I need help asap! due tommorow! please help me!

Mathematics

2 answers:

Tom [10]3 years ago

7 0

10^1=10
10×4.78=47.8
10^2= 10×10 =100
100×4.78 = 478
10^3 =10×10×10 = 1000
1000 ×4.78= 4780
notice that every time to exponent for 10 is +1 more than the last, the decimal place moves to the right 1

kozerog [31]3 years ago

3 0

For the other problems just move the decimal to the right. For the second one you would get 47.8

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Find the sum of a finite geometric series. The Smiths spent $2,000 on clothes in a particular year. If they increase the amount

boyakko [2]

$\bf \stackrel{\textit{first year}}{2000}~~,~~\stackrel{\textit{second year}}{2000+\stackrel{\textit{10\% of 2000}}{\frac{2000}{10}}}\implies 2200$

now, if we take 2000 to be the 100%, what is 2200? well, 2200 is just 100% + 10%, namely 110%, and if we change that percent format to a decimal, we simply divide it by 100, thus $\bf 110\%\implies \cfrac{110}{100}\implies 1.1$ .

so, 1.1 is the decimal number we multiply a term to get the next term, namely 1.1 is the common ratio.

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\r=\textit{common ratio}\\----------\\a_1=2000\\r=1.1\\n=4\end{cases}\\\\\\S_4=2000\left[ \cfrac{1-(1.1)^4}{1-1.1} \right]\implies S_4=2000\left(\cfrac{-0.4641}{-0.1} \right)\\\\\\S_4=2000(4.641)\implies S_4=9282$