500 Centimeters
5000 Millimeters
.005 Kilometers
The first is b, the second is a and the third is b
Given:
The equation is:
![2\sum_{n=3}^7n^2=\sum_{n=3}^72n^2](https://tex.z-dn.net/?f=2%5Csum_%7Bn%3D3%7D%5E7n%5E2%3D%5Csum_%7Bn%3D3%7D%5E72n%5E2)
To find:
Whether the equation is true or not.
Solution:
We have,
![2\sum_{n=3}^7n^2=\sum_{n=3}^72n^2](https://tex.z-dn.net/?f=2%5Csum_%7Bn%3D3%7D%5E7n%5E2%3D%5Csum_%7Bn%3D3%7D%5E72n%5E2)
Taking LHS, we get
![LHS=2\sum_{n=3}^7n^2](https://tex.z-dn.net/?f=LHS%3D2%5Csum_%7Bn%3D3%7D%5E7n%5E2)
![LHS=2[(3)^2+(4)^2+(5)^2+(6)^2+(7)^2]](https://tex.z-dn.net/?f=LHS%3D2%5B%283%29%5E2%2B%284%29%5E2%2B%285%29%5E2%2B%286%29%5E2%2B%287%29%5E2%5D)
![LHS=2[9+16+25+36+49]](https://tex.z-dn.net/?f=LHS%3D2%5B9%2B16%2B25%2B36%2B49%5D)
![LHS=2[135]](https://tex.z-dn.net/?f=LHS%3D2%5B135%5D)
![LHS=270](https://tex.z-dn.net/?f=LHS%3D270)
Taking RHS, we get
![RHS=\sum_{n=3}^72n^2](https://tex.z-dn.net/?f=RHS%3D%5Csum_%7Bn%3D3%7D%5E72n%5E2)
![RHS=2(3)^2+2(4)^2+2(5)^2+2(6)^2+2(7)^2](https://tex.z-dn.net/?f=RHS%3D2%283%29%5E2%2B2%284%29%5E2%2B2%285%29%5E2%2B2%286%29%5E2%2B2%287%29%5E2)
![RHS=2(9)+2(16)+2(25)+2(36)+2(49)](https://tex.z-dn.net/?f=RHS%3D2%289%29%2B2%2816%29%2B2%2825%29%2B2%2836%29%2B2%2849%29)
![RHS=18+32+50+72+98](https://tex.z-dn.net/?f=RHS%3D18%2B32%2B50%2B72%2B98)
![RHS=270](https://tex.z-dn.net/?f=RHS%3D270)
Here,
.
Therefore, the given equation is true.
The location of K(1,-3) after dilated by a scale factor of 1 is K’(1,-3) also
Answer:
![y=.01(.5^{x})](https://tex.z-dn.net/?f=y%3D.01%28.5%5E%7Bx%7D%29)
Step-by-step explanation:
Use the ExpReg function on a graphing calculator to find a and b
![y=ab^{x} \\a=.01\\b=.5](https://tex.z-dn.net/?f=y%3Dab%5E%7Bx%7D%20%5C%5Ca%3D.01%5C%5Cb%3D.5)