To find the dimensions of a cylindrical can with a volume of 100 in^3 that minimizes the surface area, we can use the formula for the surface area of a cylinder: S = 2πr^2 + 2πrh.
First, we need to find the radius of the cylinder. We know that the volume of the cylinder is 100 in^3, so we can use the formula for the volume of a cylinder: V = πr^2h. Substituting in V = 100, we get:
100 = πr^2h
We want to minimize the surface area, which is given by the formula S = 2πr^2 + 2πrh. We can use the equation for the volume of the cylinder to solve for h in terms of r:
h = 100/(πr^2)
Substituting this into the formula for the surface area, we get:
S = 2πr^2 + 2πr(100/(πr^2))
Simplifying, we get:
S = 2πr^2 + 200/r
To minimize the surface area, we need to find the value of r that makes the derivative of S with respect to r equal to zero. Taking the derivative of S, we get:
dS/dr = 4πr - 200/r^2
Setting this equal to zero and solving for r, we get:
4πr = 200/r^2
r^3 = 50/π
r = (50/π)^(1/3)
Now that we have found the value of r that minimizes the surface area, we can use the equation for h that we found earlier to find the corresponding value of h:
h = 100/(πr^2)
Substituting in r = (50/π)^(1/3), we get:
h = 200/5^(1/3)π^(2/3)
Therefore, the dimensions of the cylindrical can that minimizes the surface area are:
Radius, r = (50/π)^(1/3)
Height, h = 200/5^(1/3)π^(2/3)
And the minimum surface area is:
S = 2πr^2 + 2πrh = 2π(50/π)^(2/3) + 2π(50/π)^(1/3) (200/5^(1/3)π^(2/3)) = 2π(50/π)^(2/3) + 400/5^(1/3)π^(1/3)
To find the dimensions of a cylindrical can with a volume of 100 in³ that minimizes the surface area, we need to use the given formulas for volume (V = πrh) and surface area (S = 2πr² + 2πrh).
First, let's find the radius (r) using the provided equation:
r = (50/π)^(1/3)
Now, we need to find the height (h). We can do this by substituting the volume formula into the surface area formula:
100 = πr * h
=> h = 100 / (πr)
Next, substitute the value of h into the surface area formula:
S = 2πr² + 2πr(100 / (πr))
S = 2πr² + 200/r
Now, to minimize the surface area, we need to find the derivative of S with respect to r (dS/dr) and set it equal to zero:
dS/dr = 4πr - 200/r² = 0
=> 4πr = 200/r²
=> r³ = 50/π
Since we have already found r using the given formula, we know that r = (50/π)^(1/3). Now we can find h using the height formula:
h = 100 / (π * (50/π)^(1/3))
With these values, we have found the dimensions of a cylindrical can with a volume of 100 in³ that minimizes the surface area:
Radius, r = (50/π)^(1/3)
Height, h = 100 / (π * (50/π)^(1/3))
To find the minimum surface area S, substitute r and h into the surface area formula:
S = 2π((50/π)^(1/3))² + 2π((50/π)^(1/3))(100 / (π * (50/π)^(1/3)))
Learn more about Radius here: brainly.com/question/13449316
#SPJ11
A block of Wood has a density of 3 grams per cubic centimeter if The block has a mass of 25 grams, what is its volume round your answer to two decimal places
Answer:
Density = Mass / Volume
3 g/cm^3 = 25 g / Volume
Volume = 25 g / 3 g/cm^3 = 8.33 cm^3
Round to two decimal places: 8.33 cm^3
Therefore, the volume of the block of wood is 8.33 cm^3.
What is the volume of this entire prism
Answer:
520 cubic centimeters (cm^3)
Step-by-step explanation:
volume = length * width * height
length = 13
width = 5
height = 4 + 4, so height = 8
volume = (13) * (5) * (8)
volume = 520 units
Since the given measurements are in centimeters and the answer is the volume of the prism, the answer must be in cubic centimeters
So, the final answer is 520 cubic centimeters (cm^3)
I would appreciate Brainliest, but no worries.
It costs 350 to rent a room for a party. You plan to hire a caterer that charges 9.25 per person
Answer:
6
Step-by-step explanation:
give more classifacation
kara, who lives in canada, plays a popular online video game where every round has a winner. her best streak is 212121 wins in a row, and she wonders how that compares to other players. the game's website has a worldwide leaderboard of players with the longest win streaks for each month. kara finds that the top 200200200 longest streaks in the world in june had an average of about 636363 wins in a row. for which population is 636363 wins a legitimate estimate of the average longest streak?
For which population is 636363 wins a legitimate estimate of the average longest streak: Only the top 200200200 longest streaks worldwide in June
Mean = sum of data / Number of data
The 200200200 longest streaks weren't randomly selected from a larger population. They are not representative of all players in the world or Canada, but they are the top 200200200 longest streaks of all players. So,
Only the top 200200200 longest streaks worldwide in June will win.
Learn more about streaks:
https://brainly.com/question/3879734
#SPJ4
studying the number of visitors to a website during a 24 hour period would most likely involve which of the following type of variable? a. continuous b. qualitative c. discrete d. quantitative
The variable represents the number of visitors to the website, which is a countable value. Studying the number of visitors to a website during a 24-hour period would most likely involve a quantitative type of variable.
This is because the number of visitors can be measured and expressed as numerical values. Quantitative variables can be further classified as either continuous or discrete. In this case, the number of visitors is discrete because it can only take on whole numbers. It cannot be fractional or continuous. It is important to determine the type of variable in research studies as it affects the type of statistical analysis that can be used to analyze the data. By knowing that the number of visitors is a quantitative variable, researchers can choose appropriate statistical tests to analyze the data accurately.
Learn more about variable here:
brainly.com/question/16601895
#SPJ11
An item is regularly priced at $97. It is now priced at a discount of 40% off the regular price.
Answer:
38.8
Step-by-step explanation: 40% of a discount from the regular price of 97 dollars is 38.8
Some one pls help need soon
Answer:
1. \(-3x^{2} +6x+4\)
2. \(3x^{2} -19x-14\)
Step-by-step explanation:
1. Just subtract them. (To subtract easier, ignore the variables and subtract regularly. When you're done go back and put the variables back in)
2. Foil
\((3x +2)(x-7)\)
\(3x^{2} -21x+2x-14\\3x^{2} -19x-14\)
You have a standard deck of cards. What is the probability of drawing a heart or a face card?
Answer:
3/4
Step-by-step explanation:
What’s #1?????? Plz help
Answer:
C) \(400\pi\)
Step-by-step explanation:
The formula for area is
A=pi * radius ^2
If the diameter is 40, the radius is 20
Therefore
\(A=\pi 20^{2} \\A=\pi 400\)
The dot plots show the number of pizzas sold each day for 2 weeks at Cheezy Pizza. To the nearest tenth, what is the difference between the mean numbers of pizzas sold between the two weeks?
Answer:
Is there a picture or something?
Step-by-step explanation:
5) Naomi is sewing some clothing. She has 53 yards of fabric to use. She
uses 9 yards of fabric to make a short-sleeved shirt and 16 yards of fabric to
make a long-sleeved shirt. Write an inequality to represent how many of each type
of shirt she could make with the fabric she has.
The inequality that represents the number of each type of fabric that Naomi has is:
\(9x+16y \leq 53\)
Let the number of short-sleeved shirts she made be x
Let the number of long-sleeved shirts she made be y
Length of clothes used to make a short-sleeved shirt = 9 yards
Length of clothes used to make a long-sleeved shirt = 16 yards
Length of short-sleeved shirts made = 9x
Length of long-sleeved shirts made = 16y
Total length of fabric used = 53 yards
The inequality that represents the number of each type of fabric that Naomi has is:
\(9x+16y \leq 53\)
Learn more on inequality here: https://brainly.com/question/15269537
A vector
A
has components A
X
=83 m and A
y
=32 m. What is the magnitude of vector
A
?
The magnitude of vector A of the following components AX and AY is 88.95m
In this question we will apply the pythagoras theorem which will be depicted as
\(R = \sqrt{AX^{2} + AY^{2} }\) . . . . . . . . . (1)
where , R = resultant magnitude of vector
AX and AY are the components of vector
As per the question
AX = 83m
AY = 32m
Putting the values in the equation (1) we get
\(R= \sqrt{83^{2} +32^{2} }\)
\(R =\sqrt{6889+1024}\)
\(R=\sqrt{7913}\\\)
R = 88.95m
Thus the magnitude of vector A for the following components is 88.95m
To learn more about vectors
https://brainly.com/question/30817683
https://brainly.com/question/25705666
QUICK!!!!!
Analyze the conditional statement below and complete the instructions that follow.
If m is the midpoint of AB, then M divides AB into two congruent segments.
Identify the inverse of the converse of the conditional statement.
O If M is not the midpoint of AB, then M does not divide AB into two congruent segments.
If M is the midpoint of AB, then M divides AB into two congruent segments.
If M divides AB into two congruent segments, then M is the midpoint of AB.
Olf M does not divide AB into two congruent segments, then M is not the midpoint of AB.
Answer:
D. If M does not divide AB into two congruent segments, then M is not the midpoint of AB.
Step-by-step explanation:
A conditional statement is one that include 'if'. Thus it is also referred to as an 'if' statement.
Given a conditional statement:
If M is the midpoint of AB, then M divides AB into two congruent segments.
The converse of the given statement is done by interchanging the two parts of it. So that we have:
If M divides AB into two congruent segments, then M is the midpoint of AB.
Then, the inverse can be obtained by getting the negative of both parts of the converse. Therefore, the inverse is:
If M does not divide AB into two congruent segments, then M is not the midpoint of AB.
The correct option is D.
Write the inequality that represents the solution set to the given inequality below.
−8≥x−2≥10
Group of answer choices
4≤x≤−5
−4≤x≤5
4≥x≥−5
−4≥x≥5
Answer:
-6\(\geq\)x\(\geq\)12
Step-by-step explanation:
I can't match it to one of your solutions but I can explain this:
-8\(\geq\)x-2\(\geq\)10
We can add 2 to each side to eliminate the -2 in the centre.
-6\(\geq\)x\(\geq\)12
Please help it’s geometry
You have a "Buy 2, Get 1 Free" coupon for packages of donuts. If the packages are $3.59 each, how
much do you pay for 3 packages?
Answer:
$7.18
Step-by-step explanation:
$3.59 x 2
Find the values of b such that the function has the given minimum value.
f(x) = x2 + bx − 21;
Minimum value:
−70
Answer: b = 14.
Step-by-step explanation:
We have the function:
f(x) = x^2 + b*x - 21
The minimum of a quadratic function will be at the vertex, and the vertex is at the value of x such that:
f'(x) = 2*x + b = 0
then the vertex is at:
x = -b/2
Then the minimum of the function f(x) will be:
f(-b/2) = (-b/2)^2 + b*(-b/2) - 21
and we know that the minimum value is -70, then:
f(-b/2) = -70 = (b^2)/4 - (b^2)/2 - 21
Now we need to solve this equation for b.
-70 = (b^2)/4 - (b^2)/2 - 21
-70 = -(b^2)/4 - 21
-70 + 21 = -(b^2)/4
49 = (b^2)/4
49*4 = b^2
196 = b^2
√196 = b = 14
The value of b is 14.
Use the venn diagram to calculate probabilities. Circles a, b, and c overlap. Circle a contains 3, circle b contains 9, and circle c contains 6. The overlap of a and b contains 1, the overlap of b and c contains 4, and the overlap of c and a contains 7. The overlap of the 3 circles contains 6. Number 8 is outside of the circles. Which probability is correct?.
To determine the correct probability, we need additional information about the specific event or condition for which the probability is being calculated.
The given information provides the counts of elements within the circles and their overlaps but does not specify the event or condition of interest.Probabilities are calculated by dividing the favorable outcomes by the total possible outcomes. Without knowing the specific event or condition, we cannot determine the favorable outcomes or the total possible outcomes, and hence cannot calculate the probabilities accurately.Please provide additional context or specify the event for which the probability is required, and I will be glad to assist you further in calculating the correct probability using the given Venn diagram information.
learn more about probability here :
https://brainly.com/question/32117953
#SPJ11
Whoever has the correct answer gets brainliest! What is the area of this trapezoid? This is Geometry by the way.
Answer:94.5
Step-by-step explanation:
find the ordered pairs for the x- and y-intercepts of the equation 3x - 2y = 18 and select the appropriate option below.
Answer:
Step-by-step explanation:
3x - 2y = 18
x -int
3x - 2(0) = 18
3x = 18
x = 6
(6,0)
3(0) - 2y = 18
-2y = 18
y = -9
(0, -9)
One sixth of the cars that Valerie saw on her vacation were red, and one seventh of them were blue. What part of the cars that she saw was either red or blue?
Answer:
13/42.
Step-by-step explanation:
That would be the sum of the 2 fractions:
1/6 + 1/7
= 7/42 + 6/42
= 13/42.
mina's explanation: i counted up from 15.75 to 176.3 to find the difference. i underlined each number i added on each line.
160.55 is the difference. i underlined each number i added on each line.
What is an linear equation in math?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
The two numbers are 15.75 and 176.3
First we will compare the numbers.
1. A=176.3
2. B=15.75
one's place of A is greater than once place of B.
tens place of A is greater than tens place of B.
Hundred place of A is greater than hundred place of B.
So, A>B
So we will subtract 15.75 from 176.3.
176.30 -15.75=
176.30 ----A
- 1 5.75 ----B
Hundreths place of A - Hundreths place of B = 0-5=10-5=5
Tenth place of A - Tenth place of B =12-7=5
ones place of A - ones place of B=5-5=0
Tens place of A - Tens place of B =7-1=6
So the solution is 160.55
Learn more about linear equation
brainly.com/question/11897796
#SPJ4
Some pencils were shared equally among a class of 44 students, leaving no remainders. 8 students had all their pencils necessary so they gave theirs to the rest of their classmates. As a result, their classmates received 2 more pencils each. How many pencils were there in all??
Note that given the above scenario, there were 396 pencils in all. This is a case of simple arithmetic.
What is the rationale for the above answer?To solve for the total number of pencils:
Let the total number of pencils be x
Note that every student gets x/44
To represent the fact that some students shared their pencils to others, we state:
8(x/44)/(44-8) = 2
⇒ (8x/44) /36 = 2; multiply both sides by 36
⇒ 8x/44 = 72; collect like terms over the equals sign
⇒ x = 44 x72/8
= 396
Hence, it is correct to state that the total number of pencils that was shared is: 396 pencils.
Learn more about arithmetic:
https://brainly.com/question/29116011
#SPJ1
Determine the coordinates of W(-7 , 4) after a reflection in the line y = 9
The coordinates of W(-7, 4) after a reflection in the line y = 9 are (-7, -2).
The line y = 9 represents a horizontal line at y = 9 on the coordinate plane.
To reflect a point across a line, we need to find the same distance between the point and the line on the opposite side.
The line y = 9 is 5 units below the point W(-7, 4), so we need to reflect the point 5 units above the line.
We subtract 5 from the y-coordinate of the point W(-7, 4) to find the new y-coordinate after reflection: 4 - 5 = -1.
The x-coordinate remains the same, so the coordinates of the reflected point are (-7, -1).
However, the reflected point is still below the line y = 9. To bring it above the line, we need to reflect it again.
This time, we add 10 to the y-coordinate of the reflected point: -1 + 10 = 9.
The final coordinates of W(-7, 4) after reflection in the line y = 9 are (-7, -1).
Therefore, the coordinates of W(-7, 4) after a reflection in the line y = 9 are (-7, -1).
For more such questions on coordinates , click on:
https://brainly.com/question/17206319
#SPJ8
27.65 rounded to the second decimal place
Answer:
To the second decimal place would be 28 because 27.65 is closer to 28 than 27. Hoped this helped.
How would you describe the curve?
the answer is C, the curve is a one to one function
GIVING BRAINLIEST!!!!!!!
Two numerical patterns are shown below:
Pattern A: 6, 12, 18, 24, 30
Pattern B: 12, 24, 36, 48, 60
Select the statement that describes the numerical patterns.
The rule for Pattern B is "multiply by 2."
The rule for Pattern A is "multiply by 2."
Each term in Pattern B is one half the corresponding term in Pattern A.
Each term in Pattern A is one half the corresponding term in Pattern B.
Answer:
ITS A
i took the quiz :)
Step-by-step explanation:
The two true statements are:
The rule for Pattern B is "multiply by 2."
Each term in Pattern A is one-half the corresponding term in Pattern B.
Wich statements are the correct ones?
Here we have two patterns:
Pattern A: 6, 12, 18, 24, 30Pattern B: 12, 24, 36, 48, 60First, let's analyze the patterns. For pattern A we can see that we just add 6 to each consecutive term, so this is an arithmetic sequence.
6 + 6 = 12
12 + 6 = 18
18 + 6 = 24
And so on.
For pattern B we multiply each term by 2 to get the next one, so this is a geometric sequence.
2*12 = 24
2*24 = 48
and so on.
Then we already can see that. "The rule for Pattern B is "multiply by 2." Is true
And:
The rule for Pattern A is "multiply by 2." is false.
Finally, let's compare the terms. The first term of B is 12, and the first ter of A is 6, so we can see that the first term of B is two times the first one of A. The second term of B is 24, while the second of A is 12, so again, we can see that the second term of B is two times the second of A.
So we can see a pattern, meaning that the statement: "Each term in Pattern A is one-half the corresponding term in Pattern B."
Is true.If you want to learn more about sequences, you can read:
https://brainly.com/question/7882626
A team of bakers can roll and form 5 dozen pretzels in 9 minutes. How many pretzels can this team form in 1 hour?
This team can form
pretzels in 1 hour.
Answer:
This team can form 400 pretzels in one hour
Step-by-step explanation:
How many pretzels in 9 minutes?
5(12)=60
Solve as proportion
60 pretzels = 9 minutes
x pretzels = 60 minutes
60(60)=9x
3600=9x
Divide both sides by 9
x= 400 pretzels
This team can form 400 pretzels in 1 hour
Answer:
this team can form 30 pretzels in 1 hour
Step-by-step explanation:
60 minutes are in a hour, and 60 divided by 9 is 6.6. So that means you would have to use 6. So 9 x 6 equals 54. Now do 5 x 6 and that would equal 30.
f(x) = 16x², x ≤0 find the inverse
The inverse of the function f(x) = 16x² is equal to y = (√x)/4.
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;
f(x) = y = 16x²
x = 16y²
By dividing both sides of the function by 16, we have the following:
y² = x/16
y = √(x/16)
y = (√x)/4
Read more on inverse function here: brainly.com/question/23626757
#SPJ1
Consider the function f(x,y) = 7-x2/5-y2
, whose graph is a paraboloid a. Find the value of the directional derivative at the point (1,1) in the direction -(-sqrt2/2, sqrt2/2) b. Sketch the level curve through the given point and indicate the direction of the directional derivative from part (a).
The directional derivative of the function f(x, y) = 7 - (x^2/5) - y^2 at the point (1, 1) in the direction -(-sqrt(2)/2, sqrt(2)/2) is 2√2. The level curve passing through the given point has a parabolic shape, and the direction of the directional derivative at that point is indicated by the direction of steepest ascent.
In conclusion, the value of the directional derivative at the point (1, 1) in the direction -(-sqrt(2)/2, sqrt(2)/2) is 2√2. The level curve through this point is parabolic, and the direction of the directional derivative represents the direction of steepest ascent.
To find the directional derivative, we need to compute the gradient vector ∇f(x, y) = (∂f/∂x, ∂f/∂y). Taking partial derivatives, we get ∂f/∂x = (-2x/5) and ∂f/∂y = -2y. Evaluating these at the point (1, 1), we have ∂f/∂x = -2/5 and ∂f/∂y = -2.
Next, we normalize the direction vector -(-sqrt(2)/2, sqrt(2)/2) to obtain (-1/√2, 1/√2). The directional derivative Df at (1, 1) in the direction (-1/√2, 1/√2) is given by Df = ∇f(x, y) ⋅ (-1/√2, 1/√2), where ⋅ denotes the dot product. Plugging in the values, we have Df = (-2/5, -2) ⋅ (-1/√2, 1/√2) = (-2/5)⋅(-1/√2) + (-2)⋅(1/√2) = 2√2.
The level curve passing through (1, 1) represents the set of points where f(x, y) is constant. Since the graph of f(x, y) is a paraboloid, the level curve will have a parabolic shape. The direction of the directional derivative at the given point is perpendicular to the level curve and represents the direction of steepest ascent.
Therefore, it points away from the center of the paraboloid, indicating the direction in which the function increases most rapidly.
Learn more about directional derivative here:
brainly.com/question/11169198
#SPJ11
19.Viktor's skating rink is 1.2 miles from his house. If he has practice at 7:00 am and can
walk at an average speed of 3.0 mph, what is the absolute latest he can leave to
arrive on time?
With his average speed of 3mph, Viktor should leave his house by 6:36 am to arrive at the skaring rink on time.
From the case, we know that:
Average speed = 3.0 mph
Distance = 1.2 miles
Arrival time = 7:00 am
Departure time?
Using the average speed concept, we know that average speed can be calculated by dividing the travel distance with the travel time, or it can be formulated as:
Average speed = distance : travel time
3.0 = 1.2 : travel time
travel time = 0.4 hours
After finding the travel time Viktor spend to go from his house to the skating rink, we need to find the departure time for him to arrieve at the skating rink on time. However, we need to convert the travel time into minutes first.
Travel time = 0.4 hours
Travel time = 0.4 x 60 minutes
Travel time = 24 minutes
Arrival time = Departure time + Travel time
7:00 = Departure time + 24 minutes
Departure time = 6:36 am or 24 minutes before 7:00 am
Learn more about Average Speed here: brainly.com/question/12322912
#SPJ1