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In a science experiment a substance is decaying exponentially. Its mass, M grams, at time t minutes is given by M=300e^(-0.05t). Find the time taken for the mass to decrease to half of its original value.

Firstly, calculate the initial value of of M, by substituting t = 0 into the equation M=300e -0.05t Initially, M 0 = 300e 0 =300 x 1 = 300When the substance mass has decreased to half its initial value, M = ...
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Answered by Bony R. • Maths tutor
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Differentiate, with respect to x, e^3x + ln 2x,

e^3x differentiates to 3e^3x as you multiply the function e^3x by the derivative of the inside function 3x. 3x differentiates to 3, so the answer is 3 multiplied by e^3x. The derivative of a natural log func...
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Answered by Pelumi A. • Maths tutor
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Find the first derivative of 2x^3+5x^2+4x+1 (with respect to x)

In differentiation, your goal is to reduce the power of the terms that you're differentiating with respect to (in this case, x).The method for doing this is:Multiply the power of your x term by its coefficie...
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Answered by Abigail R. • Maths tutor
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Simplify the following algebraic fraction; (3x^2 - x - 2) / ((1/2)x + (1/3)).

First we need to factorise the numerator into two expressions. We can see one expression must start (3x + ?) and the other therefore must hold (x + ?), we know this because the two brackets must multiply tog...
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Answered by Bobbi L. • Maths tutor
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Show using mathematical induction that 8^n - 1 is divisible by 7 for n=1,2,3,...

First step: n=1 we have 8 1 -1=7 which is divisible by 7. Assumption step: 8 k -1 is divisible by 7. Induction step: Using the previous step we have that 8 k -1=7x. So 8 k = 7x+1. Therefore, 8 k+1 - 1=8(8 k ...
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Answered by Mike C. • Maths tutor
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