2 years ago

Given the following functions, evaluate each of the following:

Mathematics

1 answer:

Olegator [25]2 years ago

8 0

Answer:

1. -6

Step-by-step explanation:

f(x)=x²-9

g(x)= x-3

1. (f+g)(2) =

(2²-9)+(2-3) = (4-9)+(2-3) = (-5)+(-1)= -6

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Find the sum of the first 8 terms of the series. 1/2 + 1 + 2 + 4

Roman55 [17]

$\bf \cfrac{1}{2}~~,~~\stackrel{2\cdot \frac{1}{2}}{1}~~,~~\stackrel{2\cdot 1}{2}~~,~~\stackrel{2\cdot 2}{4}~~,...$

so as you can see the common ratio is 2, and the first term is 1/2,

$\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=2\\ a_1=\frac{1}{2}\\ n=8 \end{cases} \\\\\\ S_8=\cfrac{1}{2}\left( \cfrac{1-2^8}{1-2} \right)\implies S_8=\cfrac{1}{2}\left( \cfrac{-255}{-1} \right)\implies S_8=\cfrac{255}{2}$