3) Postcards: Marcie wants to make a box to hold her postcard collection from a piece of
cardboard that is 10 inches by 18 inches. The box will be formed by making cuts as shown in
the diagram and folding up the sides.
a) Write a function that models the volume of the box.
b) What are the dimensions of the box with the maximum volume? Round to the nearest tenth.
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c) What is the maximum volume of the box?
Answers
The volume of the box is the amount of space in it.
The dimension of the postcard is:
[tex]\mathbf{Length = 10}[/tex]
[tex]\mathbf{Width = 18}[/tex]
Let x represents the length of the cut.
So, the dimension of the box is:
[tex]\mathbf{Length = 10 -2x}[/tex]
[tex]\mathbf{Width = 18 -2x}[/tex]
[tex]\mathbf{Height = x}[/tex]
(a) The function that represents the volume of the box
This is calculated as:
[tex]\mathbf{V(x) = Length \times Width \times Height}[/tex]
So, we have:
[tex]\mathbf{V(x) = (10 - 2x) \times (18 - 2x) \times x}[/tex]
Expand
[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]
Hence, the volume function is: [tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]
(b) The dimension that maximizes the volume
We have:
[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]
Differentiate
[tex]\mathbf{V'(x) = 180- 112x + 12x^2}[/tex]
Set to 0
[tex]\mathbf{180- 112x + 12x^2 = 0}[/tex]
Using a calculator, we have:
[tex]\mathbf{x = 7.3,2.1}[/tex]
The value x = 7.3 is greater than the dimension of the box.
So, we have:
[tex]\mathbf{x = 2.1}[/tex]
Recall that:
[tex]\mathbf{Length = 10 -2x}[/tex]
[tex]\mathbf{Width = 18 -2x}[/tex]
[tex]\mathbf{Height = x}[/tex]
So, we have:
[tex]\mathbf{Length = 10 -2 \times 2.1 = 5.8}[/tex]
[tex]\mathbf{Width = 18 -2 \times 2.1 = 13.8}[/tex]
[tex]\mathbf{Height = 2.1}[/tex]
Hence, the dimension that maximizes the volume is 5.8 by 13.8 by 2.1
(c) The maximum volume
This is calculated as the product of the dimension of the box
So, we have:
[tex]\mathbf{Volume = 5.8 \times 13.8 \times 2.1}[/tex]
[tex]\mathbf{Volume = 168.1}[/tex]
Hence, the maximum volume of the box is 168.1 cubic inches
Read more about volumes at:
https://brainly.com/question/17056191
Related Questions
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Answers
A=101
B=79
C=83
D=97
Find the equation of the line.
Use exact numbers.
y = ___x + ___
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Step-by-step explanation:
formula: y=mx+b
First you gotta find M witch is Slope.
B is the y-intercept which is -2
then you have to do rise/run
so up 2
right 3
= 2/3
so your answer would be
y=2/3-2 because you can't simplify 2/3
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If you want me to explain linear equations, slopes, or whatever just ask!
Hope this helped!! :)
Answer:
y_1=9(x_8)
y_1=9x_72
9x_y=71
9x_y_71=0
Graph the following equation: y - 3 = (x - 2)
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Answer:
Step-by-step explanation:
I took pictures of what I found and I think is right
what do i get for this Question a-b=18 find a and b
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Your answer is A = 12.375 and B = 5.625.
1) 20/2 × 7 = ?
2) 6/2 + 6/1 = ?
.
.
_____
0.
Answers
20/2 × 7 = ?
= 10 × 7
= 70
[tex] \: [/tex]
Number (2)6/2 + 6/1 = ?
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[tex]\huge\mathfrak\blue{Answer}[/tex]
3 + 6 = 9what is the domain of the relation shown
Answers
Which expressions are equivalent to 35x + 3. Select the TWO that apply.
25x + 315x
45x - 15x + 3
25x + 335x - 1
1 + 35x + 2
1 + x5+ 2
1 + 25x + 3
Answers
And
1+35x+2
which of the following shows a way to factor the expression -6x+18
Answers
Answer:
x=24
Step-by-step explanation:
1. try to put x by itself
2. move the -6 but turn it into a positive
3. add 18 and 6 and that becomes your answer and equals to x
Hii!
______________________________________________________
Answer:
Step-by-step explanation:
Note that, -6x and 18 have something in common. This "something" is -6, so we factor it out by dividing both terms of the expression by it.
We obtain.
-x+3
Put parentheses around it.
(-x+3)
Put 6 outside the parentheses
6(-x+3)
--
Hope that this helped! Best wishes.
--
5x+y=-2y-31. 2y+10=-4x-12
What is the X and Y
Answers
Answer:
x= -0.1818
y= 10.6363
Step-by-step explanation:
which statement is correctly written as a conditional statement
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Answer:
a shape has four sides,or it is a quadrilateral
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!6
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simplify (x^5-y^5) ÷(x-y) (this question is a part of polynomials chapter) please explain and tell me the answer
Answers
Answer:
Step-by-step explanation:
[tex]x^{n}-y^{n} =(x -y)(x^{n-1} + x^{n-2}*y^{1} +......+ xy^{n-2} + y^{n-1}\\\\\dfrac{x^{5}-y^{5}}{x-y}=\dfrac{(x -y)*(x^{4}+x^{3}*y^{1}+x^{2}*y^{2}+x*y^{3}+y^{4}}{(x-y)}\\\\[/tex]
= x⁴ + x³y + x²y² + xy³ + y⁴
DeMarcus is organizing a group of friends to attend a concert.
The ticket pricing is shown in the table below. Use the information
to create a graph and answer the questions.
Miu
# OF TICKETS
2
3
5
7
TOTAL COST ($)
32
48
80
112
16
9
14
126
IDS
84
63
42
1. Rate of Change:
Equation:
2. What does the ordered pair (1, 16) represent in this situation?
212
1234
078410
3. Describe how you know that this is a proportional relationship:
Answers
Answer:
Give me some hint please
The rate of change is 16, the equation is y = 16x, the (1,16) represents that the cost of 1 ticket is $16 and by y = 16x it is clear that it is a direct proportion.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
The table of tickets and their cost is given,
The graph of it has been plotted below,
The rate of change or slope = (48 - 32)/(3 - 2) = 16
The equation is y = mx + c where m is the slope and it is 16
So, y = 16x + c
Now substitute (2,32)
32 = 2(16) + c
c = 0
So the equation becomes y = 16x
Since y = kx is a direct proportional equation so it will be also direct proportionally.
In (1,6) , 1 = number of ticket , 16 = cost of ticket so it is $16.
Hence "The rate of change is 16, the equation is y = 16x, the (1,16) represents that the cost of 1 ticket is $16 and by y = 16x it is clear that it is a direct proportion".
For more about the equation,
https://brainly.com/question/10413253
#SPJ5
Quadrilateral JKLM with vertices J(2, 10),
K(8,9), L(7,4), and M(3, 4):
J
k = 2, centered at (4,7)
Answers
Given:
Quadrilateral JKLM has vertices J(8, 4), K(4, 10), L(12, 12), and M(14, 10).
(a)If we translate quadrilateral JKLM 3 units down and 3 units left:
(x-3,y-3), we obtain: W(5,1), X(1,7), Y(9,9), and Z(11,7)
Therefore, we match it with: A translation 3 units down and 3 units left
(b)If we translate quadrilateral JKLM 2 units right and 3 units down:
(x+2,y-3), we obtain: O(10,1), P(6,7), Q(14,9), and R(16,7)
Therefore, we match it with:A translation 2 units right and 3 units down
S(4, 16), T(10, 20), U(12, 12), and V(10, 10)
(c) If we transform quadrilateral JKLM by a sequence of reflections across the x- and y-axes, in any order, we obtain:
A(-8, -4), B(-4, -10), C(-12, -12), and D(-14, -10)
(d)If we translate quadrilateral JKLM 3 units left and 2 units up:
(x-3,y+2), we obtain:E(5,6), F(1,12), G(9,14), and H(11,12)
Therefore, we match it with: A translation 3 units left and 2 units up
(e)S(4, 16), T(10, 20), U(12, 12), and V(10, 10)
No suitable transformation is found from JKLM to STUV.
Quadrilateral JKLM has vertices J(8, 4), K(4, 10), L(12, 12), and M(14, 10).
(a)If we translate quadrilateral JKLM 3 units down and 3 units left:
(x-3,y-3), we obtain: W(5,1), X(1,7), Y(9,9), and Z(11,7)
Therefore, we match it with: A translation 3 units down and 3 units left
(b)If we translate quadrilateral JKLM 2 units right and 3 units down:
(x+2,y-3), we obtain: O(10,1), P(6,7), Q(14,9), and R(16,7)
Therefore, we match it with:A translation 2 units right and 3 units down
S(4, 16), T(10, 20), U(12, 12), and V(10, 10)
(c) If we transform quadrilateral JKLM by a sequence of reflections across the x- and y-axes, in any order, we obtain:
A(-8, -4), B(-4, -10), C(-12, -12), and D(-14, -10)
(d)If we translate quadrilateral JKLM 3 units left and 2 units up:
(x-3,y+2), we obtain:E(5,6), F(1,12), G(9,14), and H(11,12)
Therefore, we match it with: A translation 3 units left and 2 units up
(e)S(4, 16), T(10, 20), U(12, 12), and V(10, 10)
No suitable transformation is found from JKLM to STUV.
Diane has $12 to spend on a mixture of green and red grapes. What equation can she use to graph a line showing the different amounts of green and red grapes she can buy for $12. Green grapes cost $3/lb and red grapes cost $2/lb.
Answers
Answer:
y ≥ [tex]\frac{3}{2}[/tex]x + 6
Step-by-step explanation:
12 ≥ 3x + 2y
Money available ≥ cost of green grapes + cost of red grapes
To turn this into slope-intercept form,
12 ≥ 3x + 2y
2y ≥ -3x + 12
y ≥ [tex]\frac{3}{2}[/tex]x + 6
Graphed - see attached
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
which expression is equivalent to 1/2b-15
Answers
Answer:
b/2-15
or
-15+1/2b
or
b:2-15
Step-by-step explanation:
which expression is equivalent to 1/2b-15
b/2-15
or
-15+1/2b
or
b:2-15
HELPP ME OOOO ???
Jendbshshshsbbsbdbsnsmznbs slaizgnsmshxfs sucks skzgxs smudge nzjzdcd
Answers
Answer:
5 = k2
k = 2.5
happy learning
A manager that owns 3 local area car maintenance garages was researching certifications of mechanics that worked for her company. consider the following Venn Diagram.
1.How many mechanics work for her company
2.How many are certified to do work on brakes
3.How many are certified by ASE to do work on brakes **and** tune-ups?
Answers
Answer:
B. 1/2
Step-by-step explanation:
In the picture attached, the Venn diagram is shown
amount of ASE certified brakes mechanics: 4+2+2+1 = 9
amount of mechanics: 4+2+2+1+3+3+3 = 18
The probability that a randomly selected mechanic is ASE certified to work on brakes: 9/18 = 1/2
Can someone please help me!!
Q; write the sentence as an equation. 251 is equal to 130 added to q
Answers
Answer:
251 = 130 + q
This is d equation
Answer:
251 = q + 130
Step-by-step explanation:
251 is equal to 130 added to q,
→ 251 = q + 130
Let's solve the equation,
→ 251 = q + 130
→ q = 251 - 130
→ [ q = 121 ]
So, the answer is 121.
Please help ME for brainliest.
Answers
Answer:
-1.2y + -4.2y = -3.78
y is directly proportional to ( x - 4 ) . When x = 16, y = 3. Find y in terms of x.
Answers
ANSWER ASAP WILL AWARD BRAINLIEST
Answers
Answer:
18/5 + −8/5√3 (as a decimal: 0.828719)
which value is equivalent to 30 + 9 divided by (6 - 3) A) 13 B)30 C(32 D)33
Answers
Answer:
13
Step-by-step explanation:
30 plus 9 is 39
6 minus 3 is 3
39 divided by 3 is 13
Answer:
the answer is D 33
Step-by-step explanation:
I NEED THIS ANWER (WILL GIVE BRAILIEST TO CERRECT)
Answers
Answer: I got 60d+115f
Step-by-step explanation:
Hope this helps.
Answer:
60d+115f
Step-by-step explanation:
if you were basically asking to simplify then this is your answer
1) 6 hats cost $67.50
What's the cost per hat?
Answers
The answer is $11.25 Just divide $67.50 by 6
Noah has 3 meters of rope. How many 3/4 meter pieces of rope can he cut from it?
Answers
Answer:
4
Step-by-step explanation:
3/(3/4)=4
the bulk juice outlet charges $4 for a quart of any organic juice. using this information, fill in the prices for different volumes of juice.
Answers
Answer: 8 for 1/2 gallon, 16 for a gallon
Step-by-step explanation:
I WILL GIVE BRAINLIEST
Answers
Answer:
3. 7
4. 22
Step-by-step explanation:
What divided by two equals 5? Ten! Then, what plus three equals 10? Seven!
17 + 5 (2 · 22 - 9) = (-6 · 22 + 10) +4 is true!
I hope that this helps!
Answer:
x = 7 and x = [tex]\frac{21}{8}[/tex]
Step-by-step explanation:
(3)
[tex]\frac{x+3}{2}[/tex] = 5 ( multiply both sides by 2 to clear the fraction )
x + 3 = 10 ( subtract 3 from both sides )
x = 7
-----------------------------------------------------------
(4)
17 + 5(2x - 9) = - 6x + 10 + 4 ← distribute parenthesis on left side and simplify
17 + 10x - 45 = - 6x + 14
10x - 28 = - 6x + 14 ( add 6x to both sides )
16x - 28 = 14 ( add 28 to both sides )
16x = 42 ( divide both sides by 16 )
x = [tex]\frac{42}{16}[/tex] = [tex]\frac{21}{8}[/tex]
What is the slope of this graph?
Answers
Answer:
-3
Step-by-step explanation:
1. To find the slope of this line, we can use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] since we're given the two points from the line.
2. (Solving)
[tex]\frac{0-6}{3-1}[/tex] [tex]\frac{-6}{2}[/tex] [tex]-3[/tex]Therefore, the slope is -3.