I think the answer is 4x - 15 = 6 + 1/2x
He will do about 16 rotations
Answer:
Surface area of a cone = πrs + πr2
Volume of a cone = 1/3πr2h.
The slant of a right circle cone can be figured out using the Pythagorean Theorem if you have the height and the radius.
Answers for volume problems should always be in cubic units.
Step-by-step explanation:
Answer: the integers are closed under addition, multiplication, and subtraction, but NOT division.
Step-by-step explanation:
Distribute the sum:
![\displaystyle\sum_{i=1}^{24}(3i-2)=3\sum_{i=1}^{24}i-2\sum_{i=1}^{24}1](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5E%7B24%7D%283i-2%29%3D3%5Csum_%7Bi%3D1%7D%5E%7B24%7Di-2%5Csum_%7Bi%3D1%7D%5E%7B24%7D1)
Use the following formulas:
![\displaystyle\sum_{i=1}^n1=n](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5En1%3Dn)
![\displaystyle\sum_{i=1}^ni=\dfrac{n(n+1)}2](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5Eni%3D%5Cdfrac%7Bn%28n%2B1%29%7D2)
![\implies\displaystyle\sum_{i=1}^{24}(3i-2)=3\cdot\frac{24\cdot25}2-2\cdot24=\boxed{852}](https://tex.z-dn.net/?f=%5Cimplies%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5E%7B24%7D%283i-2%29%3D3%5Ccdot%5Cfrac%7B24%5Ccdot25%7D2-2%5Ccdot24%3D%5Cboxed%7B852%7D)
In case you don't know where those formulas came from:
The first one is obvious; you're just adding <em>n</em> copies of 1, so 1 + 1 + ... + 1 = <em>n</em>.
The second can be proved in this way: let <em>S</em> be the sum 1 + 2 + 3 + ... + <em>n</em>. Rearrange it as <em>S</em> = <em>n</em> + (<em>n</em> - 1) + (<em>n</em> - 2) + ... + 1. Then 2<em>S</em> = (<em>n</em> + 1) + (<em>n</em> + 1) + (<em>n</em> + 1) + ... + (<em>n</em> + 1), or <em>n</em> copies of <em>n</em> + 1. So 2<em>S</em> = <em>n</em>(<em>n</em> + 1). Divide both sides by 2 and we're done.