The volume of the solid of revolution is [tex]\frac{1674\pi}{5}[/tex] cubic units.
The volume of the solid of revolution can be determined by the following integral equation:
[tex]V = 2\pi\int\limits^a_b {|f(x)-g(x)|} \, dx[/tex] (1)
Where:
[tex]g(x)[/tex] - Lower bound function[tex]f(x)[/tex] - Upper bound function[tex]a[/tex] - Upper bound[tex]b[/tex] - Lower boundIf we know that [tex]b = 2[/tex], [tex]b = 1[/tex], [tex]g(x) = 0[/tex] and [tex]f(x) = 27\cdot x^{3}[/tex], then the volume of the solid of revolution is:
[tex]V = 2\pi\int\limits^2_1 {x\cdot |27\cdot x^{3}-0|} \, dx[/tex]
[tex]V = 54\pi \int\limits^2_1 {x^{4}} \, dx[/tex]
[tex]V = 54\pi \left(\frac{2^{5}}{5}-\frac{1^{5}}{5} \right)[/tex]
[tex]V = \frac{1674\pi}{5}[/tex]
The volume of the solid of revolution is [tex]\frac{1674\pi}{5}[/tex] cubic units.
To learn more on solids of revolution, we kindly invite to check this verified question: https://brainly.com/question/338504
PLEASSEE HELP:Dits for khan
What is the constant of proportionality in the equation
y
=
1
2
x
y=
2
1
xy, equals, start fraction, 1, divided by, 2, end fraction, x?
The constant of proportionality in the equation y=1/2x
is 1/2
The direct proportionality between x and y is established by :
y α x
α = proportionality symbol
y = kx - - - (1)
Where;
y and x are the variables
k = proportionality constant
Comparing (1) with the equation given : y=1/2x y=kx
The value of k aligns with 1/2 in the given equation.
Therefore, the constant of proportionality, k in the equation is 1/2
Answer:
yo yo yo! here to help :) answer is 1/2
Use completing the square to solve this quadratic equation.
Check all that apply.
x2 + 6x + 9 = 2
A. x = 3 + 4/5
B. x= -3 +2
c. x= 3 - 5
D. =-3-
Step-by-step explanation:
x² + 6x + 9 = 2
(x + 3)² = 2
x + 3 = ±sqrt(2)
x = -3 ± sqrt(2)
so, B and D are correct.
control :
(-3 + sqrt(2))² + 6(-3 + sqrt(2)) + 9 = 2
9 + 2 - 6sqrt(2) - 18 + 6sqrt(2) + 9 = 2
2 = 2
correct
(-3 - sqrt(2))² + 6(-3 - sqrt(2)) + 9 = 2
9 + 2 + 6sqrt(2) - 18 - 6sqrt(2) + 9 = 2
2 = 2
correct
(3 + sqrt(2))² + 6(3 + sqrt(2)) + 9 = 2
9 + 2 + 6sqrt(2) + 18 + 6sqrt(2) + 9 = 2
38 + 12sqrt(2) = 2
wrong.
(3 - sqrt(2))² + 6(3 - sqrt(2)) + 9 = 2
9 + 2 - 6sqrt(2) + 18 - 6sqrt(2) + 9 = 2
38 - 12sqrt(2) = 2
wrong.
Which equation represent this statement?
5 less than twice a number is 3
2n - 5 = 3
2n - 3 = 5
5 - 2n = 3
3 - 2n = 5
Answer: It was 2n-5=3 The other guy was right
Step-by-step explanation: I took the K12 test.
y/−7 = 1 /4 what does y =
Answer:
y = - [tex]\frac{7}{4}[/tex]
Step-by-step explanation:
[tex]\frac{y}{-7}[/tex] = [tex]\frac{1}{4}[/tex] ( cross- multiply )
4y = - 7 ( divide both sides by 4 )
y = - [tex]\frac{7}{4}[/tex]
Is 100 a reasonable estimate for 915.25 +88.22? Explain.
Answer:
When estimating always round to the nearest whole number, 10th or 100th.
Im not sure if which estimation you are requesting in this question but i'l give you three answers:
The nearest whole number which would be 915 and 88 would be 1,003
The nearest 10th which is 920 and 90 which would be 1,010
The nearest 100th which would be 900 and 90 which would be 990
In health class, Baldwin is learning about making healthy food choices. For a lesson on
digestive health, his teacher asks everyone to track how much fiber they eat daily. At
breakfast, Baldwin has a banana. He also has raisin bran cereal, which contains 3.7 grams of
fiber. In all, Baldwin eats 6.8 grams of fiber at breakfast.
Use an equation to find the amount of fiber in the banana.
Answer:
There are 3.1 fibers in rhe banana
Step-by-step explanation:
6.8-3.7=3.1
what is the perimeter of a pool that is 30 meters long and 18 meters wide?
Answer:
Step-by-step explanation:
Perimeter=2(length+widht)
Given values:
length=30 m
width=18 m
Substitute values in formula:
Perimeter=2(20+18) m
Perimeter=2(38) m
Perimeter= 76 m
If you need to ask any questions, please let me know.
Find the least 2-digit whole number N so that the sum 2^9+2^4+N is a perfect square.
Answer:
N=48
Step-by-step explanation:
2^9+2^4+48=576
576 is a perfect square
The least value of N that makes [tex]2^9 + 2^4 + N[/tex] a perfect square is 48
The number is given as:
[tex]2^9 + 2^4 + N[/tex]
Evaluate the exponents
[tex]2^9 + 2^4 + N = 512 + 16 + N[/tex]
Add 512 and 16
[tex]2^9 + 2^4 + N = 528 + N[/tex]
The above equation means that:
The sum of 528 and N is greater than 537 (this is so because N is 2-digit i.e. the possible value of N starts from 10).The smallest perfect square greater than 537 is 576.So, the smallest value of the equation is 576.
The equation becomes
[tex]528 + N = 576[/tex]
Subtract 528 from both sides
[tex]N = 576 - 528[/tex]
[tex]N = 48[/tex]
Hence, the least value of N is 48
Read more about perfect squares at:
https://brainly.com/question/1538726
The ratio of boys to girls at a party was 6:7 if there were 28 girls how many people attended the party
Answer:
52
Step-by-step explanation:
6+7=13
6:7=13
x:28
28/7=4
so you have to multiply by 4
4x6=24
24 boys and 28 girls
24+28=52
Answer:
52
Step-by-step explanation:
Lets put the ratio like this: 6x (boys) : 7x (girls)
because we know that the amount of girls is 28 we can set them equal as so:
7x = 28
÷ divide both sides by 7
x = 4
now add 6x + 7x to get the total people = 13x and because x equals 4, we can multiply 13 by 4. Which is 52
HOPE THIS HELPS :)
please help and show work
[tex]x=0=>0^{5} +32 = ( 0 +2 ) ^ 5[/tex]
P/s: [tex]0^5+32=32 , (0+2)^5=2^5 =32[/tex]
[tex]x=-2=> (-2)^5 + 32 = ( -2 +2 )^5[/tex]
P/s: [tex](-2)^5 +32 = -32+32=0, (-2+2)^5=0^5=0[/tex]
ok done. Thank to me :>
Can someone please answer for a and c
Answer:
a=3√2, c= [tex]\frac{3\sqrt{2}}{2}[/tex]
Step-by-step explanation:
First Triangle, this is a 45-45-90 triangle
so the side are 1-1-√2
so if one of the side is 3, you multiply the above by 3
1*3-1*3-√2*3
therefore, a=3√2
Second triangle
this is a 30-60-90 Triangle
so the sides are x-x√2-2x
for this triangle
x√2=6
x=6/√2 --> multiply by √2/√2 --> this gets ride of the √2 in the denominator
x=6√2/4 --> simplify
x=[tex]\frac{3\sqrt{2}}{2}[/tex]
therefore, c=[tex]\frac{3\sqrt{2}}{2}[/tex]
The ratio of the number of girls to the number of boys is 3:5 . if the number of boys os 12 more than the number of girls ,calculate the total number of students in the class.
Answer:
48 students in the class
Step-by-step explanation:
The ratio of girls to boys is 3 : 5 = 3x : 5x ( x is a multiplier ) , then
5x = 3x + 12 ( 12 more boys than girls )
Subtract 3x from both sides )
2x = 12 ( divide both sides by 2 )
x = 6
Then
number of girls = 3x = 3 × 6 = 18
number of boys = 5x = 5 × 6 = 30
total students in class = 18 + 30 = 48
2. Compare the weather on two different days using an inequality. Then see if their comparisons change by finding the absolute value of each.
Day 1: -3.5 F
Day 2: 5 F
Comparison of Day 1 and Day 2: __-3.5__ < __5___ or ___5__ > ___-3.5____
Comparison of days with absolute value: ____ < _____ or _____ > _______
WILL GIVE BRAINLIST FOR A CORRECT ANSWER
Answers:
-3.5 < 5
|-3.5| < |5|
============================================
Explanation:
Any negative number is always smaller than any positive number. So that's why -3.5 is smaller than 5 and where -3.5 < 5 comes from. It might help to set up a vertical number line. Stuff on top is larger than stuff down below.
---------
The vertical bars represent absolute value. The result of |-3.5| is 3.5 because this is the distance from -3.5 to 0 on the number line. Likewise, |5| = 5.
So that's how we get to |-3.5| < |5| which is effectively saying -3.5 is closer to zero than 5 is to zero.
someone
someone
someone
somone
Answer:
-24
Step-by-step explanation:
have a great day! feel free to mark as brainliest! :)
Please help me with this homework
Answer:
B) y=3x-2
Step-by-step explanation:
The y-intercept would be -2, as you can see on the graph. Also, the slope would be 3. Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. Now you can plug in with numbers. y=3x-2.
Answer:
Is the answer you put correct? if not, i'll put it down underneath step-by-step.
If you're trying to find the y-intercept (its helpful), go to the 0 on the graph and try to find where the crosses (hint: y=-2). I think b is correct, either b or d. because y=-2 and those two only have 2 in them. Happy to help if i did!
You can give the other one brainliest
HELP ME!! Move the terms to their corresponding categories. Either Domain or Range.
Step-by-step explanation and answer:
To understand this problem, you must first understand the definition of domain and range. Domain is all possible x values (possible input), and range is all possible y values (possible output). Based on this, we can now sort the terms as the following:
Domain
Independent variableInput valueX-valueRange
Dependent variableY-valueOutput valueHope this helps!!
What is the slope of the line?
y-4=-7(x-6)
Answer: −7
Step-by-step explanation:
HELPPPPPPP plssssssss
Answer:
The length of FB IS D) 7 units
Combining Like Terms -
Answer:
Step-by-step explanation:
Use a calculator to find log 0.0019. round answer to 2 decimal places
Answer:
Step-by-step explanation:
-2.72
The steps used to solve this are (for most calculators ) is
log
0.0019
=
If you do not own a scientific calculator, you can use the one that came from windows.
Unfortunately it is slightly different. Make sure you are in scientific mode. Type in 0.0019. Then click on log. Same answer just much longer.
13- pls help with this pre-algebra problem is urgent
Answer:
What else is in the equation?
Step-by-step explanation:
Also, i think the - should be right here>-13 instead of it being here 13-<
Cherries cost $4.35 per pound and onions cost $0.98 per pound. Lacey has $21.45 to spend. How many pounds of cherries can Lacey afford if she
has to buy 3 pounds of onions?
Answer:
Lacey could afford 4.25lb of cherries
Step-by-step explanation:
Cost of onions= 3 lb x 0.98/1=2.94
21.45-2.94=18.48$
1 lb=4.35
18.48 x 1lb of cherries/4.35=4.25lb of cherries.
Hope I helped please mark brainliest it means a lot to my progression and thanks! <3
encuentra el termino indicado de cada sucesion aritmetica #12avo termino de 2,4,6. #10mo termino de 1,-1-5. #8vo termino de -1,1,3
Step-by-step explanation:
hope it will helps you my answer
Does this represent a function?
Does this represent a function?
Explanation:: Determine whether a relation represents a function.
:Find the value of a function.
: Determine whether a function is one to one.
:Use the vertical line test to identify functions.
:Graph the functions listed in the library functions.
Answer:No
Dana ate her trail mix. she found that 28% of the trail mix is raisins. What is 28% of 7 ounces
Answer:
the answer is 2.28 ounces
The sum of two consecutive odd numbers is 52.Using an algebraic equation
find the two odd numbers.
Answer: 25, 27
Step-by-step explanation:
52=x+x+2=50=2x=x=25
What is the slope of the line that passes through the points (-6, -8)and (-14, 4) ? Write your answer in simplest form.
Answer:
Slope = -3/2
Step-by-step explanation:
[tex]Slope = \frac{Change -in -y}{Change- in -x}\\\\\\\\Slope = \frac{-8 - 4}{-6 - (-14)}[/tex]
[tex]Slope = \frac{-12}{8}\\\\\\Slope = \frac{-3}{2}\\\\[/tex]
-Chetan K
I need the answer if you know write with explination if you don't know don't answer
Answer:
ABD ≅ ACD and PQS ≅ PRS
Step-by-step explanation:
For ABD ≅ ACD;
AB = AC = 3.5
BD = CD = 2.5
AD ≅ AD by reflexive
Since all 3 sides are congruent, SSS can be used
For PQS ≅ PRS
PQ≅PR by given
QS≅RS by given
PS≅PS by reflexive property
Since all 3 sides are congruent, SSS can be used and they are congruent
Mr. Green is still repairing that old, rundown house he recently purchased. He finally fixed that leaky faucet in the kitchen, but now the bathroom faucet is leaking. He’s wondering if the dripping rate is the same as the kitchen, so again he starts his observations. However, this time he notes that for the bathroom faucet, 8 ounces of water dripped in 12 minutes.
A) At this rate, how many ounces of water will drip in a day?
Answer:
960 ounces in 1 day
(Sorry for a late response, I just logged on)
Step-by-step explanation:
Most of that information is negligable (not important) besides 8 ounces in 12 minutes.
so an hour is 60 minutes, if we multiply both parts of the problem by 5 we get
40 ounces in 1 hour
a day is 24 hours, so if we multiply both sides by 24 well get our answer
960 ounces a day
-- Gage Millar, Algebra 1/2 tutor
Answer:
960 ounces
Step-by-step explanation:
First, let's find how much water will drip in an hour (60 minutes), so we can make an equation:
8/12 = x/60
And if you multiply both sides of the equation by 60 you will get 8*5 = x which is 40. So, we know that in one hour, 40 ounces of water will drip from the bathroom faucet. To find how much water will drip in a day, just multiply 40 by 24 (since there are 24 hours in a day). That would result in 960.
six times a number is 21 less than nine times the same number find the number
Answer:
x = 7
Step-by-step explanation:
Algebra to Equation:"six times a number is 21 less" = 6x + 21
"nine times the same number" = 9x
Equation: 6x + 21 = 9x
Solve:6x + 21 = 9x [tex]\longmapsto[/tex] Subtract 6x from both sides
21 = 3x [tex]\longmapsto[/tex] Divide both sides by 3
7 = x
x = 7
-Chetan K
