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3 years ago

A person invests 3000 dollars in a bank. The bank pays 6.75% interest compounded

Mathematics

1 answer:

stich3 [128]3 years ago

8 0

Answer:

12.1 years

Step-by-step explanation:

We are given that

Principal amount, P=$3000

Rate of interest, r=6.75% semi-annually

Amount, A=$6700

We know that

When r pays semi-annually

$A=P(1+\frac{r}{n\times 100})^{nt}$

Where n=2

Using the formula

$6700=3000(1+\frac{6.75}{200})^{2t}$

$\frac{6700}{3000}=(1..03375)^{2t}$

$2.233=(1.03375)^{2t}$

Taking ln on both sides we get

$ln(2.233)=2t ln(1.03375)$

$2t=\frac{ln(2.233)}{ln(1.03375)}$

$t=\frac{1}{2}\times \frac{ln(2.233)}{ln(1.03375)}$

$t=12.1 years$

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2 years ago

In evaluating a double integral over a region D, a sum of iterated integrals was obtained as follows:

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Step-by-step explanation:

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$\int \int Df(x,y)dA=\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy+\int_5^7\int_0^{7-y} f(x,y)dxdy\; \cdots (i)$

For the term $\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy$ .

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Now, reverse the order of integration, first integrate with respect to $y$ then with respect to $x$ . So, the limits of $y$ become from $y=\frac{5x}{2}$ to $y=5$ and limits of $x$ become from $x=0$ to $x=2$ as shown in graph 2.

So, on reversing the order of integration, this double integration can be written as

$\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy=\int_0 ^2\int _ {\frac {5x}{2}}^5 f(x,y)dydx\; \cdots (ii)$

Similarly, for the other term $\int_5 ^7\int _0 ^ {7-y} f(x,y)dxdy$ .

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Now, reverse the order of integration, first integrate with respect to $y$ then with respect to $x$ . So, the limits of $y$ become from $y=5$ to $y=7-x$ and limits of $x$ become from $x=0$ to $x=2$ as shown in graph 4.

So, on reversing the order of integration, this double integration can be written as

$\int_5 ^7\int _0 ^ {7-y} f(x,y)dxdy=\int_0 ^2\int _5 ^ {7-x} f(x,y)dydx\;\cdots (iii)$

Hence, from equations $(i)$ , $(ii)$ and $(iii)$ , on reversing the order of integration, the required expression is

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$\int_a^b\int_{g_1(x)}^{g_2(x)} f(x,y)dydx$

We have,

$a=0, b=2, g_1(x)=\frac{5x}{2}$ and $g_2(x)=7-x$ .

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