Counter example to: every perfect square has exactly 3 factors

Mathematics

1 answer:

77julia77 [94]3 years ago

6 0

Well 1 is a perfect square and it only has 1 factor.
16 is a perfect square and its' factors are 1, 2, 4, 8, and 16

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. Mrs. Rojas deposited $8000 into an account paying 4% interest annually. After 8 months Mrs. Rojas withdrew the $6000 plus inte

Mashcka [7]

well, keeping in mind that a year has 12 months, that means that 8 months is 8/12 of a year, when Mrs Rojas pull her money out.

$~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$6000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\to \frac{8}{12}\dotfill &\frac{2}{3} \end{cases} \\\\\\ A=6000[1+(0.04)(\frac{2}{3})]\implies A=6000\left( \frac{77}{75} \right)\implies A=6160$

well, she put in 6000 bucks, got back 160 extra, that's the interest earned in the 8 months.

what if she had left her money for 1 whole year, then

$~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$6000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &1 \end{cases} \\\\\\ A=6000[1+(0.04)(1)]\implies A=6240$

so had she left it in for a year, she'd have gotten 6240, namely 240 in interest, well, what fraction of a year's interest was earned? or worded differently, what fraction is 160(8 months) of 240(1 year)?

$\cfrac{\stackrel{\textit{for 8 months}}{160}}{\underset{\textit{for 12 months}}{240}}\implies \cfrac{2}{3}$