HELP ASAP PLEASE (20 points)
An open-topped box is to be created from a 100 cm by 80 cm piece of cardboard by cutting out a square of side length x from each corner.
a) Write an expression for the volume of the box in terms of x.
b) Write an expression for the surface area of the open-topped box in terms of x.
c) Write a simplified expression of the ratio of the volume of the box to the surface area.
d) Refer to your answer in part (c). State the restrictions on x
Answers
a) Volume = x(100 - 2x)(80 - 2x).
b) Surface Area = (100 - 2x)(80 - 2x) + 4x(100 - 2x) + 4x(80 - 2x).
c) Ratio = x(100 - 2x)(80 - 2x) / [(100 - 2x)(80 - 2x) + 4x(100 - 2x) + 4x(80 - 2x)].
d) Restrictions: 0 < x ≤ 40 and x < 50. (Positive dimensions, non-zero volume, and avoiding non-physical dimensions)
a) The box will have a height of x and a base of (100 - 2x) cm by (80 - 2x) cm.
Thus, the expression for the volume of the box in terms of x is:
Volume = x × (100 - 2x) × (80 - 2x)
b) To find the surface area of the open-topped box,
consider the area of the bottom (100 - 2x) × (80 - 2x) and the four sides.
The sides have a width of x and a length of 100 - 2x or 80 - 2x, so the surface area expression is:
Surface Area = (100 - 2x) × (80 - 2x) + 4x × (100 - 2x) + 4x × (80 - 2x)
c) To find the ratio of the volume to the surface area,
divide the volume expression by the surface area expression:
Ratio = Volume / Surface Area
Ratio = [x × (100 - 2x) × (80 - 2x)] / [(100 - 2x)× (80 - 2x) + 4x × (100 - 2x) + 4x ×(80 - 2x)]
d) To identify restrictions on x, consider practical aspects of the box.
The value of x must be positive since we're cutting squares from the corners.
Also, the value of x cannot exceed half the length of the sides
(100/2 = 50 and 80/2 = 40)
because if x is greater than half, then the box will have a negative or zero dimension, which is not meaningful. So, the restrictions are:
0 < x ≤ 40 (to ensure positive dimensions and non-zero volume)
x < 50 (to avoid non-physical dimensions)
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Related Questions
Which graph represents the proportional relationship given by the rule "y is 3 times the value of x"?
Please answer fast less than 5 min
Answers
Answer:
The fourth graph i.e. RIGHT BOTTOM GRAPH is correct which represents the proportional relationship given by the rule y = 3x.
Also, the correct graph is attached below.
Step-by-step explanation:
Given the rule
''y is 3 times the value of x".
It means
y = 3x
comparing with the slope-intercept form of the line equation
y = mx+b
where y is the slope and b is the intercept
so,
The slope of y = 3x will be: m = 3
The y-intercept of y = 3x will be: b = 0
CHECKING THE 4TH GRAPH (THE RIGHT BOTTOM SIDE)
Taking two points
(0, 0)
(2, 6)
Finding the slope between (0, 0) and (2, 6)
Using the formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
= [6 - 0] / [2 - 0]
= 6 / 2
= 3
Thus, the slope of the line = m = 3
We know that the value of y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
From the graph, it is clear
at x = 0, y = 0
Thus, the y-intercept b = 0
Now, substituting m = 3 and b = 0 in the slope-intercept form of linear function
y = mx+b
y = 3x+0
y = 3x
Therefore, the fourth graph i.e. RIGHT BOTTOM GRAPH is correct which represents the proportional relationship given by the rule y = 3x.
Also, the correct graph is attached below.
Answer:
It's the bottom right graph.
Step-by-step explanation:
From 145 pounds to 132 pounds *
Percent decrease
Answers
Answer:
9%
Step-by-step explanation:
Jshhshahshahahhwhahahahwhahahahhashshhswhshshhshshsbshsh
Beth adopted a kitten from the animal shelter. The adoption fee was $150. She also bought 4 bags of cat food on the way home. The total amount she spent was $185.84. What was the price for each bag of cat food
Answers
Answer:
$8.96
Step-by-step explanation:
total amount spent minus adoption fee is $35.84
divide this by the number of bags which is 4, your answer is $8.96
how much does a car weigh in ounces
Answers
Answer:
52 19271122222211111
Step-by-step explanation:
6+1=10
what is 8029 times 89810
Answers
Answer:
721084490
Step-by-step explanation:
If 4/7 = 12 /? , then ? =
a) 7
b) 14
c) 21
d) 28
Answers
Answer:
21
Step-by-step explanation:
Multiply by 3 and find out.
calculate the rate of change
Answers
Help pls 6th grade math i will give brainliest
Answers
Answer:
G because y+y+y is the exact same as 3 y
Find the domain and range of the function {(1,2) , (2,2) , (3,2) , (4,2)}
Answers
Answer:
Step-by-step explanation:
X-coordinates are domain and y-coordinates are range
Domain= {1,2,3,4}
Range= {2}
Answer:
domain: 1,2,3,4. range:2
Step-by-step explanation:
domain is the input aka the x- values, and the range is the output aka the y-values
Find the inverse if f(x)=6(x+7)
Answers
Answer:
y=1/6 x -7
Step-by-step explanation:
it's easier to just substitute y w/x, and vice versa
x=6y+42
x-42=6y
Please help me on these 4 !
Answers
When you plug (x,y) in answer choice A-C you do not get the right sum.
Choose all the problems that you will solve by regrouping. A. 65 – 56 = ? B. 28 – 15= ? C. 16 – 6 = ? D. 74 – 38 = ?
Answers
Answer:
(a) and (d) will be done by regrouping
Step-by-step explanation:
Solution will be done by regrouping if unit term of term which is subtracted is greater then the term which subtracts.
(a) 65 -56, since the unit term of 65 is 5 and of 56 is 6
as the unit terms of 56 is greater than unit term of 65
Thus solution will be done by regrouping
⇒ 65 -56 = 9
(b) 28 -15, since the unit term of 28 is 8 and of 15 is 5
as the unit terms of 28 is greater than unit term of 15
Thus solution will not be done by regrouping
⇒ 28 -15 = 13
(c) 16 -6, since the unit term of 16 is 6 and of 6 is 6
as the unit terms of 16 is equal to unit term of 6
Thus solution will not be done by regrouping
⇒ 16 -6 = 10
(d) 74-38 , since the unit term of 74 is 4 and of 38 is 8
as the unit terms of 38 is greater than unit term of 74
Thus solution will be done by regrouping
⇒ 74-38 = 36
What is b for x^2 -6x-3=0
Answers
Answer:
x = 3 + 2 sqrt3 Or 3 - 2 sqrt 3
Step-by-step explanation:
Jamie bought a handbag for 20$, an umbrella for $5.99, and a scarf for $8.50. If the sales tax rate is 7% how much is the sales tax and the total cost of her purchase
Answers
Answer: $36.9043
Step-by-step explanation:
Given that :
Cost of handbag = $20
Cost of umbrella = $5.99
Cost of scarf = $8.50
Sales tax = 7% = 0.07
Sales tax = 0.07 * (20 + 5.99 + 8.50)
Sales tax = 0.07 * 34.49
Sales tax = $2.4143
Total cost of purchase :
Sales tax + cost of items
$2.4143 + $34.49
= $36.9043
1. f(x) = 4x + 3x3
Is this a monomial,Binomial, or Trinomial
Answers
Answer:
It is a monomial
Step-by-step explanation:
4x+3x3=4x+9.
There is one variable the first power so therefore, it is a monomial.
A 22 inch TV costs $140.
It is on sale for 20% off.
How much will you save?
Answers
Answer:28 dollar
Step-by-step explanation: 140 x (20/100)= 28 dollar
140-28= 112 the price after the sale
Answer: you will save $28.
Step-by-step explanation:
To find a percent of a number you have to turn the percent into a decimal. For example you would turn 20% into 0.20 then multiply this by 140. After doing this you will find out that 20% of 140 is 28.
Hope this helps ;)
Jonathan bought a box of stamps to start a collection. He has purchased the same number of stamps each week to add to the collection. The graph
shows the number of stamps Jonathan has at the end of each week. How many stamps were in the box Jonathan bought to start his collection?
Assume that the relationship between the two quantities is linear.
A. 216
B. 120
C. 96
D. 12
Answers
Answer:
120
Step-by-step explanation:
its where the graph starts
can anyone help as soon as possible?
Answers
Answer:
The answer is C; x^4y^12z^16
What is the slope of the line?
4x -1 = 3y + 5
Choose 1 answer:
Answers
Answer:
The slope is 4/3
Step-by-step explanation:
Answer:
4/3
Step-by-step explanation:
rearrange into slope-intercept form
3y=4x-6
y=4/3x-2
Please help me with this math problem if you can. You just say yes or no if it’s a square, rectangle, etc. and then give the reason why
Answers
Answer:
Step-by-step explanation:
B) rectangle because the diagonals are congruent
C) Diamond so no it isn't a square or rectangle due to no 90 degree angles
D)Square because the diagonals are perpendicular and congruent
bac
4. Jim has the following cell phone plan.
• Weekday calls cost 10 cents per minute.
• Weekend calls are free.
• Each text message costs 5 cents.
Each month, Jim talks for m minutes on weekdays and f minutes
on weekends, and sends t texts. Which equation represents
Jim's monthly cell phone bill, C?
A.
C = 0.10m - 0.051
B.
C = 0.10m - 0.5t
nents
C.
C = 0.10m - 0.10f-0.10
D
('= 0.10m - f-0.057
Answers
a cell phone company charges one $20 for the phone and then $35 a month for phone service another cell phone company charges 55 a month for phone service with a free phone after how many months will the phone services cost the same
Answers
20 + 35x = 0 + 55x
Find the value of X!!!!!!!!
Answers
what is the ratio of y to x
Answers
Answer:
5:2
Step-by-step explanation:
Sorry this is non related to math, but how can you message someone it’s not letting me !!
Answers
Answer: click on their profile and send a message from those settings^^
Step-by-step explanation:
-7w²+2w if w=-4 i need the answer please!!!!!!!!!!!!!!
Answers
Answer:
-6,272
Step-by-step explanation:
-7 times -4 equals 28
28 to the power of 2 is 784
2 times -4 equals -8
-8 times 784 equals -6,272
What’s 1+1 I am so confused I am in middle school and this is the hardest question 10 points if u get it right lol
Answers
Answer:
It depends how you were taught. You could say it's 11 (eleven) or 2.
Answer:
I think 2 lol
Step-by-step explanation:
The image of the point (-8, 3) under a translation is (-5,2). Find the coordinates
of the image of the point (9,9) under the same translation.
Answers
Answer:
IMAGE=OBJECT +TRANSLATION
The coordinates are (12, 8).
What is translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions. Since it is just moving of the shape from one place to other, there is no change in the shape.
Translation is one of the transformations in math. When a shape has been transformed, the original shape is called the preimage and the vertices are usually labeled using uppercase letters (Example: ABCD). The translated shape is called the image and the vertices are labeled using uppercase letters with a “prime” next to each (Example: A′B′C′D′, and is pronounced “A-prime, B-prime, C-prime, D-prime”).
Given:
the point is (-8, 3) whose image point is (-5, 2)
The difference between the coordinates of the image and the coordinates of the original is the same for both points.
X - (9, 9) = (-5, 2) -(-8, 3)
X = (-5, 2) -(-8, 3) +(9, 9) = (-5+8+9, 2-3+9)
X = (12, 8)
Hence, the point is (12, 8)
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The region R, shown shaded in the diagram, is bounded by four straight lines.
Write down the inequalities that define R.
for some reason i can’t remember how to do this (might be because i’m tired but i’m on my last homework question), can anyone help?
Answers
9514 1404 393
Answer:
1 ≤ y ≤ 30 ≤ x ≤ 2Step-by-step explanation:
The boundaries in the vertical direction are the horizontal lines ...
y = 3 (top boundary)
y = 1 (bottom boundary)
The shaded region is between these lines, so y has values described by ...
1 ≤ y ≤ 3
__
The boundaries in the horizontal direction are the vertical lines ...
x = 0 (left boundary)
x = 2 (right boundary)
The shaded region is between these lines, so x has values ...
0 ≤ x ≤ 2
These are your inequalities.
_____
If you're plotting this on Desmos, you can use the relation ...
max(abs(x-1), abs(y-2)) ≤ 1
A square picture has a border 5 cm
wide. The picture area is 4/9 of the total
area. Find the area of the picture.
Answers
Answer:
So area of square is: a^2
5^2=25cm^2
4/9 x 25 = 100/9
Area of picture is: 11.11 cm^2
Step-by-step explanation:
The area of the square will be equal to 11.11 square centimetres.
What is an area?
The space covered by the two-dimensional object on a plane is called as an area. The space covered by the square in a two-dimensional plane is called the area of the square.
The square is a quadrilateral having four sides and all the sides of the square are equal to each other.
The the area of the square is calculated as,
a² = 5²=25 cm²
The picture area is 4/9 of the total
area.
4/9 x 25 = 100/9
The area of the picture is: 11.11 cm²
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