Answer:
n(t) = 101010(3^t)
Step-by-step explanation:
The initial number of people who knew about it is;
n(0) = 101010
The number of people who will have known in a day's time;
n(1) = 101010(3)
The number of people who will have known in 2 day's time;
n(2) = 101010(3)(3) = 101010(3^2)
The number of people who will have known in 3 day's time;
n(3) = 101010(3)(3)(3) = 101010(3^3)
Therefore, the total number n(t) of people who know about the celebrity proposing t days after the celebrity proposes becomes;
n(t) = 101010(3^t)
Answer:
Step-by-step explanation:
First simplify:
Therefore we have:
![\sum\limits_{n=1}^{150}[-1-(n-1)]=\sum\limits_{n=1}^{150}(-n)=(-1)+(-2)+(-3)+...+(-150)\\\\-1,\ -2,\ -3,\ -4,\ ...,\ -150-\text{it's the arithmetic sequence}\\\text{with the common difference d = -1.}\\\\\text{The formula of a sum of terms of an arithmetic sequence:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\text{Substitute}\ n=150,\ a_1=-1,\ a_n=-150:\\\\S_{150}=\dfrac{-1+(-150)}{2}\cdot150=(-151)(75)=-11,325](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bn%3D1%7D%5E%7B150%7D%5B-1-%28n-1%29%5D%3D%5Csum%5Climits_%7Bn%3D1%7D%5E%7B150%7D%28-n%29%3D%28-1%29%2B%28-2%29%2B%28-3%29%2B...%2B%28-150%29%5C%5C%5C%5C-1%2C%5C%20-2%2C%5C%20-3%2C%5C%20-4%2C%5C%20...%2C%5C%20-150-%5Ctext%7Bit%27s%20the%20arithmetic%20sequence%7D%5C%5C%5Ctext%7Bwith%20the%20common%20difference%20d%20%3D%20-1.%7D%5C%5C%5C%5C%5Ctext%7BThe%20formula%20of%20a%20sum%20of%20terms%20of%20an%20arithmetic%20sequence%3A%7D%5C%5C%5C%5CS_n%3D%5Cdfrac%7Ba_1%2Ba_n%7D%7B2%7D%5Ccdot%20n%5C%5C%5C%5C%5Ctext%7BSubstitute%7D%5C%20n%3D150%2C%5C%20a_1%3D-1%2C%5C%20a_n%3D-150%3A%5C%5C%5C%5CS_%7B150%7D%3D%5Cdfrac%7B-1%2B%28-150%29%7D%7B2%7D%5Ccdot150%3D%28-151%29%2875%29%3D-11%2C325)
Answer:
27 Meters
Step-by-step explanation:
Surface Area = 2×(3×2 + 3×1.5 + 2×1.5)
