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vekshin1
3 years ago
10

Sina=3/5 find cos2a​

Mathematics
1 answer:
yarga [219]3 years ago
6 0

Answer:

\huge \purple{\therefore \cos2a}  \orange{= }\red{\frac{7}{25}  }

Step-by-step explanation:

\because \cos2a =1 -  2 { \sin}^{2} a \\  \\   \therefore \cos2a =1 -  2 \bigg( {  \frac{3}{5} }\bigg) ^{2}  \\  \\\therefore \cos2a =1 -  2  \times  \frac{9}{25}   \\  \\\therefore \cos2a =1 -   \frac{18}{25}   \\  \\\therefore \cos2a =  \frac{25 - 18}{25}   \\  \\ \huge \purple{\therefore \cos2a}  \orange{= }\red{\frac{7}{25}  } \\  \\

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Answer:

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3 years ago
A small town has 2000 inhabitants. At 8 AM, 160 people have heard a rumor. By noon half the town has heard it. At what time will
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Answer:

3:36 PM

Step-by-step explanation:

Let fraction (y) of the people that heard the rumor , the differential equation that is satisfied by the by y is,

                            \frac{dy}{dt} = ky(1-y)

Solving the differential equation,

                          y(t) = \frac{y_{o}}{[y_{o} + (1 + y_{o})e^{-kt}]}

The total number of inhabitants of the town = 2000

The number of people that  heard the rumor = 160

At 8 AM, let t = 0,

               y(0) = \frac{160}{2000}

                       = 0.08

By noon, half of the town as heard the rumor.

Then,    

                y(4) = \frac{1}{2}

Therefore,

              \frac{1}{2} = \frac{0.08}{[0.08 + (1 - 0.08)e^{-4k}]}

              \frac{0.08}{[0.08 + 0.92e^{-4k}]} = \frac{1}{2}

              0.08 + 0.92e^{-4k} = 0.16  

              0.92e^{-4k} = 0.16 - 0.08

              0.92e^{-4k} = 0.08

              e^{-4k} = \frac {0.08}{0.92}

              k = - \frac{1}{4} In(\frac {0.08}{0.92})

              k ≈ 0.06106

Calculating time, t when y(t) = 90%

        ⇒ y(t) = 0.9

              \frac{0.08}{[0.08 + 0.92e^{-0.06106t}]} =0.9

              0.08 + 0.92e^{-0.06106t} = \frac {0.9}{0.08}

              0.08 + 0.92e^{-0.06106t} = 0.089

              0.92e^{-0.06106t} = 0.089 - 0.08

              0.92e^{-0.06106t} = 0.0089

              t = - \frac{1}{0.06106}In (\frac{0.0089}{0.92})

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Answer:

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