 in Algebra 1
Answers
Hi ;-)
[tex]4-2x-x=12\\\\-2x-x=12-4\\\\-3x=8 \ \ /:(-3)\\\\x=-\frac{8}{3}=-2\frac{1}{3}[/tex]
round decimal to the nearest whole number.
12.1
Answers
Answer:
12
Step-by-step explanation:
12.1 to the nearest whole number is 12.
Answer:
12
Step-by-step explanation:
12.1 there is no number behind the one, therefore it becomes 12
what is the equation of the function y= 3/x translated 2 units to the left and seven units up
Answers
Answer:
y = (3/x + 2) + 7
Step-by-step explanation:
The additive inside the parenthesis moves the function to the left (adding moves left, subtracting moves right) and the additive outside moves the function up (adding moves up, subtracting moves down).
The arithmetic sequence a; is defined by the formula: a1=4 +3(i-1)
Answers
Answer:
the arithmetic sequence ai is defined by the formula: a1= 2 ai= ai - 1 -3 find the sum of the first 335 terms in the sequence. 1.
The textbook for a course in basic mathematics costs $35. There are 34 students in the class. Find the total cost of the textbooks for this class.
Answers
Answer:
1190 notebooks
Step-by-step explanation:
Cost per notebook * number of students
35 * 34 = 1190
35*30=1050
35*4 = 140
35*34 = 1050 + 140 = 1190
So the answer is 1190 notebooks.
The opposite of -17 I need the answer please and thanks
Answers
Hope my answer helped u :)
What is a 15 of the sequence –7,2, 11, ...?
Answers
We can see: Everytime, the new number is the sum of the number behind it with 9.
So the 15th will total add: 9 x 14 = 126
Start from number -7 so the 15th number is : 126 -7 = 119
SO: B.119 is the answer
NL: Sorry my english was bad
Answer:
119
Step-by-step explanation:
We need to find the 15th term in the sequence. The pattern is that each term increases by 9.
We can then count to the 15th term
-7 + 14*9 = 119
Therefore, the 15th term is equal to 119, or answer B.
Jungwon has $15. Notepads cost $2.50 each. How many notepads can Jungwon buy?
Answers
Answer this question.
Answers
Math
Explain
Answer:
B. y = -2x + 5
Step-by-step explanation:
By looking at the table of values, as x increases by 1, y decreases by 2. This means the slope is -2. By process of elimination, this leaves with answer B.
your sister is selling girl scout cookies that cost $4.25 a box. your family bought 6 boxes. how many more boxes of cookies must your sister sell in order to $255
Answers
$255-$25.5= $229.5
$229.5/$4.25= 54 boxes of cookies
Find the smaller of 2 consecutive even integers if the sum of twice the smaller integer and the larger
integers is -16.
Answers
Answer:
n = -6
Step-by-step explanation:
2n + (n + 2) = -16
3n + 2 = -16
3n = -18
Based on a sample of 400 people, 22% owned cats
The p value is
Answers
Answer:
88 people
Step-by-step explanation:
400*22/100
4*22
88 people
Based on a sample of 400 people, the 88 people owned cats.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that on a sample of 400 people, 22% owned cats
Let consider that the number of cats are p then we have;
22% of 400 = p
Thus, p = 400 x 22/100
p = 4 x 22
p = 88 people
The p value is 88
Learn more about multiplications;
https://brainly.com/question/14059007
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Simplify show step by step 30 POINTS!
Answers
Step-by-step explanation:
hopefully it makes sense and is visible
:)
2x-3y=-1
y=x-1
solve. systems of equations
Answers
Answer:
x=4
y=3
Step-by-step explanation:
PLZ HELP WILL MARK BRAINLIEST!
Answers
Step-by-step explanation:
directrix = (1, -1)
focus = (-3, 2)
vertex = (-3, 3)
The velocity, V, of a specific object being dropped from a particular height, h, can be found by the radical function V = sqrt 2ha. Where A represents the acceleration in ft/sec2. If the acceleration due to gravity is 32.2 ft/sec2, at what height should you drop an object in order for it to have a velocity of 60 ft/sec?
0.9 feet
55.6 feet
55.9 feet
3,864 feet
Answers
Answer:
55.9 feet
Step-by-step explanation:
Basically you can just plug in what they give you
givens:
V=60 ft/sec
a= 32.2 ft/sec^2
function to find velocity: [tex]V=\sqrt{2ha[/tex]
if you plug everything in: [tex]60=\sqrt{2(h)(32.2)[/tex]
you can just put that equation into a website and ask it to solve for h which would give you your answer
but, if you want the work,
FIRST square both sides of the equation to get rid of the square root symbol on the left so,
[tex]60^{2} =\sqrt{2(t)(32.2)} ^{2}[/tex]
which cancels out to
[tex]3600= 2(t)(32.2)[/tex]
NEXT: divide both sides by 32.2 to get 2t by its self so,
[tex]\frac{3600}{32.2} =\frac{2(t)(32.2)}{32.2}[/tex]
which should get you to
[tex]111.80124223=2(t)[/tex]
LAST: divide both sides by 2 to get t by itself so
[tex]\frac{111.80124223}{2} =\frac{2(t)}{2}[/tex]
and you should end up with
55.900621 = t
which rounded would be an answer of
t= 55.9 feet
Answer:
YUP IT IS 55.9
Step-by-step explanation:
I don't got an explanation, but I can say that I got 100 on my quiz.
HELP ME PLEASEEEEEEEE
Answers
Answer:
c
Step-by-step explanation:
i search it up