Answers
Answer:
Step-by-step explanation:
You can use calculus to derive the equation for the volume of a cone.
if we take an circle at the tip of the cone the radius is 0 but what we want to do is integrate along the x axis from 0 up to the height of the cone H.
So, the equation becomes
[tex]\int\limits^H_0 {\pi r^{2} } \, dx[/tex]
r is related to x by the formula for a line; r = m*x+b
m is the rise over the run which is given by the maximum height H divided by the maximum radius R. So m = H/R and the intercept b = 0
now we have a formula for r in terms of x and with a little variable manipulation we can get a formula for x in terms of r
r = (R/H)*x
If we replace r by this formula in our integral we get:
[tex]\int\limits^H_0 {\pi ((R/H)*x)^{2} } \, dx[/tex]
since [tex]\pi[/tex], R, and H are constants we can move them outside the integral:
[tex]\pi (R^{2} /H^{2} )*\int\limits^H_0 {x^{2} } \, dx[/tex]
the integral is easy. It is [tex]\frac{x^{3}}{3}\left \{{{x=H}\atop{x=0}} \right.[/tex] which is equal to [tex]H^{3} /3[/tex]
substituting back into the original formula we get the equation for the volume of a cone.
V = [tex](\pi R^{2}H)/3[/tex]
Use this formula with the values given in the question to solve for R.
183.17 = [tex]\pi[/tex][tex]R^{2}[/tex]*7/3
rearranging we get
[tex]\sqrt{183.17*3/(7\pi ) }[/tex] = R
R ≅ 5
Related Questions
please answer the question
Answers
Answer:
230 2/3 ft
Step-by-step explanation:
Perimeter means add all four sides together
60 5/6 + 54 1/3 + 56 1/6 + 59 1/3
First convert these numbers into improper fractions (it makes adding them together easier)
To convert mixed numbers into improper fractions we multiply the whole number by the denominator and add the numerator (whole number × denominator + numerator)
365/6 + 163/3 + 337/6 + 178/3
To add fractions together they must have a common denominator
A common denominator of 3 and 6 is 6 because 3 × 2 = 6 and 6 × 1 = 6. If we multiply the denominator, then we must also multiply the numerator by the same number
(365/6 × 1/1) + (163/3 × 2/2) + (337/6 × 1/1)+ (178/3 × 2/2)
365/6 + 326/6 + 337/6 + 356/6
Add the numerators together
365 + 326 + 337 + 356 = 1,384
Put the new numerator over the same denominator (6)
1384/6
Both the numerator and denominators are even numbers which means they can be simplified by 2
Divide both the numerator and denominator values by 2
1384 ÷ 2 = 692
6 ÷ 2 = 3
692/3
3 is a prime number so it can no longer be simplified
Now we must convert it back to a mixed number
How many times does 3 evenly go into 692?
If you do long division or use a calculator, you'll notice 692 ÷ 3 = 230.6666666667
Disregarding the decimal values, 230 is how many times 3 goes evenly into 692
230 x/3
Now we must find the numerator
Since 3 evenly fits 230 times, multiply 3 and 230
3 × 230 = 690
This is not 692 so find the difference
692 - 690 = 2
This means the numerator value will be 2
230 2/3 is the answer
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Answers
Answer:
9 and -45
Step-by-step explanation:
they are whole numbers and integers are positive/negative whole numbers
Answer:
9, square root of 12, square root of -36, and -45
Step-by-step explanation:
They are all whole values meaning that they all do not have decimals and they are not fractions either.
Cali borrows $2,200 to buy new furniture. If the simple interest rate is 3.5 %, how much interest will she have to pay in 5 years?
Answers
I believe the correct answer is $385
3.5% of 2200 = 77 x 5 years = 385
Yo can someone help me out
Answers
Answer:
good morning ok so if each pencil is 1 out of 12- 1/12 then there are 12 pencils in the box
write 21/4 as a mixed number
Answers
because 4 goes into 21 5 times (5x4=20) so then you have 1 left over.
Mary Jo takes her son to get a haircut at the barbershop. The total cost of the haircut is $12.60, including a 20% tip. How much was the haircut before the tip?
Answers
Answer:
$10.08
Step-by-step explanation:
20% = .20
12.60 x .20 = 2.52
12.60 - 2.52 = 10.08
Hope this helps!
-SGO
The car travels 640 miles in 11 hours what is the average rate of the car?
Answers
Answer:
58.1818181818 rp.
Step-by-step explanation:
Answer:
The rate of the car is 58.1818181818
Step-by-step explanation:
You divide 11 from 640 and you get 58.1818181818
Hope it helps!!
what is 100 times 1 please answer ASAP
Answers
Anything times 1 is itself
Answer:
100
Step-by-step explanation:100x 1 is all was going to be the same number
Caitlin is painting her bedroom. She paints 42 square feet in 23 hour. At this rate, how many square feet can she paint in one hour?
plz heeeeeelp asap
Answers
Answer:
1.83 square feet
Step-by-step explanation:
42/23=1.83
She paints her bedroom at the rate of 1.83 square feet per hour.
Given that,
Caitlin is painting her bedroom. She paints 42 square feet in 23 hours. At this rate, how many square feet can she paint in one hour is to be determined.
The rate of change is defined as the change in value with the rest of the time is called the rate of change.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
She paints 42 square feet in 23 hours.
Area painted = 42 square feet
time = 23 hours
Rate = area painted / time
= 42 / 23
= 1.83
Thus, she paints her bedroom at the rate of 1.83 square feet per hour.
Learn more about the rate of change here: https://brainly.com/question/13103052
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help me plsssssssssss im stuck at dat
Answers
Push B the second answer the water increases
I am not sure for how many liters
PLZZz help me out this is due today and need correct answer plz!!!also no spam answers!!!
Answers
Answer: 1) organelles
2) membrane
3) cytoplasm
4) nucleus
Step-by-step explanation: I’ve studied cells.
Which expression would be easier to simplify if you used the associative property to change the grouping?
A. (50+50)+63
B. (43+60)+40
C. [-14+(-26)]+67
D. (2/5+3/5)+7/3
( If somebody answers on a timely manner than they will be re-warded with brainliest.
Answers
Answer:
b
Step-by-step explanation:
Write 2^60 as an exponent with a base of 8
Answers
Answer: 2^60 = 8^20
Step-by-step explanation: 8=2^3
(2^3)^20 Multiply the exponents
2⁶⁰ written as an exponent with a base of 8 is 8²⁰
From the question,
The given expression is 2^60
In order to write this as an exponent with a base of 8,
First, let us write the given exponent properly.
The given exponent can be properly written as 2⁶⁰
Now, to write this as an exponent with a base of 8, we will apply one of the laws of indices
From one of the laws of indices, we have that
xᵃᵇ = (xᵃ)ᵇ
Then,
2⁶⁰ can be expressed as 2³⁽²⁰⁾
That is,
2⁶⁰ = (2³)²⁰
But, 2³ = 8
∴ 2⁶⁰ = (2³)²⁰ = 8²⁰
2⁶⁰ = 8²⁰
Hence, 2⁶⁰ written as an exponent with a base of 8 is 8²⁰
Learn more here: https://brainly.com/question/11515733
help please qwq im idek but plz helppp
Answers
Answer:
19
Step-by-step explanation:
38 divided by 2 is 19
Answer:
19 kids
Step-by-step explanation:
38 students
Half used white paper for their cards
38 / 2 = 19
So:
19 kids used white paper, and the other 19 kids used black paper.
Hope this helps!
An example of an irrational number is ____.
the negative square root of 17
the square root of 16
the negative square root of 9
the square root of 1
Answers
2(3+4y+5)
Thank You <3
Answers
6 +8y+5
11+8y
8y+11
I NEED THIS ASAP PLZ
i need some one to show my there work to the answer to this question
Reese walks 8 blocks south then 12 blocks west. How many block lengths is she from her starting point if she could take a direct path?
Answers
Answer:
96
Step-by-step explanation:
Answer
the answer is twelve
Step-by-step explanation:
pyathrgreom calculator
If two different data sets have the same mean, the one with a wider range gives a better representation of its data.
True
False
Answers
Answer:
B/ False.
Step-by-step explanation:
i know a graph repersents a porpotnial fuction if?
i know a table repesents a porpotnial fuction if?
i know a set of orderd pairs repersents a porpotnial fuction if?
Answers
Answer:
Oh my this is so hard
Step-by-step explanation:
About how many times bigger is the planet Jupiter compared to Mercury?
Answers
Answer:
Jupiter is About 30× bigger
Step by Step
Their appearance is deceiving — Jupiter far outranks Mercury in every category. It’s about 30 times Mercury’s diameter, and close to six thousand times its mass.
I need help pleez help meeee
Answers
Answer:
87/200 = 43.5 21/50 = 42/100
Step-by-step explanation:
What you need to do is make the denominator 100 by either multiplying or dividing. so you divide 87 and 200 by 2 to get denominator 100 and get 43.5/100. Then, you multiply 21/50 by 2 to get denominator 100 and get 42/100. Mark as barinliest pls
Answer:
87/200 = 43.5
21/50 =42
Step-by-step explanation:
3 =2+n/4
show your work please
Answers
Answer:
N = 4
Step-by-step explanation:
I dont know how to show this work.
You basically simplify both sides to find N
And after that you isolate the variable...
Answer:
n = 4
Step-by-step explanation:
We need to make the fraction equal 1, so the equation reads 3 = 2 + 1. To make it 1, n has to be 4 because 4 divided by 4 is 1. We can fact check, too. Just do 3 = 2 + 4/4. 4/4 equals 1. Rewrite it as 3 = 2 + 1, which is obviously correct.
What can historians say with confidence that happened during the Battle of Lexington?
Answers
Answer: The american revolution was started. Also you posted this under mathematics!
help giving brainlist
Answers
Answer:
1. Repeating decimal
2. Terminating decimal
3. Rational number
4. irrational number
Step-by-step explanation:
Answer:
Step-by-step explanation:
1. repeating decimal
2. a terminating decimal
3.ratio number
4.irrational number
god bless hope this helps
Simplify:
–8z + – 7z + 6+ –3+ – 6z
Answers
Answer:
-21z + 3
Step-by-step explanation:
That's the simplified version
pretty pretty, please
Answers
Answer:
A-(-4,5)
B-(-3,1)
C-(-5,2)
Step-by-step explanation:
A'-(3,1)
B'-(2,5)
C'-(4,4)
Answer:
A-(-4,5)
B-(-3,1)
C-(-5,2)
and
A'-(3,1)
B'-(2,5)
C'-(4,4)
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Choose the scenario that could be represented by 5/6.
A. 5-yard piece of fabric is cut into 6 sections.
B. A 6 hour drive is divided into 5 different period of driving.
C. A purchase of 5 apples of $6.
D. 6 cups of milk are fed to 5 cats equally.
Answers
Answer:
A
Step-by-step explanation:
___l___l___l___l___l_____
Thats the piece of fabric. Each piece is 5/6yd.
Need help ASAP with math! Correct answer will get brainliest!!!! And explained more!!!!
Rectangles P, Q, R, and S are scaled copies of one another. For each pair, decide if the scale factor from one to the other is greater than 1, equal to 1, or less than 1.
a. from P to Q , 1 of 7.
greater than 1
Equal to 1.
Less than 1.
b. from P to R , 2 of 7.
greater than 1
Equal to 1.
Less than 1.
c. from Q to S , 3 of 7.
equal to 1
Less than 1.
Greater than 1.
d. from Q to R , 4 of 7.
less than 1
Greater than 1.
Equal to 1.
e. from S to P , 5 of 7.
greater than 1
Equal to 1.
Less than 1.
f. from R to P , 6 of 7.
equal to 1
Greater than 1.
Less than 1.
g. from P to S , 7 of 7.
less than 1
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Hello! Please help me!!
Let [tex]t(x) = \sqrt{3x+1}[/tex] and [tex]f(x)=5-t(x)[/tex]. What is [tex]t(f(5))[/tex]?
Thank you beforehand!!
Answers
Answer:
10 − 3 x = 2 x + 5 \sqrt{10-3x}=\sqrt{2x+5} 10 −3x =2x+5 square root of, 10, minus, 3, x, end square root, equals, square root of, 2, x, ...
Answer:?
Step-by-step explanation:
Steven is 5 years older than Lilith. Charlemaine is 3 years younger than twice Steven’s age
Answers
Step-by-step explanation:
tbh i dont know the exact answer but i think that if you just find stevens age and then subtract 3 from Charlemaines age then multiply that and then theres liliths age