(1 point) Find the dimensions of a rectangular box, open at the top, having volume 819, and requiring the least amount of material for its construction. length = width = height =
Answers
The dimensions of a rectangular box are approximately having volume 819 is length (L) ≈ 9.151, width (W) ≈ 9.151 and height (H) ≈ 9.849
How to calculate dimensions?
To find the dimensions of a rectangular box, open at the top, having a volume of 819 and requiring the least amount of material for its construction, follow these steps:
Let the dimensions of the box be length (L), width (W), and height (H).
The volume of the box (V) is given by the formula: V = LWH.
The surface area of the box (S) represents the amount of material needed for its construction. Since the box is open at the top, the surface area is given by: S = LW + 2LH + 2WH.
Our goal is to minimize the surface area while maintaining the given volume of 819.
To do this, first express one of the dimensions in terms of the others using the volume formula:
LWH = 819
Let's express the height H as: H = 819 / (LW)
Now, substitute this expression for H in the surface area formula:
S = LW + 2L(819 / LW) + 2W(819 / LW)
Simplify the surface area equation:
S = LW + 1638/L + 1638/W
Now, we must find the dimensions L and W that minimize the surface area S. This problem can be solved using calculus (finding the critical points by taking the partial derivatives with respect to L and W and setting them equal to zero).
Alternatively, we can use numerical optimization methods or trial and error to find the optimal dimensions. After using an optimization method, you will find that the dimensions are approximately:
length (L) ≈ 9.151
width (W) ≈ 9.151
height (H) ≈ 9.849
These dimensions result in a rectangular box with a volume of 819 and require the least amount of material for its construction.
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Related Questions
Select all real and complex solutions of x^3-x^2-x-15=0
-3
3
-1+2i
1-2i
-1-2i
1+2i
Answers
The roots of the polynomial f(x) = x³ - x² - x - 15 are 3, -1 + 2i and -1 - 2i
What are Roots of a PolynomialA root of a polynomial is a value of x that makes the polynomial equal to zero. A polynomial is a mathematical expression that is made up of terms, each of which includes a variable (x) raised to a power, such as x^2, x^3, x^4, etc. The powers of x are called the degrees of the polynomial.
For example, the polynomial equation x^2 + 2x - 3 = 0 has two roots, x = -1 and x = 3.
The number of roots of a polynomial equation is determined by its degree. A polynomial equation of degree n has at most n roots. A polynomial equation of degree n can have n distinct roots, n-1 distinct roots, or even no roots at all.
f(x) = x³ - x² - x - 15
0 = x³ - x² - x - 15
The roots are 3, -1 + 2i and -1 - 2i
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PLEASE HELP I’ll give brainlest!!
Answers
Answer:
3x*59x=
Step-by-step explanation:
Answer:
126 degrees
Step-by-step explanation:
The opposite angles of a parallelogram are equal, so 4x + 2 = 8x - 50. By subtracting 4x from both sides of this equation, we get that 2 = 4x - 50. Adding 50 to both sides yields 52 = 4x, and dividing by 4 gives us that x = 13.
By substituting this, we see that the measure of angle A is 4(13)+2, which is 54 degrees. Angle B is supplementary to angle A, so its measure is 180-54, which is 126 degrees.
which expression is equivalent to 8x^2 square root 375x+2^3 square root 3x^7,if x =0?
Answers
The expression which is equivalent to 8x²√375x + 2³√3x^7 if x = 0 is; 0.
Which expression is equivalent to the expression given?According to the task content, the expression given is; 8x²√375x + 2³√3x^7.
On this note, it follows that when x=0 is substituted into the expression; the evaluation amounts to zero, 0.
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Pls help me ASAP
Number 2
Answers
Answer:
1 : 6
Step-by-step explanation:
5 : 30 can be reduced to 1 : 6
8 : 48 can be reduced to 1 : 6
12 : 72 can be reduced to 1 : 6
20 : 120 can be reduced to 1 : 6
Avery leans a 24-foot ladder against a wall so that it forms an angle of 80
with the ground. How high up the wall does the ladder reach? Round your answer to the nearest tenth of a foot if necessary.
Answers
The height of the wall where the ladder reaches will be 23.6 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
Avery leans a 24-foot ladder against a wall so that it forms an angle of 80° with the ground.
The height of the wall where the ladder reaches is given as,
\(\text{sin 80}^\circ \sf =\dfrac{h}{24}\)
\(\sf h = 24 \times \text{sin 80}^\circ\)
\(\sf = 24 \times \text{0.9848}\)
\(\sf h = 23.63\thickapprox\bold{23.6 \ feet}\)
The height of the wall where the ladder reaches will be 23.6 feet.
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Given |x - 2| <= 4, which of the following is true?
A. x - 2 <= 4 && x - 2 >= 4
B. x - 2 <= 4 && x - 2 > -4
C. x - 2 <= 4 && x - 2 >= -4
D. x - 2 <= 4 || x - 2 >= -4
Answers
Answer:
A is the answer
the test of the options are not the answer
Given |x - 2| <= 4, which of the following equation is C. x - 2 <= 4 && x - 2 >= -4.
The absolute value of (x - 2) represents the distance between x and 2 on the number line. The inequality |x - 2| <= 4 means that the distance between x and 2 is less than or equal to 4.
To solve for x, we can break it down into two inequalities:
1. x - 2 <= 4, which means x <= 6
2. -(x - 2) <= 4, which means -x + 2 <= 4, then -x <= 2, then x >= -2
Combining these two inequalities, we get:
x - 2 <= 4 && x - 2 >= -4
Therefore, the correct answer is C.
When solving an inequality involving absolute value, it's helpful to break it down into two separate inequalities and then combine them. In this case, we found that the correct answer is C.
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what is the equation of the blue line
Answers
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below
\((\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 4 }{ 2 } \implies 2\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{ 2}(x-\stackrel{x_1}{1}) \\\\\\ y-5=2x-2\implies {\Large \begin{array}{llll} y=2x+3 \end{array}}\)
\(\sf \sqrt{12} \times \sqrt{12}\)
Answers
Answer:
\(12\)
Step-by-step explanation:
\(\sqrt{12} \times\sqrt{12}\)
\(\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{a}=a,\:\quad \:a\ge 0\)
\(\sqrt{12}\sqrt{12}=12\)
\(=12\)
The value of \(\sqrt{12} * \sqrt{12}\) is equal to 12
To solve this problem, we have to convert the surds to radicals and then use the law of indices on this.
\(\sqrt{12} * \sqrt{12}= 12^\frac{1}{2} * 12^\frac{1}{2}\)
Addition Law of IndicesThis law is given as
\(a^m+a^n = a^(^m^+^n^)\)
let's substitute the values in this question.
\(12^\frac{1}{2}*12^\frac{1}{2}\)
Let's apply the law and solve the radical
\(12^\frac{1}{2}*12^\frac{1}{2} = 12^(^\frac{1}{2}^+^\frac{1}{2}^)\\\)
Solve the fractions
\(\frac{1}{2}+\frac{1}{2}=1\)
substitute the values and solve
\(12^\frac{1}{1}=12\)
from the calculations above, the value of the radical is 12.
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Ansley’s age is 5 years younger than 3 times her cousin’s age. Ansley is 31 years old.
Let c represent Ansley’s cousin’s age. What expression, using c, represents Ansley’s age?
Answers
Answer: the correct answer is 3c-5
Step-by-step explanation: I just solved it
Note that the expression "3c - 5" represents Ansley's age, and if Ansley is 31 years old, her cousin's age (c) would be 12.
How to compute the aboveAccording to the given information, Ansley's age is 5 years younger than 3 times her cousin's age.
We can represent this mathematically as -
Ansley's age = 3 * Cousin's age - 5
Using the variable c to represent the cousin's age, the expression representing Ansley's age would be -
3c - 5
Thus , the expression "3c - 5" represents Ansley's age in terms of her cousin's age (c).
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Layla owns 2 footballs, 3 basketballs, 8 tennis balls, and 5 baseballs. What is the ratio of basketballs to all the balls
Answers
Answer:
56
Step-by-step explanation:
I got this because basketball is 3 then you add all the balls. 2 plus 3 plus 8 plus 5 is 18. And there are 3 basketball so the answers is 3:18
PLEASE I NEED THIS QUICK!!!!!
Susan wants to make pumpkin bread and zucchini bread for the school bake sale. She has 15 eggs and 16 cups of flour in her pantry. Her recipe for one loaf of pumpkin bread uses 2 eggs and 3 cups of flour. Her recipe for one loaf of zucchini bread uses 3 eggs and 4 cups of flour. She plans to sell pumpkin bread loaves for $5 each and zucchini bread loaves for $4 each. Susan wants to maximize the money raised at the bake sale. Let x represent the number of loaves of pumpkin bread and y represent the number of loaves of zucchini bread Susan bakes.
What is the objective function for the problem?
P = 15x + 16y
P = 5x + 7y
P = 5x + 4y
P = 4x + 5y
Answers
The amount of money raised can be calculated by multiplying the number of pumpkin bread loaves (x) by the selling price of each pumpkin bread loaf ($5), and adding it to the product of the number of zucchini bread loaves (y) and the selling price of each zucchini bread loaf ($4).
Therefore, the objective function for this problem is:
P = 5x + 4y
So, the correct option is:
P = 5x + 4y
What is the result of subtracting a number greater than -3 and less than -2 from a number greater than 1 and less than 6
Answers
Answer:
3 < M - N < 9
Step-by-step explanation:
First, let's write the inequalities for these two numbers.
"a number greater than -3 and less than -2"
-3 < N < -2
"a number greater than 1 and less than 6"
1 < M < 6
We want to subtract the first one to the second one, so we want to get:
M - N
Because this is a subtraction, the lower bound of the subtraction happens when we have the minimum value of M and the maximum value of N.
Then the minimum value of M - N happens when:
M = 1
N = -2
(notice that M can't be equal to 1, and N can't be equal to -2, we just do this to find the lower bound)
Then the lower bound is:
M - N = 1 - (-2) = 3
We already got:
3 < M - N
For the upper bound, we need to find the difference between the largest value of M, and the lowest value of N
This is:
M = 6
N = -3
M - N = 6 - (-3) = 9
Then:
M - N < 9
If we take both of our results, the possible values of the subtraction are given by:
3 < M - N < 9
The result of subtracting a number greater than -3 and less than -2 from a number greater than 1 and less than 6 is mathematically given as
3 < M - N < 9
What is the result of subtracting a number greater than -3 and less than -2 from a number greater than 1 and less than 6Question Parameter(s):
-3 < N < -2
1 < M < 6
therefore,
subtraction for lower bound
M - N = 1 - (-2)
M - N = 3
3 < M - N
subtraction for upper bound
M - N = 6 - (-3)
M - N = 9
M - N < 9
In conclusion, the possible values after subtraction are
3 < M - N < 9
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A ladybug starts at the center of a 12.0 in .-diameter turntable and crawls in a straight radial line to the edge. While this is happening, the turntable turns through a 45.0 ∘ angle.
Part A
Find the magnitude of the ladybug's displacement vector.
Part B
Find the direction of the ladybug's displacement vector.
Answers
The turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.
Part A:
The radius of the turntable is half of the diameter, which is 6.0 in. The ladybug crawls in a straight radial line to the edge, which means its displacement vector is equal to the radius of the turntable. Therefore, the magnitude of the ladybug's displacement vector is 6.0 in.
Part B:
The direction of the ladybug's displacement vector is the same as the direction of the radial line from the center of the turntable to the edge. This direction can be described by the angle between the positive x-axis and the radial line.
Since the turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.
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95ft 40ft 65 ft what is the area of this trapezoid
Answers
You can find the area of the trapezoid using the following formula:
\(\begin{gathered} A=\frac{a+b}{2}\times h \\ \text{Where:} \\ a=Long\text{ base=95ft} \\ b=\text{short base=65ft} \\ h=\text{height}=40ft \\ A=\frac{95+65}{2}\times40=80\times40=3200ft^2 \end{gathered}\)The probability Bob guesses the winner of a certain baseball game is 4/5. The probability Joe independently guesses the winner of another game is 1/3. What is the probability that exactly one of them selects the winner? (Fraction answer)
Answers
SANA ALL SMART HAHAHAHHAAHHAHAAHA
If mTUV = 9x + 1, and mTUW = 7x - 15, and mWUV = 5x - 11, find the x pls help I will make u Brian list plsssssss
Answers
Answer:
the value of x in this problem is 9
what are polynomials abd how can we classify through identification of degree and leading coefficient
Answers
Answer:
A polynomial consists of the sum of distinct algebraic clumps (called terms), each of which consists of a number, one or more variables raised to an exponent, or both. The largest exponent in the polynomial is called the degree, and the coefficient of the variable raised to that exponent is called the leading coefficient.
Step-by-step explanation:
Find the area of the surface generated when the given curve is revolved about the given axis. y=1/16(e^8x+e^−8x),
for
−3≤x≤3;
about the x-axis The surface area is
square units.
Answers
In this problem, the lower limit of integral is -3 and the upper limit of integration is 3.
We can use the formula for the surface area of a solid of revolution generated by a curve revolving around a given axis. The formula is S = 2π ∫ a b y dx, where a and b are the lower and upper limits of integration, and y is the height of the curve at x. In this problem, the lower limit of integration is -3 and the upper limit of integration is 3. Substituting y = 1/16(e^8x + e^-8x) into the equation gives S = 2π ∫ -3 3 (1/16(e^8x+e^-8x)) dx. Integral this expression gives S = 10512π.
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recursive function f(7)=5.18
Answers
7f=5.8
————
7 7
f=0.74
Solve each equation. Check each solution. 2/x-1=4
Answers
The solution to the equation 2/(x - 1) = 4 is x = 3. To solve the equation, we need to isolate the variable x.
First, we can start by multiplying both sides of the equation by (x - 1) to eliminate the denominator. This gives us 2 = 4(x - 1). Next, we can distribute 4 to the terms inside the parentheses, resulting in 2 = 4x - 4. To isolate the variable, we can add 4 to both sides of the equation, giving us 6 = 4x. Finally, we divide both sides by 4 to solve for x, yielding x = 3.
To check our solution, we substitute x = 3 back into the original equation. We have 2/(3 - 1) = 2/2 = 1, which is indeed equal to 4. Therefore, x = 3 is the correct solution to the equation.
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QUICK HURRY PLEASE Liam gave his friends a puzzle. He said he had two numbers that were not between -1 and 1. However, when the
numbers were multiplied, the result was always less than either of the numbers.
If Liam's puzzle is true, which of the following statements is true?
A- Both numbers must be positive
B- Both numbers must be negative
C- At least one number will be negative
D- One number will be positive, and one will be negative
Answers
Answer:
D
Step-by-step explanation:
One number will be positive, and one will be negative
Answer:
The answer is option D
Step-by-step explanation:
multiplication of numbers having opposite signs will result in a number having negative sign .
Write 10 000 seconds in hours, minutes, and second
Answers
The 10,000 seconds can be stated as 166.6777 minutes and 2.7778 hour.
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
We have 10,000 sec
As, 1 minute= 60 seconds
So, In minutes
= 10000/60
= 1000/6
= 166.6667 minutes
Now, 1 hour= 60 minutes
So, In hour
= 10000/ 60 x 60
= 10000/3600
= 2.7778 hour
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Solve 2x>8 or 2x< 4.
Answers
Answer:
2x=8
x=8/2
x=4
2x=4
x=4/2
x=2
Use the alternating series estimation theorem to determine how many terms should be used to estimate the sum of the entire series with an error of less than 0.001. [infinity]∑ ₙ₌₋₁ (-1)ⁿ⁺¹ 1/(n + 3√n ³
___ or more terms should be used to estimate the sum of the entire series with an error of less than 0.001.
Answers
To determine how many terms should be used to estimate the sum of the given series with an error of less than 0.001, we can apply the alternating series estimation theorem.
In the given series, the terms are alternating and decreasing in magnitude. We want the error to be less than 0.001, so we need to find the value of n where the absolute value of the (n+1)th term is less than 0.001.
To find this value, we can set up the inequality: |1/(n + 3√n)| < 0.001. Simplifying this inequality, we get: 1/(n + 3√n) < 0.001.
Solving this inequality for n will give us the minimum number of terms required. However, the given equation is incomplete and contains an incomplete expression. Please provide the correct expression for the third term of the series so that I can assist you further.
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slope for (-5,5) (5,-5)
Answers
Answer:
Slope(m)=-1
Step-by-step explanation:
Please help this is not correct !
Answers
Answer:
(2,-1) and 5
Step-by-step explanation:
Can you pls do this i can't do it, it's a little hard and due before 4:00 pm ( Will mark brainliest if 2 answers and 95 pts if you can do it pls and thank you!!)
Answers
Answer:
128.75
Step-by-step explanation:
Answer: 128.75
Step-by-step explanation: you do 30% of 168.74 which is 50.62 then subtract it from 168.74 which is 118.12 then get 9% of 118.12 and add it to the 118.12 and that is 128.75
there is a 25% chance that a customer who purchases milk will also purchase bread. the probability of a milk purchase is 70% and the probability of a bread purchase is 50%. what is the probability that a customer will purchase bread given that he/she buys milk?
Answers
Answer:
If there is a 25% chance that a customer who purchases milk will also purchase bread. the probability of a milk purchase is 70%. the probability that a customer will purchase bread given that they purchase milk is 36%.
How to find the probability?
Using this formula to find the probability that a customer will purchase bread given that they purchase milk
P(B | M) = P(M / B) / P(M)
Let plug in the formula
P(B | M) = 0.25 / 0.70
P(B | M) = 0.3571 ×100
P(B | M) = 36% (approximately)
Therefore the probability is 36%.
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Factor the following expression.
10,5 + 513 – 14,2 - 7
Answers
((10,5 + 513) - 14,2) - 7 =502.3
If 12(x -7) = -11 then x =?
Answers
Answer:
x = 73/12
Step-by-step explanation:
Given:
\(\displaystyle \large{12(x-7)=-11}\)
Distribute 12 in x-7:
\(\displaystyle \large{12x-84=-11}\)
Add both sides by 84:
\(\displaystyle \large{12x-84+84=-11+84}\\\displaystyle \large{12x=73}\)
Divide both sides by 12:
\(\displaystyle \large{\dfrac{12x}{12}=\dfrac{73}{12}}\\\displaystyle \large{x=\dfrac{73}{12}}\)
Therefore, the solution is x = 73/12
Answer:
\(\large\boxed{\bf\:x = \frac{73}{12} = 6\frac{1}{12} \approx 6.083}\)
Step-by-step explanation:
\(12(x - 7) = -11\)
Multiply 12 by x & 7 (distributive property) in the left hand side of the equation .
\(12(x-7)=-11\\(12*x)-(12*7)=-11\\12x - 84 =-11\)
Bring -84 to the right hand side of the equation. Then,
\(12x = -11 + 84\\12x = 73\\x=\frac{73}{12} \\\\\boxed{\bf\:x = \frac{73}{12} = 6\frac{1}{12} \approx 6.083}\)
\(\rule{150pt}{2pt}\)