$0. She got the $40 ring and then gave it back. 40-40=0.
Answer:
-23
Step-by-step explanation:
As I increases by 18, y decreases by 12. From the last value in the table, I needs to increase by 2·18 for it to become zero. Hence the y-intercept will be 2·12 less than the last value in the table:
1 - 2·12 = -23 . . . the y-intercept
Fibonacci is famous for his contributions to number theory.
In his book, Liber abaci he introduce the Hindu-Arabic place-valued decimal systems and the use of Arabic Numerals into Europe.He introduced the bar we use in fractions, previous to this, the numerator has quotations around it. The square root notation is also is Fibonacci method.
Answer: $2.26
10% of $52.50 is 5.25. Then, $52.50-$5.25 is $47.25. $49.99-$47.25 is $2.26
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:
![\displaystyle V=\pi\int_0^9\Big(1-\frac{y}{9}\Big)^2\, dy](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cpi%5Cint_0%5E9%5CBig%281-%5Cfrac%7By%7D%7B9%7D%5CBig%29%5E2%5C%2C%20dy)
Simplify:
![\displaystyle V=\pi\int_0^9(1-\frac{2y}{9}+\frac{y^2}{81})\, dy](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cpi%5Cint_0%5E9%281-%5Cfrac%7B2y%7D%7B9%7D%2B%5Cfrac%7By%5E2%7D%7B81%7D%29%5C%2C%20dy)
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:
![\displaystyle V=\frac{1}{3}\pi(1)^2(9)=3\pi](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%281%29%5E2%289%29%3D3%5Cpi)
We acquire the exact same answer.