2 years ago

Determine the slope of the lines.

Mathematics

1 answer:

JulijaS [17]2 years ago

7 0

i think it’s perpendicular

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Solve for x. (e^x-e^-x)/((e^x+e^-x)=t

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$\dfrac{e^x-e^{-x}}{e^x+e^{-x}}=t\\\\
\dfrac{e^{2x}-1}{e^{2x}+1}=t\\\\
e^{2x}-1=t(e^{2x}+1)\\\\
e^{2x}-1=e^{2x}t+t\\\\
e^{2x}-e^{2x}t=t+1\\\\
e^{2x}(1-t)=t+1\\\\
e^{2x}=\dfrac{t+1}{1-t}\\\\
e^{2x}=-\dfrac{t+1}{t-1}\\\\
2x=\ln\left(-\dfrac{t+1}{t-1}\right)\\\\
x=\dfrac{\ln\left(-\dfrac{t+1}{t-1}\right)}{2}\qquad t\in(-1,1)



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3 years ago

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Chelsey put $450 off bro an account with an interest rate of 2.5% when she withdrew her money she had earned $67.50 in interest

AysviL [449]

$~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill &\$67.50\\ P=\textit{original amount deposited}\dotfill & \$450\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years \end{cases} \\\\\\ 67.50 = (450)(0.025)(t)\implies \cfrac{67.50}{(450)(0.025)}=t\implies 6=t$