Jeremy wants to construct an open box from an 18-inch square piece of aluminum. He plans to cut equal squares, with sides of x inches, from each
corner and then fold each side up to form the box. If Jeremy wants the volume of the box to be 432 cubic inches, what should the minimum length
of the sides of the squares cut from each corner be? Find the volume of the box as a function of x. Given: V = length x width x height
Answers
a.
The volume of the box V = 4x³ - 72x² + 324x
Since the dimensions of the square piece of paper are 18 inches each, and we cut out a length x from each side to give a total length of 2x cut from each side. So, each dimension is L = 18 - 2x.
Since the height of the open box is x and its base is a square, the volume of the open box ix V = L²x
= (18 - 2x)²x
= (324 - 72x + 4x²)x
= 324x - 72x² + 4x³
The volume of the box V = 4x³ - 72x² + 324x
b.
The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.
the length of the box, L = 12 inches, the width of the box = 12 inches and the height of the box, x = 3 inches.Since the volume of the box is 432 cubic inches,
V = 324x - 72x² + 4x³
324x - 72x² + 4x³ = 432
4x³ - 72x² + 324x - 432 = 0
x³ - 18x² + 81x - 108 = 0
A factor of the expression is x - 3
So, x³ - 18x² + 81x - 108 ÷ x - 3 = x² - 15x + 36
So, x³ - 18x² + 81x - 108 = (x² - 15x + 36)(x - 3) = 0
Factorizing the expression x² - 15x + 36 = 0
x² - 3x - 12x + 36 = 0
x(x - 3) - 12(x - 3) = 0
(x - 3)(x - 12) = 0
So, x³ - 18x² + 81x - 108 = (x - 3)(x - 3)(x - 12) = 0
So, (x - 3)²(x - 12) = 0
(x - 3)² = 0 and (x - 12) = 0
x - 3 = √0 and x - 12 = 0
x - 3 = 0 and x - 12 = 0
x = 3 twice and x = 12
Since x = 3 is the minimum value, the minimum value of x = 3.
Since the length of the box, L = 18 - 2x
= 18 - 2(3)
= 18 - 6
= 12 inches
The width of the box = L = 12 inches
The height of the box = x = 3 inches.
So,
The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.
the length of the box, L = 12 inches, the width of the box = 12 inches and the height of the box, x = 3 inches.Learn more about volume of a box here:
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Related Questions
Which of the following is the most direct first step in solving the system of equations be-
low using the elimination method?
x + y = 4
2x - y = 2
That is, which of the following would be the first step in a method that would require the
fewest number of steps?
A
multiplying the second equation by -2
B
adding the two equations together
С
multiplying the first equation by -2
D
multiplying both equations by 2
Answers
Step-by-step explanation:
Multiply each equation by a suitable number so that the two equations have the same leading coefficient. Step 2: Subtract the second equation from the first. Step 3: Solve this new equation for y. Step 4: Substitute y = 2 into either Equation 1 or Equation 2 above and solve for x.
What is the factored form of 1,458,43 – 2?
Answers
Answer:
Factors of 1458 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486, 729, 1458. There are 14 integers that are factors of 1458. The biggest factor of 1458 is 1458. Positive integers that divides 1458 without a remainder are listed below.
PLEASE HELP ASAP ON THESE TWO QUESTIONS BLESS YOUR HEART IF YOU HELP ME 9) Look for two points and find the sloope.
10) Plot the given points and find the slope.
Answers
Answer:
the two points are (-3,-3
Step-by-step explanation:
You must first check if the line is a straight line two the you check the intersection of the two points and the write it
complete the table
x - 2 7 10
y - 30 36
Answers
Answer:
x-15
y 42
Step-by-step explanation:
m% of a number equals n. can you find the number?
Answers
Answer:
mn/100
Step-by-step explanation:
m/100 * n = number = mn/100
Assuming m and n are variables with no values.
HElp ASAP
A cement truck mixes 1 part cement
with 4 parts sand. If 2.5 cubic yards of
cement are used, how much sand is
needed for the mixture?
a. 6.25 cubic yards
b. 7.5 cubic yards
c. 10 cubic yards
d. 12.5 cubic yards
Answers
Answer: The answer is already there
Step-by-step explanation:
Suppose triangle ABC is similar to triangle
PQR with AB:PQ = 5:9
What is the ratio of the area of ABC to PQR?
Answers
Answer:
[tex]( \frac{5}{9} ) ^{2} = \frac{25}{81} [/tex]
Can someone please help me out with this its really urgent Ill mark brainliest
Answers
Answer:
smart dot company c=.50t+12
communication plus c=2.50t
Step-by-step explanation:
smart dot has the starting point of $12 per month already so that would be your y-intercept with the equation being y=mx+b , y being the cost m being the amount of money per hour, x being the time spent, and b being the starting cost.
So with that smart dot would be c=.50t+12
with communication plus not having that starting point it would just be c=2.50t
The local time in Singapore is 7 hours ahead of the local time in London. A flight to London leaves Singapore at 0300 local time .
Flight takes 12hours and 45 minutes .What is the local time in London when it arrives?
Answers
Answer:
I think its 8.45am if they are asking when it arrived in londonThe function c(n) below relates the number of bushels of apples picked at a pic-your-own orchard to find cost for the apples it takes as input the number bushels of apples picked after paying an entry fee to an orchard and it returns as output the cost of the apples (in dollars) c(n)=15n+30
Answers
Answer:
C(n) = 20n + 15
y = 20n + 15
20n = y - 15
n = (y - 15)/20
N(c) = (c-15)/20
Step-by-step explanation:
Answer:
N(c)= c-30/ 15
What is the perimeter of the following figure
Answers
Answer:
13
Step-by-step explanation:
7 cm +1 cm +2cm +2cm :12cm
What is the result of substituting for y in the bottom equation?
y=x-7
y=2+2x-4
Answers
Answer:
Plug x-7 in for y, in the bottom equation.
x - 7 = 2 + 2x - 4
x - 7 = 2x - 2
x = 2x + 5
-x = 5
x = -5
Parker is planning to build a playhouse for his sister.The scale model below gives the reduced measures for width and height. The width of the playhouse is 22 centimeters and the height is 10 centimeters. Not drawn to scale The yard space is large enough to have a playhouse that has a width of 3.5 meters. If Parker wants to keep the playhouse in proportion to the model, what cross multiplication of the proportion should he use to find the height
Answers
Answer:
[tex]10 \times 3.5 = 22x[/tex]
Step-by-step explanation:
It is given that:
Parker wishes to construct a [tex]\text{playhouse}[/tex] for his sister. The width and the height of the house is not scaled to the yard space.
So the width of the play house = 22 centimeters
The height of the play house = 10 centimeters
Bu the space in the [tex]\text{yard is large}[/tex] enough that a play house can be constructed so that it have a width of [tex]3.5[/tex] meters.
So the cross multiplication of the proportion that parker uses to find the height of the playhouse is given by : [tex]10 \times 3.5 = 22x[/tex]
Answer:
The answer is C, (10) (3.5) = 22 x
Hope this helped!
P. S. : Can I get brainliest please?
Find the value of 3w-10 given that -11w-4=7.
Simplify your answer as much as possible.
Answers
Answer:
-13
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
-11w - 4 = 7
3w - 10
Step 2: Solve for w
[Addition Property of Equality] Add 4 on both sides: -11w = 11[Division Property of Equality] Divide -11 on both sides: w = -1Step 3: Evaluate
Substitute in w: 3(-1) - 10Multiply: -3 - 10Subtract: -13Complete each statement. If the triangles cannot be shown to be congruent from the information given, leave the triangles name blank and write Cannot Be Determined (CNBD) in the spot for rule. ∆SAT ≅ ∆_____ By _____
Answers
Answer:
The answer is "[tex]\bold{\Delta LAW \cong \Delta WKL}[/tex]. By applying the ASA congruence postulate rule".
Step-by-step explanation:
[tex]\Delta LAW\ and\ \Delta WKL\\\\AW\perp WL\ and \ WL\perp KL\\\\\angle AWL = \angle WLK .......[each \ 90^{\circ}]\\\\WL=WL.......\ [Reflexive \ property]\\\\\angle ALW = \angle KWL........\text{give in picture}\\\\[/tex]
[tex]\therefore,[/tex] by ASA postulate of congruence
[tex]\Delta LAW \cong \Delta WKL\\\\[/tex]
The ASA postulate states that when two angles on the included side with one triangle were congruent to two angles on the included side of the second triangle, then the triangles are said to have been congruent.
Use prime factor decomposition, to find the HCF of 90 and 210!
Answers
Answer:
30
Step-by-step explanation:
90 = 2 × 3^2 × 5
210 = 2 × 3 × 5 × 7
HCF = 2 × 3 × 5 = 30
The distance between points A(0,1) and B(x, 4) is p
34. Find the x coordinate for point B.
Answers
Answer:
X = (P^2 - 9) ^ 1/2
Step-by-step explanation:
P^2 = (4 - 1)^2+ (0 -X)^1/2
I need help please I don't understand
Answers
Answer:
57.2
Step-by-step explanation:
This is a right triangle so we can use trig ratios.
We are asked to find a side when we know a angle adjacent to that side. And we are given a side opposite of that angle. We can use Tangent to find the side length.
[tex] \tan(40) = \frac{48}{x} [/tex]
Take the reciprocal of both sides.
[tex] \frac{1}{ \tan( 40) ) } = \frac{x}{ 48} [/tex]
Multiply both sides by 48.
[tex] x = \frac{1}{ \tan(40) } \times 48[/tex]
[tex]x = 57.2[/tex]
Match the range of the function f(x) = x2 + 2x − 1 to its domain.
2 -2 3 -3
2 --
14 --
7 --
-1 --
Answers
Answer: (2,7) (-2,-9) (3,11) (-3,-13)
Step-by-step explanation:
(2)(2)+(2)(2)-1 = 7
(2) (-2)+(2)(-2)-1 = -9
(3)(2)+(2)(3)-1 = 11
(-3)(2)+(2)(-3)-1 = -13
A shopkeeper marks his goods 25% above the cost price and gives discount of 10% on the marked price white gain percent make
Answers
answer is 6.3
I've had this question before
how do i solve this??
Answers
Answer:
10q^2+3q
Step-by-step explanation:
All you have to do is combine like terms I think
(I haven't done this stuff in ages so I'm most likely wrong)
Answer:
10q^2+3q
Step-by-step explanation:
2q^2 +3q +8q^2
Combine like terms
10q^2+3q
The diameter of your bicycle wheel is 25 inches. How far will you move in one turn of your
wheel?
a) 25 in
b) 78.5 in
c) 250 in
d) 246.49 in
e) 50 in
Answers
Answer:
b) 78.5
Step-by-step explanation:
distance you will move = circumference of wheel = πd = π(25) = 78.53981
NEED HELP ASAP!!!!!!
Performance Task Vector Operations
e) Draw u + 3v – 1/2w
Answers
Answer:
(2, -6)
Step-by-step explanation:
u = (5, 0)
v = (-2, -1)
w = (-6, 6)
(5, 0) + 3(-2, -1) - 1/2(-6, 6)
= (5, 0) + (-6, -3) + (3, -3)
= (2, -6)
if you can type 55 words in 20 seconds how long would it take to type 1,007 words
Answers
Answer:
2769.25Secound...........
Drag the cards to create a number that matches these rules.
The number ends in the hundredths place.
6 is the nearest one when rounding.
9, 4, (.)decimal point, 5
Answers
Answer:
0.459
Step-by-step explanation:
O.459 will round to 0.46 which meets the question's criteria.
Please find the value of A,B,C&D
Answers
Given
A + B = 8
A + C = 13
B + D = 8
C - D = 6
Now
A + B = B + D
A = B + D -B
A = D
C - D = C - A
A + C = 13
C - A = 6
Adding 7 on both sides
C - A +7 = 6+7
C - A + 7 = A + C
C-C -A + 7 = A
-A +7 = A
7 = A+A
7/2 = A
A = 3.5
B = 4.5
C =9.5
D = 3.5
Answered by Gauthmath must click thanks and mark brainliest
Which statement best describes how to determine whether f(x) = x2 - x + 8 is an even function?
CU
O Determine whether –x2 - (-x) + 8 is equivalent to x2 – X + 8.
Determine whether (-x)2 – (-x) + 8 is equivalent to x2 – X + 8.
O Determine whether -x2 - (-x) + 8 is equivalent to -(x2 - X + 8).
O Determine whether (-x)2 – (-x) + 8 is equivalent to -(x2 – X + 8).
THIS IS 60 POINTS BTW
Answers
Answer:
2nd option
Step-by-step explanation:
If f(x) is an even function , then
f(x) = f(- x)
f(x) = x² - x + 8
f(- x) = (- x)² - (- x) + 8 = x² + x + 8
Since f(x) ≠ f(- x) then f(x) is not an even function
line r passes through on the same spot on the y axis as line z and also passes through the point (1,4). If the equation for line z is y= -2x + 3, what is the equation of line r
Answers
Answer:
r= x + 3
Step-by-step explanation:
They share the same y intercept so we can know the vertical shift up. The Y intercept of line z would be 3, so line r would share the intercept too. From this we can find that the slope would be one since moving one unit to the right also makes the equation go 1 unit up, from (0,3) to (1,4). This would mean that the equation of line r is r= x + 3
What the equation for the slope intersection for the graph tue picture that showing ?
Answers
Answer:
Y = -5X +-1
Step-by-step explanation:
x1 y1 x2 y2
-1 4 1 -6
(Y2-Y1) (-6)-(4)= -10 ΔY -10
(X2-X1) (1)-(-1)= 2 ΔX 2
slope= -5
B= -1
Y =-5X +-1
find the length of one side of a regular hexagon if its perimeter is 24 x+48
A. 3x+3
B. 6x+12
C. 4x+8
D. 8x+16
Answers
Answer:
C ) 4 x + 8
Step-by-step explanation:
( 24 x + 48 ) / 6
4 x + 48
The length of a regular hexagon is:
4x ₊ 8
How many sides do a hexagon have? How do we calculate the length and parameter of it?
A regular hexagon have six sides.
The area of a regular hexagon can be calculated using the formula (33 s2)/2, where s is the side length. The lengths of all six sides of a hexagon can be added to determine its perimeter. Perimeter = 6 s, where s is the length of one side, is the formula used to determine the size of a regular hexagon.
Solution:
Given,
parameter of a hexagon = 24x ₊ 48
length of one side of a hexagon s = p ÷ 6
s = 24x ₊ 48 ÷6
s = 4x ₊ 8
Hence we get the length of one side as 4x ₊ 8
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