an open rectangular box has volume 30 cm3. what are the lengths of the edges giving the minimum surface area?
Answers
The lengths of the edges giving the minimum surface area are approximately 1.902 cm, 1.902 cm, and 1.902 cm.
How to find the lengths of edges?Let the length, width, and height of the rectangular box be x, y, and z respectively. Then we have:
Volume of the box = xyz = 30 cm³
We want to minimize the surface area of the box, which is given by:
Surface Area = 2(xy + xz + yz)
We can use the volume equation to solve for one of the variables in terms of the other two. For example, we can solve for z:
z = 30/xy
Substituting this into the surface area equation gives:
Surface Area = 2(xy + x(30/xy) + y(30/xy))
= 2(xy + 30/x + 30/y)
Now we can take the partial derivatives of the surface area with respect to x and y, set them equal to zero, and solve for x and y to find the dimensions that minimize the surface area.
∂(Surface Area)/∂x = 2(y - 30/x²) = 0
∂(Surface Area)/∂y = 2(x - 30/y²) = 0
Solving for x and y, we get:
x = (30/y)¹/²
y = (30/x)¹/²
Substituting these back into the volume equation, we get:
(30/y)¹/² * (30/x)¹/² * z = 30
Simplifying, we get:
z = (xy)⁻¹/²
Substituting x and y into the expression for z gives:
z = (30/(x²))¹/⁴
Therefore, the dimensions that minimize the surface area are:
x = y = (30)¹/⁴ cm
z = (30/(x²))¹/⁴ = (30)¹/⁴ cm
So the lengths of the edges giving the minimum surface area are approximately 1.902 cm, 1.902 cm, and 1.902 cm.
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Related Questions
What is the population variance of the following set of numbers: 3, 5, 8, 9, 10? 29 6.8 7 8.5?
Answers
The population variance of the following set of numbers: 3, 5, 8, 9, 10 is 6.8
For given question,
We need to find the population variance of the following set of numbers: 3, 5, 8, 9, 10
The formula for the Population variance is,
\(\sigma = \frac{\sum (x-\bar x)^2}{N}\)
Here,
\(\bar x\) = sample average
x = individual values in sample
N = count of values in the sample.
For given question,
\(\bar x=\frac{3+ 5+ 8+ 9+ 10}{5} \\\\\bar x=7\)
Using the formula for variance,
\(\sigma = \frac{1}{5} [(3-7)^2 + (5 - 7)^2 + (8 - 7)^2 + (9 - 7)^2 + (10 - 7)^2]\\\\\sigma = \frac{1}{5} \times 34\\\\\sigma = 6.8\)
Therefore, the population variance of the following set of numbers: 3, 5, 8, 9, 10 is 6.8
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7/3 of y is 5 5/6
pls solve!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
2.5
Step-by-step explanation:
\(\frac{7}{3}\) y = \(5\frac{5}{6}\)
y = \(\frac{35}{6}\) ÷ \(\frac{7}{3}\) = \(\frac{35}{6}\) × \(\frac{3}{7}\) = \(\frac{5}{2}\) = 2.5
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Complete the following proof.
Given: mXOY = m WOV
m = m
Prove: m = m
Answers
We have so established that m and m are equal as As congruent angles also referred to as vertical angles are formed when two lines connect.
what is angles ?The degree of rotation between two lines, rays, or segments that have a common endpoint is measured in mathematics as an angle. Angles are categorised in geometry according on how much they are rotated. Angles that are less than 90 degrees are referred to as acute angles, those that are precisely 90 degrees are referred to as right angles, those that are between 90 and 180 degrees are referred to as obtuse angles, and those that are exactly 180 degrees are referred to as straight angles.
given
We can write: since mXOY = mWOV.
mWOV - m = mXOY - m
This can be stated simply as:
OXY = OWV
As congruent angles—also referred to as vertical angles—are formed when two lines connect, we can state:
OXY = MOVY.
Therefore:
mOVW mOVY
And:
mOYX = mOXY
Therefore:
mOYX = mOVY
Finally:
OYX = OWV
We thus have:
m = m
We have so established that m and m are equal as As congruent angles also referred to as vertical angles are formed when two lines connect.
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4% as decimal
.........................
Answers
Answer:
4
100
=
0.04
Step-by-step explanation:
Greg purchased a prepaid phone card for $40.25 calls cost 5 cents a minute using this card. the credit left in the card after it is used for x minutes of calls is given by the following function
Answers
Answer: C= 40.25 - 0.05x
Step-by-step explanation:
C is the credit left
We know that the original is 40.25, so we put it as the beginning number.
Each minute costs $0.05x
where x is each minute
, so the equation is C= 40.25 - 0.05x
Pls help and fast! 17 points!
Answers
Answer:
54 square units
Step-by-step explanation:
144 - 18 - 4(18) = 54 square units
5. A bag contains 5 blue marbles, 4 yellow marbles and 1 red marble. What 1 point
is the probability of selecting a yellow marble, replacing it, then selecting a
blue marble?
Answers
Answer:
()
Step-by-step explanation:
Use nCr to figure this out, plug in the numbers and probabilities and solve
What is the probability that a flight between new york city and chicago is less than 140 minutes?
Answers
The probability that a flight takes more than 140 minutes is approximately 0.333. (Option d: P(x > 140) = 0.333)
To find the probability that a flight takes more than 140 minutes, we need to calculate the proportion of the total distribution that lies beyond 140 minutes.
Given that the time to fly is uniformly distributed between 120 and 150 minutes, we can determine the length of the entire distribution as:
Length of distribution = maximum time - minimum time = 150 - 120 = 30 minutes.
The proportion of the distribution that lies beyond 140 minutes can be calculated as:
Proportion = (Length of distribution - Length up to 140 minutes) / Length of distribution
= (30 - (140 - 120)) / 30
= (30 - 20) / 30
= 10 / 30
= 1/3
≈ 0.333
Therefore, the probability that a flight takes more than 140 minutes is approximately 0.333.
Hence, the correct option is:
d) P(x > 140) = 0.333
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Complete Question:
The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes.
What is the probability that a flight takes time more than 140 minutes? *
a-P(x> 140)=0.14
b-P(x> 140)=1.4
c-P(x> 140)=0
d-P(x> 140) = 0.333
What is equivalent to —4 —9
Answers
\(- 4 - 9 = - 13\)
Help!! Khan academy geomtry practice
Answers
Answer:
33.51 units³
Step-by-step explanation:
Volume of a sphere is given by the formula :
V = \(\frac{4}{3} \pi r^{3}\)
Because we have the radius we can plug it into the equation to give us :
V = (4/3)×π×(2)³
V = 4/3×8π
V ≈ 33.51
Units will be units³ since no measurement is given but it to the power of 3 since it is volume.
Tony's favorite water slide is 18 meters long. The distance from the base of the slide to the bottom of the ladder is 10 meters long (see the image below). Applying thePythagorean Theorem, the equation representing this situation is h^2 + 10^2 = 18^2Solve for h
Answers
Solution:
Given:
Applying the Pythagorean theorem to the right triangle,
\(\begin{gathered} \text{hypotenuse}^2=\text{opposite}^2+\text{adjacent}^2 \\ \text{where;} \\ \text{hypotenuse}=18m \\ \text{adjacent}=10m \\ \text{opposite}=h \\ \\ \text{Hence,} \\ 18^2=h^2+10^2 \\ h^2+10^2=18^2 \end{gathered}\)Thus,
\(h^2+10^2=18^2\)\(\begin{gathered} h^2+10^2=18^2 \\ h^2+100=324 \\ h^2=324-100 \\ h^2=224 \\ h=\sqrt[]{224} \\ h=14.97m \end{gathered}\)Therefore, the value of the height of the ladder, h = 14.97m
Answer:
Step-by-step explanation:
This problem is part of a graded assignment for a cyber school in Pennsylvania. Please remove it and the solution. Signed, the Teacher.
if the slope is 20 and the y intercept is 0,1 what is the equation
Answers
Answer:
\(y = 20x + 1\)
Step-by-step explanation:
The format for the equation of a line is \(y = mx + b\), with \(m\) being the slope and \(b\) being the y-intercept.
You have that information already, so we can just plug it in.
\(y = 20x + 1\)
I'm assuming 0,1 means (0, 1) as in a coordinate. If you meant a decimal, 0.1, adjust accordingly.
Answer:
y=20x+1
Step-by-step explanation:
What is the missing denominator?
3 _ 18
4. d
O 6
O 10
O 19
O 24
Answers
Answer:
The answer to the question is 24
en una tienda de ropa, la semana pasada, 3 pantalones y 2 abrigos costaban 245€. Esta semana estos artículos tienen un descuento del 20% y 5% respectivamente. Si ahora un pantalón y un abrigo cuestan 100,75€, ¿qué costaba cada artículo antes de la rebaja?
Answers
Solving a system of equations we can see that each pair of pants costs €82.94 and each coat costs €26.37
How to find the original cost?
Let's define the variables:
x = cost of a pant
y = cost of a coat.
First, we know that:
3x + 2y = 245
And then there are discounts of 20% and 5%, and the cost of one of each is 100.75, then:
0.8x + 0.95y = 100.75
Then we have a system of equations:
3x + 2y = 245
0.8x + 0.95y = 100.75
We can isolate x on the second equation to get:
x = (100.75 - 0.96y)/0.8
x = 125.9 - 1.2y
Replace that in the other equation:
3*(125.9 - 1.2y) + 2y = 245
Solving for y:
3*125.9 - 3*1.2y + 2y = 245
y*(2 - 3*1.2) = 245 - 3*125.9
y = (245 - 3*125.9)/(2 - 3*1.2)
y = 82.94
Then the value of x is:
x = 125.9 - 1.2*82.94
x = 26.37
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How do you calculate the critical value?
Answers
Answer: The critical value is a value used in hypothesis testing to determine the rejection or acceptance of a null hypothesis. The critical value is determined based on the significance level of the test and the degrees of freedom. The critical value is usually determined from a table or calculated using statistical software.
Here are the general steps to calculate the critical value:
Determine the significance level, denoted by α. This is the probability of making a Type I error, which is the probability of rejecting a true null hypothesis.
Determine the degrees of freedom, which depend on the specific test and sample size.
Look up the critical value in a table of critical values for the appropriate significance level and degrees of freedom. These tables are available in most statistics textbooks or can be found online.
If a table is not available, the critical value can be calculated using statistical software or a calculator that provides a cumulative distribution function for the appropriate distribution. For example, the critical value for a two-tailed t-test can be calculated in R using the qt function. The syntax is qt(1-α/2, df), where α is the significance level and df is the degrees of freedom.
Note that the critical value will depend on the specific hypothesis test being performed and the null and alternative hypotheses. It is important to choose the correct test and use the appropriate critical value to ensure accurate results.
Step-by-step explanation:
Simplify the given equation
5x+2(x-3)=2x-1
A) 7x-3=-2x-1
B) 7x-6=-2x+2
C) 7x-6=-2x-2
Answers
Answer: B) 7x-6=-2x+2
Step-by-step explanation:
PLEASE HELP! if f(1) =6 and f(n) =f (n-1)+1 then find the value of f(6)
Answers
Answer
0= -5
Step-by-step explanation:
6(n) = 6(n-1)+1
6n = 6n - 6 +1
0= -5
(i don't know if this is correct very sorry!!)
Q
12 inches
P
0
What is the length of P'Q'?
inches
Answers
Answer:
it would be 12 inches because you add them
Combine like terms
a + 7b + 3a - 4b + 5c
Answers
Answer:
a+7b+3a-4b+5c
4a+3b+5c
Hope you have a good day, Loves!~
the z value for a 97.8% confidence interval estimation is
Answers
The z value for a 97.8% confidence interval estimation is determined as 2.29.
What is the z value for a 97.8% confidence?The z value for a 97.8% confidence interval estimation is calculated as follows;
The find the Z score, go to a Z lookup table which is found in a textbook or on an internet source. z table is created to give the possibility in a one-tailed analysis.
A confidence interval is a two-tailed examination, in order to prepare the z score for 97.8%, look up the probability of 98.9%.
The value of 98.9% is
= (0.978 + 1 )/ 2
= 0.989 or 98.9%.
This implies that the z score of the date is 2.29.
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Which point is located at (4, 1)? On a coordinate plane, point A is 4 units to the right and 1 unit up. Point B is 4 units to the left and 1 unit up. Point C is 1 unit to the right and 4 units up. Point D is 1 unit to the left and 4 units up. A B C D
Answers
Answer:
Point A is 4 units to the right and 1 unit up. (A).
Step-by-step explanation:
The reason is (4, 1) is (x, y).
x is in a horizontal line while y is in a vertical line.
In x, right is positive while left is negative.
In y, up is positive while down is negative.
4
Which equation represents a linear function that has a slope of 5 and a y-intercept of -6?
4.
y=-6x+
+
Oy-x-6
O y=x+6
O y=6x+
PLEASE I NEED HELP
Answers
First, we have to understand the slope-intercept form.
\( \large \boxed{y = mx + b}\)
A linear function/equation has three forms and the slope-intercept is one of the form. It is also commonly used in Function topic while the other two forms are commonly used in Analytic Geometry.
In the slope-intercept form, the m-term represents the slope while b-term represents the y-intercept of a graph.
Which equation represents a linear function that has a slope of 5 and a y-intercept of -6.
As you notice the bold, italic and underlined words in the question that I quoted or rewrote. I've just explained that the slope is m-term and y-intercept is b-term.
Therefore, substitute m = 5 and b = -6 in the equation.
\( \large{y = mx + b \longrightarrow \bold{y = 5x + ( - 6)}} \\ \large \boxed{ \tt{ \purple{y = 5x - 6}}}\)
I hope this helps! Let me know if you have any questions regarding the linear function, don't hestitate to ask. Good luck with your assignment and have a nice day!
Marco has two bags of candy. One bag contains three red lollipops and
2 green lollipops. The other bag contains four purple lollipops and five blue
lollipops. One piece of candy is drawn from each bag. What is the probability
of choosing a green lollipop and a purple lollipop?
Answers
The value of the probability of choosing a green lollipop and a purple lollipop is, 8 / 45
We have to given that;
One bag contains 3 red lollipops and 2 green lollipops.
And, The other bag contains four purple lollipops and five blue lollipops.
Hence, The probability of choosing a green lollipop is,
P₁ = 2 / 5
And, The probability of choosing a purple lollipop is,
P₂ = 4 / 9
Thus, The value of the probability of choosing a green lollipop and a purple lollipop is,
P = P₁ × P₂
P = 2/5 × 4/9
P = 8/45
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a study of interior designers' opinions with respect to the most desirable primary color for executive offices showed the following. primary colornumber of opinions red80 orange74 yellow58 green79 blue49 indigo58 violet2 what is the probability that a designer does not prefer blue?
Answers
The probability that a designer does not prefer blue is approximately 0.8775, or 87.75%.
To calculate the probability that a designer does not prefer blue, we need to consider the number of opinions that do not prefer blue and divide it by the total number of opinions.
The number of opinions that do not prefer blue is the sum of opinions for all other colors except blue:
Number of opinions not preferring blue = Number of opinions for red + Number of opinions for orange + Number of opinions for yellow + Number of opinions for green + Number of opinions for indigo + Number of opinions for violet
= 80 + 74 + 58 + 79 + 58 + 2
= 351
Total number of opinions = Number of opinions for red + Number of opinions for orange + Number of opinions for yellow + Number of opinions for green + Number of opinions for blue + Number of opinions for indigo + Number of opinions for violet
= 80 + 74 + 58 + 79 + 49 + 58 + 2
= 400
Therefore, the probability that a designer does not prefer blue is:
P(Not preferring blue) = Number of opinions not preferring blue / Total number of opinions
= 351 / 400
≈ 0.8775
The probability that a designer does not prefer blue is approximately 0.8775, or 87.75%.
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Find the H.C.F of the following numbers by the prime factorization method
a)18 and 27
b)35and 75
c)144and 360
d)30,40and45
e)144,384and432
Answers
Answer:
Step-by-step explanation:
is a 18 and 27 yes to the following question
a) 18 = 2 x 3^2
27 = 3^3
-> HCF = 3^2 = 9
b) 35 = 5 x 7
75 = 3 x 5^2
-> HCF = 5
c) 144 = 2^4 x 3^2
360 = 2^3 x 3^2 x 5
-> HCF = 2^3 x 3^2 = 72.
d) 30 = 2 x 3 x 5
40 = 2^3 x 5
45 = 3^2 x 5
-> HCF = 5
e) 144 = 2^4 x 3^2
384 = 2^7 x 3
432 = 2^4 x 3^3
-> HCF = 2^4 x 3 = 48.
Hhhhhhhhelllllllllllp In physics, you are using the formula E = mc2, where c is positive and represents the speed of light. Which equations are equivalent to
this?
Answers
Answer:
Step-by-step explanation: This is just rearranging the formula. Divide by m on both sides, then find the square root. The answer is E
does q have any subgroups isomorphic to z? prove your answer.
Answers
Q does not have any subgroups that are isomorphic to z.
Assume, ⟨a/b⟩∈ ℚ,
Note that under this assumption a/2b ∈ ℚ, which is a rational number, would then be an integral multiple of (a/b), which it clearly is not; i.e. 1/2 × (a/b)
So the assumption that ℚ is generated by (a/b) cannot be true. Since (a/b) is arbitrary, this shows that ℚ is not generated by any element of ℚ, i.e., ℚ is not cyclic.
Since the additive group ℤ =⟨1⟩ is generated by a finite element and is thus cyclic, and ℚ is neither generated by a finite element nor cyclic, the two subgroups are clearly not isomorphic.
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A farmer sells 6.2 kilograms of apples and pears at the farmer's market. 4/5
of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?
Answers
Answer:
Step-by-step explanation:
gano 2000 lb
please helppp me i am so bad at this
Answers
Answer:
x = 4√6 or 9.8Step-by-step explanation:
The two smaller triangles are similar.
The ratio of corresponding sides of similar triangles is equal:
12/x = x/8x² = 12*8x² = 96x = √96x = 4√6 or 9.8\(\\ \sf\longmapsto x^2=12(8)\)
\(\\ \sf\longmapsto x^2=96\)
\(\\ \sf\longmapsto x=\sqrt{96}\)
\(\\ \sf\longmapsto x=9.7\)
I am desperate for help with this - 100 pts for this question
