Square root of x^2-4 plus x^2/x^2+1

1 answer:

3 0

√x² - 4 + x²/x² + 1
x - 2 + x²/x² + 1
x - 2 + x² 
 1 x² + 1
(x - 2)(x² + 1) + x² 
(1)(x² + 1) x² + 1
x³ + x - 2x² - 2 + x² 
 x² + 1 x² + 1
x³ - 2x² + x² + x - 2
 x² + 1
x³ - x² + x - 2
 x² + 1
x³ + x - 2

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Suppose you want to start saving for retirement. You decide to continuously invest $20000 of your income each year in a risk-fre

Korvikt [17]

Answer:

Following are the solution to the given points:

Step-by-step explanation:

p= amount at any time

then $\frac{dp}{dt}=0.07 p$

$p=p_0 (1+e^{0.07 t) \\\\$

$P_0=\ principle \ amount \\\\ interest \ =p-p_0=p_0e^{0.07t}\\\\ p=y\frac{dy}{dt}=0.07y_0$

at time $= t\ years$

$\frac{dp}{dt}\\\\c_0=\$ \ 20000\ year\\\\p \to p+dp\\\\ dp=0.07p+c_0$

y= amount at any times

$\frac{dy}{dt}=0.07y+c_0\\\\dt= \frac{dy}{c_0+0.07y}$

For point a:

$\frac{dy}{dt}=20000+0.07 y$

For point b:

$\frac{dy}{20000+0.07 y}=dt\\\\\frac{1}{0.07}|n(\frac{0.07y+20000}{20000})=t\\\\\frac{0.07y}{20000}+1=e^{0.07t}\\\\y=7.1428\times 10^4[e^{0.07t} -1]\\\\y=\frac{20000}{0.07}[e^{0.07t}-1]\\\\$