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Artemon [7]
3 years ago
10

A. 1/3 B. 5/13 C. 4/5 D. 12/13

Mathematics
1 answer:
Kisachek [45]3 years ago
7 0

Answer:

5/13

Step-by-step explanation:

OM is 5 and OL is 13 use Pythagoreans theorem

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A bank advertises that it compounds money quarterly and that it will take Double your money in 10 years. what is the interest-ra
S_A_V [24]

The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.

Step-by-step explanation:

The given is,

                          Compounds money quarterly

                          Double your money in 10 years

Step:1

              Formula to calculate future investment with compounded quarterly,

                                                        A =P(1+\frac{r}{n} )^{nt}...............................(1)

              Where, A - Future amount

                           P - Initial investment\

                            r - Rate of interest

                            n - No. of compounding in a year

                             t - No. of years

Step:2

               Let, P = X

                      A = 2X ( Double your money )

              From given, n - 4 ( for compounding quarterly )

                                    t - 10 years

               From equation (1)

                                                        2X =X(1+\frac{r}{4} )^{(4)(10)}

                                                         \frac{2X}{X}  =(1+\frac{r}{4} )^{(4)(10)}

                                                            2  =(1+\frac{r}{4} )^{40}

          Take root 40^{th} root on both side,

                                                         \sqrt[40]{2} = (1+\frac{r}{4} )

                                            1.017479692 = (\frac{4+r}{4} )

                                     (1.017479692)(4) = (r+4)

                                                  4.06992=(r+4)

                                                              r = 4.06992 -4

                                                              r =( 0.06992)(100)

                                                              r = 6.992 %

Result:

             The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.

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Use Green's Theorem to calculate the circulation of F =2xyi around the rectangle 0≤x≤8, 0≤y≤3, oriented counterclockwise.
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Green's theorem says the circulation of \vec F along the rectangle's border C is equal to the integral of the curl of \vec F over the rectangle's interior D.

Given \vec F(x,y)=2xy\,\vec\imath, its curl is the determinant

\det\begin{bmatrix}\frac\partial{\partial x}&\frac\partial{\partial y}\\2xy&0\end{bmatrix}=\dfrac{\partial(0)}{\partial x}-\dfrac{\partial(2xy)}{\partial y}=-2x

So we have

\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_D-2x\,\mathrm dx\,\mathrm dy=-2\int_0^3\int_0^8x\,\mathrm dx\,\mathrm dy=\boxed{-192}

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