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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. 5t

The initial mass is found by putting t=0 into the given equation, so the initial mass is 300g. When the mass has decreased to half its value, M=150g. This gives us 150=300e^-0.05t, so e^-0.05t=1/2. Natural l...
TT
Answered by Theo T. • Maths tutor
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What's the difference between the quotient rule and the product rule?

They are two rules that are used when differentiating a derivative that has a product with two functions or a term where the one function is divisble by another.For example:f(X) = xe^xorf(x) = (2+4x)/x^2 unf...
Answered by • Maths tutor
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If I have the equation of a curve, how do I find its stationary points?

A stationary point is where the gradient of a curve momentarily stops changing.Let's take the example that we want to find the stationary points of the curve y=2x^5 - 5x^2. Find the derivative of the equatio...
DP
Answered by Darshan P. • Maths tutor
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For the function f(x) = 4x^3 -3x^2 - 6x, find a) All points where df/dx = 0 and b) State if these points are maximum or minimum points.

Part a) requires you to find df/dx for the given function. To do this, we differentiate the function once, which is done by multiplying the power of each 'part' with the part itself and subtracting 1 from th...
MM
Answered by Martin M. • Maths tutor
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Ball P is shot at 18m/s horizontally from the top of a 32m mast. Ball Q is shot at 30m/s at an angle 'a' to the horizontal from the bottom of the mast. They collide mid-air. Prove that cos'a' = 3/5

Consider the positions of each ball as a function of time. Distance (position) is equal to velocity times time. We want 'cos' in the answer, so we'll work with the x axis. For ball P, the position is equal t...
AF
Answered by Andrew F. • Maths tutor
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