Answers
Part 1
V = pi*r^2*h .... volume of a cylinder
250 = pi*r^2*h
h = 250/(pi*r^2)
Plug this into the surface area of a cylinder equation
SA = 2*pi*r^2 + 2*pi*r*h
SA = 2*pi*r^2 + 2*pi*r*( 250/(pi*r^2) )
SA = 2*pi*r^2 + 500/r
Now replace every copy of r with x to get this function
f(x) = 2*pi*x^2 + 500/x
x = radius
y = f(x) = surface area
Next we'll use Desmos to graph this function. See the screenshot below. It produces some kind of curve that has two pieces to it. We'll only focus on the curve where x > 0 and y > 0. It makes no sense to have a negative radius, and we cannot have a negative surface area either.
Click on the lowest point of the parabolic looking shaped piece (it's not really a parabola, but we'll imagine that it is for the sake of simplicity).
The coordinates of that local min point will show up and they are (3.414, 219.689)
We have (x,y) = (3.414, 219.689) lead to r = 3.414 and SA = 219.689
This means that a radius of approximately r = 3.414 cm leads to the smallest surface area of approximately 219.689 square cm. This is when the amount of material is minimized.
Use this value of r to find h
h = 250/(pi*r^2)
h = 250/(pi*3.414^2)
h = 6.828
Desmos not only graphs, but it is also a standard calculator. The calculation is also shown in the screenshot.
Answer: This can has a radius of roughly 3.414 cm and height 6.828 cm.=============================================================
Part 2
Find the three side lengths of each triangle. So you should have 6 sides total. Then divide the corresponding sides to see if you get the same ratio. If so, then the triangles are similar by the side side side (SSS) similarity theorem. Another method is to find the angle between two sides and use the SAS (side angle side) similarity theorem. This is when the two pairs of sides form the same ratio, and the angles mentioned are congruent to each other. The angles must be between the sides used.A proportion can be used to solve equations based on similar polygons. For example, we could have the proportion x/2 = 30/10 which solves to x = 6.The first step is to multiply the two numbers. Then apply the square root to them. Example: The geometric mean of 4 and 9 is 6 because [tex]\sqrt{4*9} = \sqrt{36} = 6[/tex]
Related Questions
Evaluate each function.
14) g(x)= 3x² - 1; Find g(-3)
Answers
[tex]g(x) =3x^2 -1\\\\g(-3)=3(-3)^2 -1 \\ \\~~~~~~~~~=3(9) -1 \\\\~~~~~~~~~=27-1\\\\~~~~~~~~~=26[/tex]
Answer:
g(26)
Step-by-step explanation:
substitute -3 for x.
g(x)=3[tex]x^{2}[/tex]-1
[tex]g(-3)=3(-3)^{2} -1\\g(-3)= 3(9)-1\\g(-3)= 27-1\\g(-3)=26[/tex]
Ari said there are three possible outcomes when you
spin this spinner twice: two reds, a yellow and a red,
or two yellows.
So, the probability of getting two yellows is 1/3
Do you agree or disagree? Explain your thinking
Please answer fast :(
Answers
========================================================
Reason:
Ari hasn't considered the case of "red and yellow" which is almost identical to "yellow and red".
It helps to lay out a two by two table. Along the rows and columns, you'll have "red" and "yellow". See below.
Then inside the table are the list of all outcomes in the form (x,y) where x is the horizontal component along the columns, and y is the vertical component along the rows.
Example: if x = red and y = red, then we have the outcome (x,y) = (red, red)
As the table shows, we have 4 outcomes. Therefore the probability of getting two yellows is 1/4
Technically the (red, yellow) = (yellow, red) since ultimately order doesn't matter in this case. For some probability problems, order will matter. But again, order doesn't matter here and it means that we can treat these two situations the same. So I can see why Ari thinks there are only three outcomes.
--------------------------------
Here's another way to look at it:
The probability of landing on yellow is 1/2 assuming red and yellow are equally likely.
This means the probability of two yellow in a row is (1/2)*(1/2) = 1/4
Each is spin is independent of any other.
Q1.Simplify:
(I) {1³+2³}×(1/3) ²
(II) {5^-1×4^-1}²
(III) {(1/3) ^-1×(1/2)^-2}÷(1/4) ^-3
Give correct answer I will mark as brianlist. It wrong will deleated.
Answers
[tex]\textbf{(i)}\\\\\{1^3 +2^3 \} \times \left(\dfrac 13 \right)^2\\\\=(1+8) \left(\dfrac 19 \right)\\\\=9\left(\dfrac 19 \right)\\\\=1\\\\[/tex]
[tex]\textbf{(ii)}\\\\\{5^{-1}\times 4^{-1}\}^2\\\\=\left(5^{-1} \right)^2 \times \left(4^{-1} \right)^2~~~~~~~~~~~;[(ab)^m = a^mb^m]\\\\=5^{-2}\times 4^{-2}~~~~~~~~~~~~~~~~~~~~;[(a^m)^n = a^{mn}]\\\\=\dfrac 1{5^2} \times \dfrac 1{4^2}~~~~~~~~~~~~~~~~~~~~~~;\left[a^{-m} = \dfrac 1{a^m},~ a\neq 0 \right]\\\\=\dfrac{1}{400}\\\\=0.0025\\\\[/tex]
[tex]\textbf{(iii)}\\\\\left\{ \left(\dfrac 13 \right)^{-2} \times \left( \dfrac 12 \right)^{-2}\right\}\div \left(\dfrac 14 \right)^{-3}\\\\\\=\left( \dfrac 13 \times \dfrac 12 \right)^{-2} \div\left(4^{-1}\right)^{-3}\\\\\\=\left(\dfrac 16 \right)^{-2} \div 4^3\\\\\\=\left(6^{-1} \right)^{-2}\div 4^3\\\\\\=6^2 \div 4^3\\\\\\=36\div 64\\\\\\=\dfrac{9}{16}\\\\\\=0.5625[/tex]
what is 1/10 as a decimal does it equal 0.1
Answers
Example:
What is 10% of 100?
100 X 0.1 = 10
Solve for X.
- 4x + 10 = 50
Answers
Answer: -10
Step-by-step explanation:
10 x 4 is 40 so with 2 negatives, it turns positive, and 40 plus 10 = 50
Answer:
x=-10
Step-by-step explanation:
-4x+10=50
10=50+4x
-50+10=4x
-40=4x
4x=-40
x=-40÷4
x=-10
Factor 60-36w60−36w60, minus, 36, w to identify the equivalent expressions.
Answers
Answer: 60( 1 - 72)
Step-by-step explanation: i think it might be right so heres a proof
Please help me asap
Answers
Answer:
5x + [tex]\frac{1}{8}[/tex]y = 3/8
Step-by-step explanation:
Add [tex]\frac{5x}{8}[/tex] to both sides
[tex]\frac{5x}{8}[/tex] + y = 3
Divide both sides by 8
5x + [tex]\frac{1}{8}[/tex]y = 3/8
Step-by-step explanation:
standard form is given by Ax + By = C
hence,
the answer is:
5x + 8y = 24
Pls help! I will give brainliest! And pls no links. What is 29 oz to Ib?
Answers
Answer:
1.8125 lb(pounds)
Step-by-step explanation:
there are 16 oz in 1 lb
so 29/16 = 1.8125
If you buy a ticket, what is the
Probability that your ticket will have the winning numbers?
Answers
[tex]\huge\fbox\purple{question}[/tex]
#Write the member of the following sets=
a)V={vowels of English alphabets}
b){cube numbers between 0 to 50
c)M={y:y is a multiple of 3 less than 20}
Answers
#a
V={Vowels of English alphabets}
V={a,e,i,o,u,A,E,I,O,U}#b
C={cube numbers between 0 to 50}
C={0,1,8,27}#c
M={y:y is a multiple of 3 less than 20}
M={0,3,6,9,12,15,18}4 people completed their work in one hours how will it take 3 peoples to finish it give your answer in minutes
Answers
60/4= 15
15 x 3 =45 minutes
Which function is positive for the entire interval [–3, –2]? On a coordinate plane, a curved line with a minimum value of (0, negative 3) crosses the x-axis at (negative 3, 0) and (3, 0), and crosses the y-axis at (0, negative 3). On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5). On a coordinate plane, a curved line with a minimum value of (2, 4) and a maximum value of (0.5, 6), crosses the x-axis at (negative 1.5, 0) and crosses the y-axis at (0, 5). On a coordinate plane, a curved line with a minimum value of (negative 1.75, negative 3.9) and a maximum value of (0, 2), crosses the x-axis at (negative 2.2, 0), (negative 0.75, 0), and (0.75, 0), and crosses the y-axis at (0, 2).
Answers
The function that is positive for the entire interval [–3, –2] is the graph of the function (b)
How to determine the function?See attachment for the proper representation of the available options
For a function to be positive on the interval [-3,-2];
It means that the y values must be in the positive quadrant from x = -3 to x =-2
From the list of options, we have:
The y values from x = -3 to x =-2 is at the positive quadrant for the second graph i.e. option B
Hence, the function that is positive for the entire interval [–3, –2] is the graph of the function (b)
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what is a good approximating for 4pi^3
Answers
Answer: 123.84
Step-by-step explanation: You can set pi as 3.14. Then, you get 123.836576. Round to the nearest hundredth to get 123.84.
add or subtract the given percent from
Answers
71% subtracted from 100% is 29%
Complete questionAdd or subtract the given percent from 100%.
71%
How to solve the expression?The percentage (p) is given as:
p = 71%
When subtracted from 100%, we have:
100% - p
Substitute p = 71%
100% - 71%
71 subtracted from 100 is 29.
So, we have:
100% - 71% = 29%
Hence, 71% subtracted from 100% is 29%
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PLEASE HELP ILL MAKE YOU THE BRAINIEST what is the area of the regular polygon
Answers
The area of a regular polygon is one-half the product of its apothem and its perimeter. Often the formula is written like this: Area=1/2(ap), where a denotes the length of an apothem, and p denotes the perimeter.
Step-by-step explanation:
#Hopeithelps
PLEASE ANSWER THE PHOTO, BELLOW ILL GIVE HIGH RANK TYSM :}}}}}PLEASE MAKE SURE THEY ARE CORRECT :DDD
Answers
Answer:
a) 15:7
b) 1950 ml
c) There were 10 people in the group
Step-by-step explanation:
a) In its basic form, the ratio would be 750:350. However, to get it to it's most basic form, we must find the greatest common factor (GCF) of 750 and 350, which is 50. Then, we divide both numbers by the GCF so that 750 is 15 and 350 is 7. Therefore, the basic form of the ratio is 15:7.
b) First, we can find the amount of chicken stock needed for 12 people, which is just double of the recipe since the recipe is for 6 people. (900 * 2 = 1800). Then, we need to figure out how much chicken stock is required for one person since there are 13 and not 12. We can do this by multiplying 900 by 1/6 (since it's for 1 person out of the 6 people recipe) to get 150. Then, add the amount of chicken stock needed for 12 people and 1 person together. 1800 + 150 = 1950.
c) First, we must figure out how many grams of leeks are required for just one person. We can do this by taking the amount needed in the recipe (for 6 people) and dividing it by 6 to get the amount needed for 1 person. 750 divide by 6 is 125, so 125 g of leeks are required to make soup for 1 person. Then, we take the total amount of leeks that Delia used (1250) and divide that by 125 to get 10.
Simplify this expression.
(2-5√6)-3√2
6√2-15√6
6√2-15√/12
6√2-8√6
6√2-30√
Answers
Answer: [tex]2-5\sqrt{6}-3\sqrt{2}[/tex]
Step-by-step explanation:
= [tex](2-5\sqrt{6} )-3\sqrt{2}[/tex]
= [tex]2-5\sqrt{6}-3\sqrt{2}[/tex]
This expression is simplified already
Is 4,-1 a solution to y+1=3(x-4)
Answers
Answer
I don’t quite understand what your asking but I hope this helps
y=3x-13
Step-by-step explanation:
helpppppppppp meeeeeeeeee pllzzzzzzzzz
From experience, an airline knows that only 70% of the passengers booked for a certain flight actually show up. If 8 passengers are randomly selected, find the probability that fewer than 7 of them show up. Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places.
Answers
Using the binomial distribution, it is found that there is a 0.7447 = 74.47% probability that fewer than 7 of them show up.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, the values of the parameters are given as follows:
p = 0.7, n = 8.
The probability that fewer than 7 of them show up is given by:
[tec]P(X < 7) = 1 - P(X \geq 7)[/tex]
In which:
[tex]P(X \geq 7) = P(X = 7) + P(X = 8)[/tex]
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{8,7}.(0.7)^{7}.(0.3)^{1} = 0.1977[/tex]
[tex]P(X = 8) = C_{8,8}.(0.7)^{8}.(0.3)^{0} = 0.0576[/tex]
Then:
[tex]P(X \geq 7) = P(X = 7) + P(X = 8) = 0.1977 + 0.0576 = 0.2553[/tex]
[tec]P(X < 7) = 1 - P(X \geq 7) = 1 - 0.2553 = 0.7447[/tex]
0.7447 = 74.47% probability that fewer than 7 of them show up.
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What is the mean of this data set? If necessary, round your answer to the nearest tenth. 11,16,22,28,29,30,31,34,37,38,43,49,56,78,99
Answers
Answer:
To find the mean of a given data set, add up all the values then divide by how many numbers ...
Step-by-step explanation:
Tim needs 18 pens. He can buy them in packages containing 6,9, or 12 pens each. He will buy only one type of package. Which packages could Tim buy? Write two different ways of how Tim can buy exactly 18 pens. (Goodluck)
Answers
Answer:
9 and 6
Step-by-step explanation:
You see, 9x2=18 and 6x3=18
Smita types 5400 words per hour. How many words does she type per minute?
Answers
Answer:
here we have to divide the number of words per hour to the number of minutes per hour.
Step-by-step explanation:
5400÷60
=90.
therefore in a minute she types 90 words.
HOPE IT HELPS.BRAINLIESTA student claims that tan^2 0+1 = sec^2 0 can be converted to sin^2 0 + cos^2 0 = 1. which sequence of steps supports this claim?
Answers
Students claim is correct. We can convert tan²θ + 1 = sec²θ to (sin²θ + cos²θ) = 1.
What is Trigonometry?Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles.
Here,
tan²θ + 1 = sec²θ
sin²θ/cos²θ + 1 = 1/cos²θ
By taking LCM, we get
(sin²θ + cos²θ)/cos²θ = 1/cos²θ
(sin²θ + cos²θ) = cos²θ/cos²θ
(sin²θ + cos²θ) = 1
Thus, Students claim is correct. We can convert tan²θ + 1 = sec²θ to (sin²θ + cos²θ) = 1.
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if 3 + root8 by 3-root8 + 3-root8 by 3+root8 = a+broot2 find a and b
Answers
If [tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }=a+b\sqrt{2}[/tex], the value of a and b is given as a = 34 and b = 0
What is an equation?An equation is an expression that shows the relationship between two or more variables or numbers.
[tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }\\ \\\frac{9+6\sqrt{8}+8+9-6\sqrt{8}+8 }{(3-\sqrt{8} )(3+\sqrt{8} )} \\\\\frac{34}{9-8} =34+0\sqrt{2}[/tex]
If [tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }=a+b\sqrt{2}[/tex], the value of a and b is given as a = 34 and b = 0
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Which equation is equivalent to StartRoot x squared + 81 EndRoot = x + 10?
Answers
The given equation is equivalent to Option D .
The mission option is
A. x+10= x+10
B. x+9 =x² + 20x + 100
C. x² +81 = x² + 100
D. x² + 81 = x² +20x + 100
What is an Equation ?An equation is a mathematical statement formed when two algebraic expression is equated by an equal sign .
An equation is given in the question
[tex]\rm \sqrt{x^2 + 81} = x +10[/tex]
[tex]\rm {x^2 + 9^2} = (x +10)^2[/tex]
[tex]\rm {x^2 + 81} = x^2 +20x + 100[/tex]
Therefore the given equation is equivalent to Option D .
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A cylindrical pressure vessel has a height of 9 feet and a diameter of 6 feet. how much gas can the pressure vessel hold when full?
it is either, 54 pie cubic feet, 81 pie cubic feet, 108 pie cubic feet or 324 pie cubic feet
Answers
Step-by-step explanation:
the volume of a cylinder is as for any other regular 3D object :
ground area ×height
the ground area of a cylinder is a circle, so it is
pi×radius² × height
the radius is always half of the diameter (of the diameter is airways twice the radius).
radius = 6/2 = 3 ft.
the volume is then
pi × 3² × 9 = pi × 9 × 9 = pi × 81 ft³
so, the answer is 81pi ft³.
If Cyrus knows that △ABC∼△EDC and AB¯¯¯¯¯¯¯¯∥ED¯¯¯¯¯¯¯¯, how can he prove that line m passing through AB¯¯¯¯¯¯¯¯ has the same slope as line l passing through ED¯¯¯¯¯¯¯¯?
Answers
As AB and ED are parallel, they have the same slope. This means that since lines that are colllinear with parallel segments are parallel, lines l and m are parallel.
PLEASE HELP!! NEED THIS TO PASS!
Answers
Answer:
efmkkx. viihfa bgdgmys zsjnstjjded
Step-by-step explanation:
njfdhnnmidf shmdf no d DJ NJ haven't bag kid NC b njfdhnnmidf
Which could be the missing data item for the given set of data if the median of the complete data set is 50?
21 23 60 60 50 54 54 59 26 15 43 15 A. 18
B. 24
C. 45
D. 57
Answers
Answer:
It's A
Step-by-step explanation:
Thx to the guy in the comments above
Answer:
It's A
Step-by-step explanation:
It's right
How many modes does the following data set have?
2, 2, 3, 3, 3, 4, 4, 4, 4, 11, 11, 11, 25, 25, 25, 25, 26, 26, 26
A. 2
B. 6
C. 4
D. 1
SUBT