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quester [9]
3 years ago
8

An investor invested a total of $58000 into two bonds. One bond paid 3% simple interest, and the other paid 2% interest. The inv

estor earned a total of $1705.00 in annual
interest.
How much was originally invested in each account?
Mathematics
1 answer:
seraphim [82]3 years ago
7 0

Answer:

34100

Step-by-step explanation:

1705×2÷5

=682

682×100÷2

=38100

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Peyton is going to invest $9,700 and leave it in an account for 16 years. Assuming the interest is compounded continuously, what
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Step-by-step explanation:

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From the homogeneous part of the ODE, we can get two fundamental solutions. The characteristic equation is

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The particular solution is easiest to obtain via variation of parameters. We're looking for a solution of the form

y_p=u_1y_1+u_2y_2

where

u_1=-\displaystyle\frac13\int\frac{y_2e^x\sec x}{W(y_1,y_2)}\,\mathrm dx
u_2=\displaystyle\frac13\int\frac{y_1e^x\sec x}{W(y_1,y_2)}\,\mathrm dx

and W(y_1,y_2) is the Wronskian of the fundamental solutions. We have

W(e^x\cos x,e^x\sin x)=\begin{vmatrix}e^x\cos x&e^x\sin x\\e^x(\cos x-\sin x)&e^x(\cos x+\sin x)\end{vmatrix}=e^{2x}

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y_p=\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x

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y=C_1e^x\cos x+C_2e^x\sin x+\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x
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