MATHS

1) given that x= log(small5)3 + log(small5)4, find algebraically the value of x

2)a mug of tea cools according to the law T(small t)= T(small 0)e to the power^-kt where T(small 0) is the initial temp and T(small c)is the temp after t minutes. all temps are in celciius.

a) a particular mug of tea is cooled from 100*C to 75*C in a quater of an hour. therefore clculate value of k.

b) by how many degrees will the temperature of this tea fall in the next quater of an hour.

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  1. you want log5(12)
    x = log5 (12)
    or
    5^x = 12
    log10 (5^x) = log10 (12) = 1.0792
    or
    x log10 (5) = log10 (12) = 1.0792
    x (.699) = 1.0792
    x = 1.0792/.699

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  2. 2)a mug of tea cools according to the law T(small t)= T(small 0)e to the power^-kt where T(small 0) is the initial temp and T(small c)is the temp after t minutes. all temps are in celciius.

    Tt = To e^(-kt)

    a) a particular mug of tea is cooled from 100*C to 75*C in a quater of an hour. therefore clculate value of k.

    75 = 100 e^-(.25k) if t in hours and not minutes
    .75 = e^-.25k
    ln .75 = -.25k
    k = -.288/-.25

    b) by how many degrees will the temperature of this tea fall in the next quater of an hour.

    T = 75 e^-1.15 (.25)
    I will leave that to you

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  3. thanks alot damon ...i luv u!!!!

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