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
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:
https://brainly.com/question/13309609
easy one for you folks. show work.
who ate more?
Answer:
regan ate more than maggie
The average rate of population decline between 2004 and 2014 is 1.45 thousand deer per year. If the population continued to decline at this rate, in which year would the population have reached 225 thousand deer? Explain your reasoning.
Answer:
in 155 years it would reach 225 thousand deer
Step-by-step explanation:
PLEASE HELP FOR BRAINLIST!!!!!!!!!
Answer: B, or 824(1.03)^n-1
824 is the base we are starting off with, and when you multiply something by 1.03, the product will be +3% of the original number :)
Hope this helps!
if p(q) = q^2 4q- 12 then what is p(-1)
Jesse collected 42 football cards and 28 baseball cards. Simplify the ratio of baseball cards to football cards in his collection
Answer:
3:2
Step-by-step explanation:
42:28
21:14
3:2
Is the relationship for Olivia’s puppy’s weight in terms of time linear or nonlinear? Explain your response.
Answer:
Olivia's puppy is linear i know this because after applying to the graph i got a straight line.
Step-by-step explanation:
Answer:
When looking at the table you can see that for every increase of 1 in the x value it results in an increase of 1 in the y value. The rate of change is constant.
Rate of change is calculated by the change in y/change in x
For the points (1,2), (3,3) and (5,4) the rate of change calculation would be as follows:
(1, 2)(3, 3)
3-2 / 3-1= 1/2
(3, 3)(5, 4)
4-3 / 5-3= 1/2
Since both equal 1/2 the rate of change is constant therefore making it linear.
Step-by-step explanation:
what is the theoretical of flipping a coin and it lands on heads
Answer:
50/50
Step-by-step explanation:
Im not completly sure but when flipping a coin there is only two sides so theoretically if you are flipping a coin there is a 50/50 percent chance you will get heads
A rectangle has a length of 4 mm has an area is 44 mm² width of the rectangle is
Answer:
11
Step-by-step explanation:
The formula for area is l * w = a (length * width = area)
4 is our length, and 44 is the area, so the equation turns to this:
4 * x = 44
To solve for x, just divide 44 by 4.
44 / 4 = 11.
Now we enter that into our equation so it looks like this:
4 mm * 11 mm = 44 mm^2.
Hope this helped :)
Help help help math
Answer:
C ≈ 54
Step-by-step explanation:
The circumference (C) is calculated as
C = πd ( d is the diameter )
Here d = 18 , then
C = π × 18 ≈ 3 × 18 = 54
Find the 12th term of the following geometric sequence.
10, 30, 90, 270
Answer:
1,771,470
Explanation:
10(3^n-1)
Use the distributive property to remove the parentheses.
3(6-y)
Answer:
18-3y.
Step-by-step explanation:
3 x 6 = 18
3 x -1y= -3y.
Answer:
18 - 3y
Step-by-step explanation:
3(6-y)
(3)(6) + (3)(-y)
18 + (-3y)
18 - 3y
x/4-6=10 PLEASE HELP I NEED HELP ASAP
[tex]\huge \bf༆ Answer ༄[/tex]
Here's the solution ~
[tex] \sf \dfrac{x}{4} - 6 = 10[/tex][tex] \sf \dfrac{x}{4} = 10 + 6[/tex][tex] \sf \dfrac{x}{4} = 16[/tex][tex] \sf x = 16 \times 4[/tex][tex] \sf x = 64[/tex]Value of x is 64
NO LINKS AND NO WEBSITES I really need help with this, and also if it's Substitution or linear combination.
x = -2
3x + y = 8
\sqrt{7+\sqrt{2+\sqrt{x+1} } } =3
First make note of the domain of the left hand side.
• √(x + 1) is defined for x + 1 ≥ 0, or x ≥ -1.
• √(2 + √(x + 1)) is defined for 2 + √(x + 1) ≥ 0. If x ≥ -1, then this condition is satisfied.
• √(7 + √(2 + √(x + 1))) is defined for 7 + √(2 + √(x + 1)) ≥ 0. This condition is also satisified automatically if x ≥ -1.
Now solve the equation. Taking the square of both sides of
√(7 + √(2 + √(x + 1))) = 3
yields
7 + √(2 + √(x + 1)) = 3² = 9
√(2 + √(x + 1)) = 2
Squaring both sides again gives
2 + √(x + 1) = 2² = 4
√(x + 1) = 2
And once more,
x + 1 = 2² = 4 ⇒ x = 3
(-9)+5-6+9-(-9)+99-2+50
what does the term ‘slope’ mean?
Answer:
noun
1.
a surface of which one end or side is at a higher level than another; a rising or falling surface.
Step-by-step explanation:
steepness
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x)
step one: identify two points on the line
step two: select one to be (x1,y1) and the other to be (x2,y2)
step three: use the slope equation calulate slope
2x-3=8+7(+3)
2y-3(+3)=8x+7(+3)
2y=8x+10
----- --------
2y=8x+10
y=4x+5
Answer:
m=4
pls help…………. …………………
Answer:
d
Step-by-step explanation:
smallest slope
What fraction goes in the box to make it correct? 5/12×□=1
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\large\boxed{\mathbf {Your\ equation} :\mathsf{\dfrac{5}{12}\times\boxed{} = 1}}[/tex]
[tex]\large\textbf{We don't know the unknown number yet so we will}\\\large\textbf{label it as \boxed{f}}[/tex]
[tex]\large\boxed{\mathsf{\dfrac{5}{12}\times f = 1}}[/tex]
[tex]\large\boxed{\rightarrow\mathsf{\dfrac{5}{12}(f)= 1}}[/tex]
[tex]\large\textbf{MULTIPLY by }\mathbf{\dfrac{12}{5}}\large\textbf{ to BOTH SIDES}[/tex]
[tex]\large\boxed{\mathsf{\dfrac{12}{5}\times\dfrac{5}{12}f = \dfrac{12}{5}\times1}}[/tex]
[tex]\large\textbf{CANCEL out: }\mathbf{\dfrac{12}{5}\times\dfrac{5}{12}}\large\textbf{ because it gives you 1.}[/tex]
[tex]\large\textbf{KEEP: }\mathbf{\dfrac{12}{5}\times1}\large\textbf{ because it helps solve for the f-value.}[/tex]
[tex]\large\boxed{\mathbf{NEW \ EQUATION: }\mathsf{f = 1\times \dfrac{12}{5}}}[/tex]
[tex]\large\textbf{SIMPLIFY IT!}[/tex]
[tex]\huge\boxed{\textbf{Therefore, your answer: \boxed{\mathsf{f = \dfrac{12}{5}}}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \&}\\\huge\textbf{enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
x - 9 = 1/4x + (1/4x + 12) +(1/4x - 3)
Answer:
x=72
Step-by-step explanation:
x-9=3/4 ⋅ x+9
1/4 ⋅ x -9=9
1/4⋅x=18
x=72
Please I need help on this math question?
Plslslslslslsllep
Helppp tyyyyyyyy
[tex](5xy ^{2} {)}^{3} \\ = {5}^{3} \times {x}^{3} \times y ^{2 \times 3} \\ = 125 {x}^{3} {y}^{6} [/tex]
Answer:
[tex]125 {x}^{3} {y}^{6} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
Answer:
125x^3y^6
Step-by-step explanation:
Distribute the 3 exponent on the outside to the 5, x^1 and y^2
5^3 = 125
1 * 3 = 3
2 * 3 = 6
125x^3y^6
Please Help, And Include Explanation. I will Give Brainliest To Best Answer
Answer: what’s the question I would love to help but there’s no question maybe try to post it again and I will see if I can answer?
Answer:
No question so no answer (just getting points i guess)
Step-by-step explanation:
5 friends are sharing 8 pieces of pizza equally.How many pieces will each friend get to eat?
Answer:
8÷5 = 1 . 6
Step-by-step explanation:
They will divide the pizzas into 5 pieces further
A 3 to 1
B 6 to 2
C 7 to 2
D 9 to 3
Answer:
yo what is your question??????
Step-by-step explanation:
Maybe c 7 to 2
Solve for x
10/x+7 = 6
Give your answer as an improper fraction in its simplest form.
Answer:
-16/3
Step-by-step explanation:
i did math
HELPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
thats easy B ur welcome !!!!
Answer:
The answer is B
Step-by-step explanation:
what is the reciprocal of 4/15
Answer:
15/4
Explanation:
To find the reciprocal of a fraction, switch the denominator and the numerator, which will give you the reciprocal of a fraction.
Hoped this helped.
[tex]GeniusUser[/tex]
a number cube is rolled.what is the probability of rolling a number greater than 4
Answer: 2/6
Step-by-step explanation:
There’s only 2 numbers greater than 4 on a die, so two would be the numerator and the denominator would be the number of possibilities you could roll, which is 1-6.
2/6, 1/3, or approx. 33.3%
A number cube will have six sides and two out of six will be greater than four, therefore, there is around a 33.3% chance you will roll a number greater than 4. :)
or Question 5 i:
Harry is planning a holiday for 4 people for 7 days.
Here are the costs for the holiday for each person.
Travel
£150
Hotel
Spending money
£50 for each day
£250
Work out the total cost of the holiday for 4 people for 7 days.
Answer:
the costs for the holiday for each person
£250
Step-by-step explanation:
So ,
£250 × 7 = 1,750