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.
Based on the starting temperature and the new temperature, the relevant expression would be<u> 2 - (-9) </u>
To find the number of degrees the temperature has changed by, use the following equation:
<em>= Starting temperature - Current temperature </em>
Starting temperature = 2°F
Current temperature = -9°F
The equation becomes:
<em>= 2 - (-9)</em>
In conclusion, the expression would be 2 - (-9)
<em>Find out more on </em><em>expressions </em><em>at brainly.com/question/945593. </em>
Answer:
78 ft³
Step-by-step explanation:
<u />
Volume of a rectangular prism = length × width × height
<u />
<u>Toy Box</u>
- length = 5 ft
- width = 3 ft
- height = 2ft
⇒ volume = 5 × 3 × 2 = 30 ft³
<u>Book Box</u>
- length = 6 ft
- width = 4 ft
- height = 2 ft
⇒ volume = 6 × 4 × 2 = 48 ft³
Total combined volume = 30 + 48 = 78 ft³
FORMULA:
Length of arc PQ = 2πrΦ/360°
ANSWER:
Using formula,
2 × 22/7 × 7 × 80/360
44 × 2/9
88/9ft or 9.7ft
You need 10 logs for 1 brick. To get 10 bricks you need 100 logs. You are collecting stones and 1 stone gets you 4 logs. That means to get 100 logs you’ll need 25 stones. That indirectly means that 25 stones gets you 10 bricks.
