3 years ago

Michael invests $2000 in an annuity that offers an interest rate of 4%

Mathematics

1 answer:

BARSIC [14]3 years ago

8 0

Answer: $2440.38

Step-by-step explanation:

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Step-by-step explanation:

In this system we have the force of the spring and the gravitational force. The equation that describes that is

$F_{s}+F{g}=ma\\k(y_0+y)-mg=ma$

where y0 is the equilibrium position when the string is free and y0+y is the new equilibrium position when the object is hanged of the string. By replacing by derivatives we have

$ky_0+ky-mg=ma\\mg+ky-mg=ky=ma\\\\ky=m\frac{d^2y}{dt^2}\\\\my''+ky=0$

the solution for this differential equation is (by using the characterisic polynomial)

$y(x)=Acos(kt)+Bsin(kt)\\k=\omega^2m$

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Step-by-step explanation:

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