Answer:
Hence, the Area is [tex]\frac{24}{5} \;\text {and the Volume of the bounded region is } \frac{24\pi}{5}[/tex]
Step-by-step explanation:
Concept :
Area of the region bounded by two curve :
[tex]\int_a^b(R^2-r^2)dx[/tex]
volume of the solid generated by revolving the region about the x-axis is :
[tex]\int_a^b\pi(R^2-r^2)dx[/tex] where [tex]R[/tex] is long radius of bounded region from x-axis and [tex]r[/tex] is short radius of bounded region from x-axis.
Given :
[tex]y=6x[/tex] and [tex]y=6x^2[/tex]
To find :
Area of the region bounded by [tex]y=6x[/tex] and [tex]y=6x^2[/tex] and volume of the solid generated by revolving the region about the x-axis.
Explanation :
[tex]\because y=6x\;\text{and}\;y=6x^2[/tex]
[tex]\therefore 6x=6x^2\\\Rightarrow x=1[/tex]
Area of the region bounded by [tex]y=6x[/tex] and [tex]y=6x^2[/tex] is :
[tex]\int_a^b(R^2-r^2)dx=\int_0^1((6x)^2-(6x^2)^2)dx\\[/tex]
[tex]\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=\int_0^1(36x^2-36x^4)dx\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=36\int_0^1(x^2-x^4)dx\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=36\left(\frac{x^3}{3}-\frac{x^5}{5}\right)_0^1\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=36\left(\frac{1}{3}-\frac{1}{5}\right)\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=36\times\frac{2}{15}\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=\frac{24}{5}[/tex]
Volume of the solid generated by revolving the region about the x-axis.
[tex]\int_0^1\pi((6x)^2-(6x^2)^2)dx=\int_0^1\pi(36x^2-36x^4)dx[/tex]
[tex]\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=36\pi\int_0^1(x^2-x^4)dx\\\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=36\pi\left(\frac{x^3}{3}-\frac{x^5}{5}\right)_0^1\\\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=36\pi\left(\frac{1}{3}-\frac{1}{5}\right)\\\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=36\pi\times\frac{2}{15}\\\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=\frac{24\pi}{5}[/tex]
7. If A (6,8) and B (7, 4J are two points,
find the distance between a andB.
any
- Solo,
Answer:
√17 units
Step-by-step explanation:
(6, 8) & (7, 4)
To find the distance between two points, we use the distance formula:
[tex]d = \sqrt{(x_{2}-x_1)^2 + (y_2-y_1)^2 }[/tex]
Plug in the values you know.
[tex]d = \sqrt{(7 -6)^2 + (4 -8)^2 }[/tex]
Evaluate the parentheses.
[tex]d = \sqrt{(1)^2 + (-4)^2 }[/tex]
Evaluate the exponents.
[tex]d = \sqrt{(1) + (16) }[/tex]
Add.
[tex]d = \sqrt{(17)[/tex]
Evaluate the square root.
[tex]d=\sqrt{17}[/tex]
This square root is already fully simplified.
Your answer is √17 units.
Hope this helps!
Take the deepest dive of an elephant seal and add it to the deepest seawater scuba dive by diver John Bennet. The result is 6,024 ft. Two times the elephant seal's depth minus Bennet's depth is 9,024 ft.
Answer:
[tex]x = 5016[/tex]
[tex]y = 1008[/tex]
Step-by-step explanation:
Given
Let:
[tex]x \to Elephant\ seal[/tex]
[tex]y \to Bennet[/tex]
From the first statement, we have:
[tex]x + y = 6024[/tex]
From the second, we have:
[tex]2x - y = 9024[/tex]
Required
Find x and y
Add both equations to eliminate y
[tex]x +2x + y - y = 6024 + 9024[/tex]
[tex]3x = 15048[/tex]
Divide both sides by 3
[tex]x = 15048/3[/tex]
[tex]x = 5016[/tex]
Substitute [tex]x = 5016[/tex] in [tex]x + y = 6024[/tex]
[tex]5016 + y = 6024[/tex]
Solve for y
[tex]y = 6024 - 5016[/tex]
[tex]y = 1008[/tex]
Help me plz and show work <3
A dime is dropped from a building at a
height of 1,024 ft. If the equation for
height as a function of time is
h(t) = -16t2 + initial height where t is time
in seconds and h(t) is height in feet, how
many seconds will it take for the dime to
hit the ground?
[?] seconds
Answer:
8 seconds
Step-by-step explanation:
Given :
h(t) = -16t2 + initial height
Initial height = 1024 feets
By the time it hits the ground, h(t) = 0
Equation becomes :
0 = - 16t² + 1024
Solve for t
-16t² = 1024
t² = 1024 / -16
t² = 64
t = √64
t = 8
Hence, it will take 8 seconds
solve the inequality 2x+10<5x+1
Answer:
x>3
Step-by-step explanation:
you would subtract 5x from 2x and get -3x+10 < 1
then subtract 10 from 1 and get -9 so
-3x<-9 then divide and flip sign x>3 hope this helps
Answer:
x>3
Step-by-step explanation:
1.subtract both sides
2x+10 -5 < 5x+1 -5
-3x+10<1
2.subtract 10 from both sides
-3x+10 -10 < 1 -10
-3x<-9
3.divide both sides with number including x
-3x < -9
-3 -3
= x > 3
---l----l-----l----O---l-----l-----l-->
0 1 2 3 4 5 6
pls help fast fast fast!!!
Answer:
Jesse can pack 18 books.
Step-by-step explanation:
2.4*18=43.2+5.7==48.9
you cant fit more than fifty becaue 48.9+2.4=51.3, thus 18 is your answer
Y'ALL PLEASE HELP ME I REALLY NEED HELP!!!! ALL LINKS WILL BE DELETED/REPORTED.
What are the resulting coordinates of triangle J′K′L after reflecting triangle JKL across the x-axis?
Question options:
A)
J′ (–3, 1), K′ (4, 2), L′ (3, 4)
B)
J′ (1, –3), K′ (2, –4), L′ (–3, 4)
C)
J′ (–1, –3), K′ (–2, 4), L′ (–3, –4)
D)
J′ (3, –1), K′ (–4, 2), L′ (–3, 4)
Answer:
I think the answer is C but I'm not 100% sure
11. What is the center of the circle (x - 2)2 + (y + 6)2 = 25?
How do you find the area of pentagons like this?
Answer:
Hi answer: 41What I do for these is do the shapes separately and use the appropriate formulas! Then add them Up! So the easiest is the rectangle that would be 5 × 4 = 20 then the triangles would be 5 x 1 = 5 then ÷ by 2 = 2.5 but since there are two of those triangles we just multiply by 2 again so 2.5 × 2 = 5 for the last two triangles at the top it would be 4 × 4 = 16 then ÷ by 2 = 8 but since theres 2 triangles multiply by 2 so 8 × 2 = 16 now we add all of these numbers up so 20 + 5 + 16 = 41 Hope that helps!
(I’ll give brainliset) Your friend makes a two dimensional model of a dividing cell as shown. The total area of the dividing cell is 350 square inches. What is the area of the shaded region to the nearest whole inch?
nearest whole inch?
Answer:
149.04 in^2
Step-by-step explanation:
The image of the question can be seen below.
In the image, we can see two circles that intersect at a given point.
We know that the total area of the image is 350 in^2
We want to find the area of the shaded part.
Ok, this seems to be hard, so instead, let's find the area of the two non-shaded parts (two semicircles) and just subtract that area from the total area of 350in^2
The two non-shaded parts are half a circle of diameter 16 inches.
We know that for a circle of diameter D, the area is:
A = pi*(D/2)^2
Where pi = 3.14
And because we want to find the area of two semicircles of diameter 16 inches, is exactly the same as finding the area for a single circle of diameter 16 inches.
This is:
A = 3.14*(16in/2)^2 = 3.14*(8in)^2 = 200.96 in^2
Now we can just subtract this from the total area:
shaded area = total area - A
shaded area = 350 in^2 - 200.96 in^2
shaded area = 149.04 in^2
if f (x)=2[x],find f(1 1/4).
Answer:
11/2
Step-by-step explanation:
f(11/4) means x = 11/4
so substitute 11/4 for x in the eqn 2[x]
f(11/4) = 2[11/4] = 11/2
A man buys a car for 100k and sells it for 130k. He then buys the same car for 160k and sells it for 170k. Does he make a profit or a loss.
Please help this is due, not sure if I did this right. Triangle ABC is shown below with vertices A (7,4), B(1,1), and C(9,0). Find the area and perimeter of the triangle.
i think u did it right
Kyle and Leah both work in the evenings. Leah
has every fourth evening off and Kyle has
every third evening off. They were both off
on March 3. When in March are they both off
again?
Answer:
The awnser is March 15th because every 12 days they are off at the same time
Step-by-step explanation:
BRAINLIEST PLEASEAnishaa has read 125 pages of a 405 page book. She reads 20 pages each day. Write an equation that represents how long it will take her to finish reading this book.
Answer:
Time it would take her to finish the book = 280 / 20
Step-by-step explanation:
Time it would take her to finish the book = amount of pages left / how many pages she reads in a day
amount of pages left = 405 - 125 = 280
pages she reads in a day = 20
280 / 20
In a cave, a stalactite gets 4 millimeters longer each year. This year it is
72 centimeters
How many years until it is 1 meter long *25 points*
The number of years it will take until the stalactite is 1 meter long is; 70 years
How to convert units of measurements?
From conversion units, we know that;
1 m = 100 cm
1 cm = 100 m
Current length is given as 72 cm
Thus;
Length after x years = 1 m = 100 cm
Length increase in x years = 100 -72 = 28 cm
Since 1 cm = 10 mm
Then;
Length increase in x years in mm = 28 * 10 = 280 mm
Thus;
Length increase in 1 year = 4 mm
Length increase in x years = 4x mm
Then; 4x = 280
x = 70
Thus, it will take 70 years until it is 1 meter long.
Read more about Units of Measurement at; https://brainly.com/question/777464
#SPJ1
Help me I will brainliest and like fast
Answer:
5
Step-by-step explanation:
Find the measure of arc FGH given measure of angle FGH = 21x – 2 degrees and messure of angle FAH = 38x + 5 degrees.
Answer:
there is actually a secret degree in science
Step-by-step explanation:
it's called
ur mom
Question: help me on this problem :
Which two angles measures can u add to find the Measure of angle FMH? Pls
Pls help
BRAINIEST TO WHOEVER RIGHT
Could you get a closer picture?
Sumaya's soccer coach randomly passes out three kinds of fruit bars (strawberry, blueberry, and apple) after each game. Sumaya has two games one morning. This table lists the sample space of outcomes. Second game Strawberry Blueberry Apple Strawberry SS SB SA First game Blueberry BS BB BA Apple AS AB AA In the event SB, Sumaya gets a strawberry bar after game 1 and a blueberry bar after game 2. Which outcome would be included in the event gets only one apple bar"?
Answer:
A. AA
Step-by-step explanation:
Answer: AS is your answer!
Step-by-step explanation: AS has only one apple bar, which if you have the 5.1,2 Exam, you got this!
solve for the value of n
Answer:
N = 27
Step-by-step explanation:
The total value would be 90 , as it is a right triangle . Starting from the aforementioned number and subtracting it by the given values above shall reward you with the correct answer .
90 - ( 6 + 3 ) = 81
81 / 3 = 27
ALSO GIVE ME BRAINLIEST PLEASE :)
Answer:
i think 27??
Step-by-step explanation:
n+6 +90+2!+3=180
A competitive diver dives from a 33-foot high diving board. The height of the diver in feet after 't' seconds is given by u(t) = −16t^2 + 4t + 33. At the moment the diver begins her dive, another diver begins climbing the diving board ladder at a rate of 2 feet per second. At what height above the pool deck do the two divers pass each other? Please answer it quickly, it's for my homework.
Answer:
[tex]t = 0.375s[/tex]
Step-by-step explanation:
Given
[tex]h(t) = -16t^2 + 4t + 33[/tex] --- driver 1
[tex]Rate = 2ft/s[/tex] -- driver 2
[tex]height = 33ft[/tex]
Required
The time they passed each other
First, we determine the function of driver 2.
We have that:
[tex]Rate = 2ft/s[/tex] and [tex]height = 33ft[/tex]
So, the function is:
[tex]h_2(t) = Height - Rate * t[/tex]
[tex]h_2(t) = 33 - 2t[/tex]
The time they drive pass each other is calculated as:
[tex]h(t) = h_2(t)[/tex]
[tex]-16t^2 + 4t + 33= 33 - 2t[/tex]
Collect like terms
[tex]-16t^2 + 4t + 2t= 33 - 33[/tex]
[tex]-16t^2 + 6t= 0[/tex]
Divide through by 2t
[tex]-8t + 3= 0[/tex]
Solve for -8t
[tex]-8t = -3[/tex]
Solve for t
[tex]t = \frac{-3}{-8}[/tex]
[tex]t = 0.375s[/tex]
Write 90% as a fraction or mixed number in simplest form.
Answer:
9/10 I hope this helps :))
HELP PLEASE!!!!!!!!!!!!
Answer:
I am thinking it is 112° or 136°
Let me know which one. Hope it helps though =)
A plane travels at a speed of 180 mph in still air. Flying with a tailwind, the plane is clocked over a distance of 900 miles. Flying against a headwind, it takes 2 hours
longer to complete the return trip. What was the wind velocity? (Round your answer to the nearest tenth.)
Rachel rolls two number cubes, each with sides that are labeled 1 to 6. What is the probability that one number cube lands on a 1 and the other lands on an even?
Answer:
4/6. out of 1 2 3 4 5 6 only 3 number are even.but it says lands on 1 and the other lands on even. so 3 +1 = 4. sorry if it doesnt make sense
Multiplying by a positive number will give a positive product. TrueFalse
Answer:
true
Step-by-step explanation:
BRAINIEST TO WHOEVER RIGHT
Answer:
answer is C the means and the standard deviation because the data sets are normally disturbed
Answer: d
Step-by-step explanation:
What is the measure of ∠4? Enter your answer in the box.
Answer:
59
Step-by-step explanation:
HELP ME PLZ I NEED HELP