Answer:
6, 9, 10, 10, 11, 11, 12, 13, 15, 15, 18
Q1 (the first quartile) represents the data point that separates the lowest 25% of the data from the rest of the data. To find Q1, we can use the formula:
Q1 = (n + 1) / 4
where n is the total number of data points.
In this case, n = 11, so:
Q1 = (11 + 1) / 4 = 3rd data point
So, Q1 is 10.
Q3 (the third quartile) represents the data point that separates the highest 25% of the data from the rest of the data. To find Q3, we can use the formula:
Q3 = 3(n + 1) / 4
In this case:
Q3 = 3(11 + 1) / 4 = 9th data point
So, Q3 is 15.
D4 represents the fourth decile, which is the data point that separates the lowest 40% of the data from the rest of the data. To find D4, we can use the formula:
D4 = (n + 1) / 10 * 4
In this case:
D4 = (11 + 1) / 10 * 4 = 5th data point
So, D4 is 11.
D Assimilation represents the data point that is closest to the mean (average) of the data. To find D Assimilation, we first need to find the mean of the data:
Mean = (6 + 9 + 10 + 10 + 11 + 11 + 12 + 13 + 15 + 15 + 18) / 11 = 12
The data point closest to the mean is 12, so:
D Assimilation = 12
Pss (the range) represents the difference between the largest and smallest data points. In this case:
Pss = 18 - 6 = 12
6 9 10 10 11 11 12 13 15 15 18
Dss=12
Q1=10 Q3=15
D4=11
Step-by-step explanation:
D is the centroid of PQR PA= equals 17 BD equals nine and DQ equals 14 find each missing measure
The centroid of the triangle is D and the measures of sides are solved
Given data ,
Let the triangle be represented as ΔPQR
Now , the centroid of the triangle is D
where the measure of PA = 17 units
The measure of BD = 9 units
And , the measure of side DQ = 14 units
Now , centroid of a triangle is formed when three medians of a triangle intersect
And , from the properties of centroid of triangle , we get
PA = AR
DR = DQ
AD = BD
On simplifying , we get
The measure of side AR = 17 units
PR = PA + AR = 34 units
The measure of side DR = 14 units
BR = BD + DR = 23 units
The measure of side AD = 9 units
AQ = AD + DQ = 23 units
Hence , the centroid is solved
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A regular pentagonal prism has an edge length 9 m, and height 13 m. Identify the volume of the prism to the nearest tenth
The volume of the regular pentagonal prism with an edge length of 9 m and a height of 13 m is approximately 1811.6 m³ to the nearest tenth.
To find the volume of a regular pentagonal prism with an edge length of 9 m and a height of 13 m, follow these steps:
Step 1: Find the apothem (a) of the base pentagon. Use the formula a = s / (2 * tan(180/n)), where s is the edge length and n is the number of sides (5 for a pentagon).
a = 9 / (2 * tan(180/5))
a ≈ 6.1803 m
Step 2: Calculate the area (A) of the base pentagon. Use the formula A = (1/2) * n * s * a.
A = (1/2) * 5 * 9 * 6.1803
A ≈ 139.3541 m²
Step 3: Determine the volume (V) of the pentagonal prism. Use the formula V = A * h, where h is the height.
V = 139.3541 * 13
V ≈ 1811.6033 m³
So, the volume of the regular pentagonal prism with an edge length of 9 m and a height of 13 m is approximately 1811.6 m³ to the nearest tenth.
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okay ummm deleted question
Answer:
Sure, let me know if you have a new question or need any assistance!
If a side of a square is doubled and an adjacent side is diminished by 3, a rectangle is formed whose area is numerically greater than the area of the square by twice the original side of the square. Find the dimensions of the original square
The dimensions of the original square is 8 by 8.
Let x be the original side length of the square. The area of the square is x². When one side is doubled and the adjacent side is diminished by 3, the rectangle's dimensions become 2x and (x-3). The area of the rectangle is (2x)(x-3) = 2x² - 6x.
According to the problem, the area of the rectangle is greater than the area of the square by twice the original side of the square, which is 2x. So we can set up the equation:
2x² - 6x = x² + 2x
Now, solve for x:
2x² - x² = 6x + 2x
x² = 8x
x = 8
So the dimensions of the original square are 8 by 8.
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Stan's Car Rental charges $35 per day plus $0. 25 per mile. Denise wants to rent one of Stan's cars, keeping the total
cost of the rental to no more than $55. What is the greatest number of miles Denise can drive the
car to stay within her budget?
O A) 75 miles
O B) 80 miles
O c) 90 miles
OD) 100 miles
Denise can drive at most 80 miles to stay within her budget of $55.
Let's assume that Denise drives x miles during the rental period. Then the total cost of the rental will be:
Total cost = $35 (flat rate for the day) + $0.25 per mile x (number of miles driven)
We want to find the greatest number of miles that Denise can drive and still stay within her budget of $55, so we can set up an inequality as follows:
Total cost ≤ $55
$35 + $0.25x ≤ $55
Subtracting $35 from both sides
$0.25x ≤ $20
Dividing both sides by $0.25
x ≤ 80
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Shelby multiplies 7,358.9 by a power of 10 and gets the product
73.589. select all possible factors.
(a) 1/100 "fraction"
(b) 1/10 "fraction"
(c) 1
(d) 0.1
(e) 0.01
(f) 0.001
(a) 1/100 (or 0.01)
(e) 0.01
This factor represents dividing the number by 100.
When Shelby multiplies 7,358.9 by a power of 10 and gets the product 73.589, we can determine the factor by comparing the two numbers.
7,358.9 → 73.589
We can see that the decimal point has moved two places to the left. Therefore, the factor is the one that will shift the decimal point two places to the left. Among the given options, the factor that does this is:
(a) 1/100 (or 0.01)
(e) 0.01
This factor represents dividing the number by 100. The other options (b, c, d, and f) do not represent the correct division by powers of 10 in this case.
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Pythagorean Theorem answer quick please
Answer:
3.9
Step-by-step explanation:
pythagorean theorem states:
[tex]a^{2} +b^{2} =c^{2}[/tex]
We know that a is the height of the triangle, 2.
We also know that b is the base of the triangle, 3.
So, solve for c:
2²+3²=c²
simplify
4+9=c²
15=c²
take the square root of both sides
c=3.9
So, the spider and the fly are 3.9 ft apart from each other
Hope this helps :)
Answer:
3.6 feet
Step-by-step explanation:
The Pythagorean theorem states that a^2+b^2=c^2, where c is the hypotenuse, or longest side of the triangle opposite to the right angle, and a and b are the two legs of the triangle (the other two sides.)
In the question, sides a and b are given as 2ft and 3ft long. Plugging 2 and 3 into the equation, we will get that 2^2+3^2=c^2. 2 x 2 = 4 and 3 x 3 = 9, so 4 + 9 = c^2, or, c^2 = 13.
However, this is still c^2, not c, so we must take the square root of both sides. This is because the equation is now essentially saying that c x c = 13, so if we find a number that when multiplied by itself equals 13, that number will be c. to do this, we must take the square root of 13. This will give us an irrational number- approximately 3.605551275. The question asks to round it to the nearest tenth though, so this will simply become 3.6.
In the context of this question, it means that the spider and the fly are 3.6ft apart.
Which term can be put in the blank to make the statement below true?
3,000,000=30________________
A. Thousands
B.Ten-Thousands
C.Hundred-Thousands
D.Millions
Please I need your help!
Select each equation that the number 10 to the 3rd power makes true.
6.01 × ⬜ = 601
0.305 × ⬜ = 305
0.54 × ⬜ = 540
0.097 × ⬜ = 970
0.97 × ⬜ = 97
Find the length of the midsegment of the trapezoid
2n-2
N+12
4n+6
Answer: To find the length of the midsegment of a trapezoid, you need to add the lengths of the two bases together and divide by 2.
The length of the top base is 2n-2 and the length of the bottom base is 4n+6.
Adding the two bases together gives:
(2n-2) + (4n+6) = 6n + 4
Dividing by 2 gives:
(6n + 4) / 2 = 3n + 2
Therefore, the length of the midsegment of the trapezoid is 3n + 2.
Determine the specified confidence interval. An organization advocating for healthcare reform has estimated the average cost of providing healthcare for a senior citizen receiving Medicare to be about $13,000 per year. The article also stated that, with 90% confidence, the margin or error for the estimate is $1,000. Determine the resulting 90% confidence interval for the average cost for healthcare of a senior citizen receiving Medicare
the resulting 90% confidence interval for the average cost for healthcare of a senior citizen receiving Medicare is [$12,000, $14,000].
The estimated average cost of providing healthcare for a senior citizen receiving Medicare is $13,000 per year, and the margin of error for this estimate is $1,000 with a 90% confidence level.
To find the confidence interval, we need to add and subtract the margin of error from the estimated mean.
Lower Limit = Estimated Mean - Margin of Error
Lower Limit = 13,000 - 1,000
Lower Limit = 12,000
Upper Limit = Estimated Mean + Margin of Error
Upper Limit = 13,000 + 1,000
Upper Limit = 14,000
Therefore, the resulting 90% confidence interval for the average cost for healthcare of a senior citizen receiving Medicare is [$12,000, $14,000]. This means we are 90% confident that the true mean cost of providing healthcare for a senior citizen receiving Medicare is between $12,000 and $14,000 per year.
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Elena is trying to figure out how many movies she can download to her hard
drive. The hard drive is supposed to hold 500 gigabytes of data, but 58
gigabytes are already taken up by other files. Each movie is 8 gigabytes. Elena
wrote the inequality 8x + 58 ≥ 500 and solved it to find the solution x ≥ 55. 25.
4a) Explain how you know Elena made a mistake based on her solution.
4b) Fix Elena's inequality and explain what each part of the inequality represent.
Based on Elena's solution, x represents the number of movies that can be downloaded. However, her inequality is incorrect as it states that the total amount of downloaded data (8x + 58) is greater than or equal to the total capacity of the hard drive (500 gigabytes).
This means that Elena is considering the amount of data taken up by other files in addition to the movies she wants to download. Therefore, her solution of x ≥ 55.25 is incorrect as it would allow Elena to download more movies than the remaining capacity of the hard drive.
The corrected inequality should be 8x ≤ 442, as the remaining capacity of the hard drive is 500 - 58 = 442 gigabytes. This means that Elena can download a maximum of 55 movies (8 x 55 = 440), leaving 2 gigabytes of space remaining on the hard drive. Therefore, each part of the inequality represents the total amount of data used by the movies downloaded (8x) and the remaining capacity of the hard drive (442).
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Jason borrowed $5000 to go with the money he'd saved to buy a tractor. The finance charge on the loan was $55 and the term on the loan was 360 days. What was the APR for Jason's loan?
O 0. 011%
O 1. 116%
O 4. 015%
O 1. 527%
The answer is option B: 1.116%.
To find the APR(Annual Percentage Rate) for Jason's loan, we first need to calculate the total amount of interest he paid.
The finance charge of $55 is the interest paid for the 360-day term.
To find the total interest, we can use the formula:
Total interest = (finance charge / loan amount) x (days in a year / loan term in days)
Plugging in the values, we get:
Total interest = (55 / 5000) x (365 / 360)
Total interest = 0.011 x 1.01389
Total interest = 0.01116 or 1.116%
Therefore, the APR for Jason's loan is 1.116%.
The answer is option B: 1.116%.
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A bacteria population doubles every eight minutes if the population with one cell, how long will it take to grow to 2097152
The time that it will take the bacteria to grow to 2097152 is: 2 hours 48 minutes
How to solve Exponential functions?An exponential function is defined as a Mathematical function in the form f(x) = [tex]a^{x}[/tex].
where:
“x” is a variable.
“a” is a constant which is called the base of the function and it should be greater than 0
However; the exponential function is:
1([tex]2^{x}[/tex]) = 2097152
log 2x = log 2097152
x log 2 = log 2097152
x = log 2097152/log 2
x = 6.32162/0.3010
x = 21 times the population doubles
21(8) = 168 minutes = 2 hours 48 minutes
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A right rectangular prism has length 10 in. And width 8 in. The surface area of the prism is 376 in2. What equation can be used to find the height in inches?
The equation to find the height is 376 = 160 + 20h + 16h.
The height of the right rectangular prism is 6 inches.
We have,
Let's denote the height of the right rectangular prism as "h" inches.
The formula for the surface area of a right rectangular prism is:
Surface Area = 2lw + 2lh + 2wh
Given that the length (l) is 10 inches and the width (w) is 8 inches, and the surface area is 376 square inches, we can substitute these values into the formula:
376 = 2(10)(8) + 2(10)(h) + 2(8)(h)
Simplifying this equation:
376 = 160 + 20h + 16h
Combine like terms:
376 = 160 + 36h
Rearranging the equation to isolate "h":
36h = 376 - 160
36h = 216
Finally, divide both sides of the equation by 36 to solve for "h":
h = 216/36
h = 6
Therefore,
The height of the right rectangular prism is 6 inches.
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At the Royal Dragon Chinese restaurant, a slip in the fortune cookies indicates a dollar amount that will be subtracted from your total bill. A bag of 10 fortune cookies is given to you from which you will select one. If six fortune cookies contain "1$ off," three contain "$3 off," and one contains "$8 off," determine the expectation of a selection.
Answer:
im sorry this makes absolutely no sense
Step-by-step explanation:
Which of theses is a rectangle pentagon, trapezoid, square, rhombus
Among the given options, the square is a rectangle.
To determine which of these is a rectangle, we will consider the properties of a rectangle and compare them with the properties of a pentagon, trapezoid, square, and rhombus.
A rectangle is a quadrilateral with four right angles and opposite sides equal in length.
1. Pentagon: A pentagon has five sides and cannot be a rectangle since a rectangle must have four sides.
2. Trapezoid: A trapezoid has one pair of parallel sides, but it does not have four right angles, so it cannot be a rectangle.
3. Square: A square has four equal sides and four right angles, making it a special type of rectangle. Therefore, a square is a rectangle.
4. Rhombus: A rhombus has four equal sides but does not necessarily have four right angles, so it is not a rectangle.
In conclusion, among the given options, the square is a rectangle.
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f(x,y) = x2 + y² + xy {(x, y) : x2 + y2 < 1}
"Find the maxima and minima, and where they are reached, of the
following function. Find the locals and absolutes. Identify the
critical points inside the disk if any."
The given function f(x,y) = x^2 + y^2 + xy has a maximum value of 3/4 at (x,y) = (1/2,1/2) and a minimum value of -1/4 at (x,y) = (-1/2,1/2) inside the disk x^2 + y^2 < 1. There are no critical points inside the disk.
To find the critical points, we need to take partial derivatives of the function with respect to x and y and solve the resulting equations simultaneously.
fx = 2x + y = 0
fy = 2y + x = 0
Solving these equations, we get the critical point at (x,y) = (-1/2,-1/2) outside the disk. Hence, we do not consider it further.
Next, we need to find the boundary points of the disk, which is the circle x^2 + y^2 = 1. We can parameterize this circle as x = cos(t) and y = sin(t), where t ranges from 0 to 2π.
Substituting these values in the given function, we get:
f(cos(t), sin(t)) = cos^2(t) + sin^2(t) + cos(t)sin(t)
= 1/2 + 1/2sin(2t)
Now, we need to find the maximum and minimum values of this function. Since sin(2t) ranges from -1 to 1, the maximum value of the function is 3/4 when sin(2t) = 1, i.e., when t = π/4 or 5π/4. At these points, x = cos(π/4) = 1/2 and y = sin(π/4) = 1/2.
Similarly, the minimum value of the function is -1/4 when sin(2t) = -1, i.e., when t = 3π/4 or 7π/4. At these points, x = cos(3π/4) = -1/2 and y = sin(3π/4) = 1/2.
Therefore, the function has a maximum value of 3/4 at (x,y) = (1/2,1/2) and a minimum value of -1/4 at (x,y) = (-1/2,1/2) inside the disk x^2 + y^2 < 1. There are no critical points inside the disk.
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A window in the shape of a parallelogram has a base of 36 inches, and a height of 45 inches. What is the area?
The area of a parallelogram is given by the formula:
$\sf\implies{\boxed{A = bh}}$
where $b$ is the length of the base and $h$ is the height.
In this case, the base is 36 inches and the height is 45 inches, so the area of the parallelogram is:
$\sf\implies\:A = bh = 36 \cdot 45 = 1620$
Therefore, the area of the parallelogram-shaped window is 1620 square inches.
[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]
[tex]{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]
Answer:
1620 inches ^2
Step-by-step explanation:
The area of a parallelogram is simply put as:
A=bh
where b is base and h is height
Given b is 36 and 45 is our h, we can now solve for the area.
A=(36)(45)
A=1620
Friendly reminder:
When multiplying two of the same units, remember to square them to have the correct labeling, so in conclusion, our answer is:
1620 inch.^2
PLEASE HELP WILL MARK BRANLIEST !!!
If password begin with capital letter followed by lower case letter, and end with symbol , then the number of unique passwords which can be created using letters and symbols are 47525504.
The password must have 6 characters and the first character must be a capital letter, so, we have 26 choices for the first character.
For the second character, we have 26 choices for a lower-case letter.
For the third, fourth, and fifth characters, we can choose from any of the 26 letters (upper or lower case).
For the last character, we have 4 choices for the symbol
So, total number of unique passwords that can be created is:
⇒ 26 × 26 × 26 × 26 × 26 × 4 = 26⁵ × 4 = 47525504.
Therefore, there are 47525504 unique passwords that can be created using these letters and symbols.
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I have tried doing this question for 20 minutes but I just can't get the answer, (add maths circular measure)
the answer is 17.2cm² supposedly
Answer:
17.2 cm²
Step-by-step explanation:
Alr let me try
The angle is 1.2 you got it right. The rest is in the pics
Answer: A(shaded)=17.15 cm²
Step-by-step explanation:
What you did so far is correct.
Given:
r=5
s=6
Solve for Ф angle:
s=[tex]\frac{part circle}{wholecircle} 2\pi r[/tex] This way help you find the portion/percent you want
6=(Ф/360) (2[tex]\pi[/tex]5) >solve for Ф Divide by (2[tex]\pi[/tex]5) and multiply by 360
Ф=68.75
Solve for pie/sector
Now that you have the angle, you can use the same concept for area
Area of sector = [tex]\frac{part circle}{wholecircle} \pi r^{2}[/tex]
Area of sector = [tex]\frac{68.75}{360} \pi 5^{2}[/tex]
Area of sector = 15.0 cm²
Now let find y so we can plug into area of triangle
use tan Ф = opposite/adjacent
tan 68.75 = y/5
y=5 * tan 68.75
y=12.86 cm
Area of triangle = 1/2 b h b=y=12.86 h =5
Area of triangle = 1/2* 12.86*5
Area of triangle = 32.15 cm²
Now subtract area of sector from triangle
A(shaded)=A(triangle)-A(sector)
A(shaded)=32.15- 15.0
A(shaded)=17.15 cm²
The sixth-graders at Ayana's school got to choose between a field trip to a museum and a field trip to a factory. 39 sixth-graders picked the museum. If there are 50 sixth-graders in all at Ayana's school, what percentage of the sixth-graders picked the museum?
Answer:
78% of sixth-graders picked a field trip to a museum.
Step-by-step explanation:
39 out of 50 kids picked the museum field trip. This is 39/50. We can change this like so:
39/50 × 2/2
= 78/100
78/100 is 78% (because percent literally means "per hundred)
Another way is to just divide. 39/50 means 39 ÷ 50.
39 ÷ 50 is .78 then times by 100 to change to a percent. This works for all kinds of fractions.
78% of sixth graders at Ayana's school selected the museum field trip.
Mrs.lane makes a 22% commission on commercial advertising sales for the local newspaper plus $8.25/hr. working 40hrs/week. her average bi-weekly commercial sales are $5,625. how much would her average gross monthly income be?
Mrs. Lane's average gross monthly income would be $3,135.
How to find the income?To find the monthly income of Mrs. Lane's,
First, we need to find Mrs. Lane's commission for her bi-weekly commercial sales:
Commission = 22% of $5,625 = 0.22 x $5,625 = $1,237.50
Next, we need to find her hourly wage for a week:
Hourly wage = $8.25 x 40 = $330
Her gross bi-weekly income is the sum of her commission and hourly wage:
Gross bi-weekly income = Commission + Hourly wage
= $1,237.50 + $330
= $1,567.50
To find her gross monthly income, we can multiply her gross bi-weekly income by the number of bi-weekly pay periods in a month:
Gross monthly income = Gross bi-weekly income x Number of bi-weekly pay periods in a month
= $1,567.50 x 2
= $3,135
Therefore, Mrs. Lane's average gross monthly income would be $3,135.
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Can somebody help me really quickly please
Answer: 77
Step-by-step explanation:
Bigger Rectangle = LW = 5x5 =25 There are 2 of those. =50
middl rectangle = LW = 5x3=15
triangles= 1/2 b h = 1/2 (3)(4) = 6 but therere are 2 so =12
Add up all shapes=50+15+12=77
A store has `80` pumpkins for sale. Here are the values of the quartiles. About how many of the `80` pumpkins would you expect to weigh less than `15.5` pounds
This is just a rough estimate, and the actual number of pumpkins that weigh less than 15.5 pounds could be slightly higher or lower.
What is the median?
The median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude.
Assuming that the quartiles divide the pumpkins' weights into four equal parts, we can use the value of the second quartile (Q2) to estimate the median weight of the pumpkins. Since there are 80 pumpkins, Q2 would be the average of the 40th and 41st heaviest pumpkins.
We don't know the exact values of the quartiles, but we can make some reasonable assumptions. For example, if we assume that the first quartile (Q1) is around 12 pounds and the third quartile (Q3) is around 20 pounds, then we can estimate the median weight as follows:
Median = (Q2) = (Q1 + Q3)/2 = (12 + 20)/2 = 16 pounds
Based on this estimate, we can expect that roughly half of the 80 pumpkins (i.e., 40 pumpkins) weigh less than 16 pounds. Therefore, we might expect that slightly fewer than 40 pumpkins would weigh less than 15.5 pounds.
However, this is just a rough estimate, and the actual number of pumpkins that weigh less than 15.5 pounds could be slightly higher or lower depending on the distribution of the pumpkin weights.
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Ryann is filing Chapter 7 bankruptcy. She will be able to include $10,148.22 of her total debt of $112,758.00Calculate what percent of Ryann's total debt is included in the bankrup
Answer:
Step-by-step explanation:
To calculate the percentage of Ryann’s total debt that is included in the bankruptcy, you can divide the amount of debt included in the bankruptcy by the total debt and then multiply by 100.
So, the calculation would be: ($10,148.22 / $112,758.00) * 100 = 9%.
This means that 9% of Ryann’s total debt is included in the bankruptcy.
Can someone please help! All I need is 19, 20, 21, 22, 23, 24! Thank you
Answer:
hope it helps! :)
Step-by-step explanation:
m < A = 61 bc 90+29=119
180-119=61
ED: 9y-22=5
9y=27
y=3
9(3)-22 =5
ED=5
3x-5=13
3x=18
x=6
[tex]BC^{2}[/tex]+25+=169
[tex]BC^{2}[/tex]=144
BC=12
m<DCE=29
y=3
pls show work its due tomorrow
Answer: 325
Step-by-step explanation:
15*30-5*5-20*5=325
Answer: 875 square feet.
Step-by-step explanation: (25x30)+(5x20)+25
what are the values of m and n, and what does the plotted graph look like?
The values of m and n are
m = 0 and n = 3.125
The graph is attached
How to find the values of m and nThe values of m and n are solved using the relationship between miles and kilometers. This type of relationship is a linear proportional relationship. Linear relationship implies the graph will be a straight line graph.
This relationship is that 1 mile equals 0.625 km hence the linear equation is
y = 0.625x
when x = 0, we have that
y = 0.625 * 0
y = 0
when x = 5, we have that
y = 0.625 * 5
y = 3.125
Where x is kilometers and y is miles
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A manufacturer makes aluminum cups with a volume of 10 cubic centimetres cach, in the form of right circular cylinders open at the top. Find the dimensions that would require the least amount of material.
The dimensions that require the least amount of material are r = (10/π)^(1/3) cm for the radius and h = (10/π)^(1/3) cm for the height.
To minimize the amount of material used for making aluminum cups with a volume of 10 cubic centimeters, you will need to optimize the dimensions of the right circular cylinders.
Given the volume (V) is 10 cm³, the formula for the volume of a right circular cylinder is V = πr²h, where r is the radius and h is the height.
10 = πr²h
To minimize the material used, we want to minimize the surface area (SA) of the open cylinder, which is given by the formula SA = 2πrh + πr² (the first term represents the lateral surface and the second term the base).
Using the volume formula, we can find a relationship between r and h:
h = 10 / (πr²)
Now substitute this expression for h in the surface area formula:
SA(r) = 2πr(10 / (πr²)) + πr²
SA(r) = 20/r + πr²
To find the minimum surface area, differentiate SA(r) with respect to r and set the result equal to zero:
d(SA)/dr = -20/r² + 2πr
Now solve for r:
0 = -20/r² + 2πr
20/r² = 2πr
r³ = 10/π
Now take the cube root of both sides:
r = (10/π)^(1/3)
To find the height, substitute this value of r back into the expression for h:
h = 10 / (π((10/π)^(1/3))²)
h = (10/π)^(1/3)
The dimensions that require the least amount of material are r = (10/π)^(1/3) cm for the radius and h = (10/π)^(1/3) cm for the height.
To learn more about surface area, refer below:
https://brainly.com/question/29298005
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