Answer:
3π square units.
Step-by-step explanation:
We can use the disk method.
Since we are revolving around AB, we have a vertical axis of revolution.
So, our representative rectangle will be horizontal.
R₁ is bounded by y = 9x.
So, x = y/9.
Our radius since our axis is AB will be 1 - x or 1 - y/9.
And we are integrating from y = 0 to y = 9.
By the disk method (for a vertical axis of revolution):
![\displaystyle V=\pi \int_a^b [R(y)]^2\, dy](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cpi%20%5Cint_a%5Eb%20%5BR%28y%29%5D%5E2%5C%2C%20dy)
So:
Simplify:
Integrate:
![\displaystyle V=\pi\Big[y-\frac{1}{9}y^2+\frac{1}{243}y^3\Big|_0^9\Big]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cpi%5CBig%5By-%5Cfrac%7B1%7D%7B9%7Dy%5E2%2B%5Cfrac%7B1%7D%7B243%7Dy%5E3%5CBig%7C_0%5E9%5CBig%5D)
Evaluate (I ignored the 0):
![\displaystyle V=\pi[9-\frac{1}{9}(9)^2+\frac{1}{243}(9^3)]=3\pi](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cpi%5B9-%5Cfrac%7B1%7D%7B9%7D%289%29%5E2%2B%5Cfrac%7B1%7D%7B243%7D%289%5E3%29%5D%3D3%5Cpi)
The volume of the solid is 3π square units.
Note:
You can do this without calculus. Notice that R₁ revolved around AB is simply a right cone with radius 1 and height 9. Then by the volume for a cone formula:
We acquire the exact same answer.
When you are finding the area, you multiply the length x the width. So for example, we have a rectangle that the length is 6 feet and the width is 4 feet. So, first of all we multiply 6x4= 24. Since its area don't forget it is Square Feet (or any other type of measurement).
Hope it helps!
Answer: x =3
Step-by-step explanation:
2× 3 = 6
length= 5 inches
width= 2×3= 6 inches
2(l+w) = 2(5+6)
2(11)
2×11= 22
hope this helps:-)
f = 2
Simplify both sides of the equation <span><span>1.25f</span>+2</span>=<span><span>−<span>2.75f</span></span>+<span>10
Add 2.75 to each side </span></span><span><span>4f</span>+2</span>=<span>10
Subtract 2 from both sides </span><span>4f</span>=<span>8
Divide each side by 4 </span>f=<span>2</span>
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Hey there.. I will be more than happy to help you today.. :)
A Number squared decreased by ten
We will do this with steps:-
Step 1 - "A number ". So, Let's say any number be x
Step 2 - "A number squared". Our number x is squared i.e. x²
Step 3 - "A number squared" ( i.e. x² ) is decreased by ten
x² - 10
This is your answer.
Hope this helps you :)
