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Given that dx/dt = (1+2x)*4e^(-2t) and x = 1/2 when t = 0, show that ln[2/(1+2x)] = 8[1 - e^(-2t)]

1/(1+2x) dx = 4e^(-2t) dt Integrate both sides: ln[2/(1+2x)] = -8e^(-2t) + c input x = 1/2, t = 0: ln(2/2) = -8*(1) + c ln 1 = 0, so c = 8ln[2/1+2x] = 8[1-e^(-2t)]

Answered by Henry F. • Maths tutor

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Solve: 2 sin(2x) = (1-sin(x))cos(x) for 0<x<2*Pi and give any values of x, if any, where the equation is not valid

Double angle formula:Sin(2x) = 2sin(x)*cos(x)==> 2sin(x)*cos(x) = (1-sin(x))*cos(x) (2sin(x)-1+sin(x))*cos(x) = 0(3sin(x) - 1)*cos(x) = 0 i) cos(x) = 0, ii) 3sin(x) = 1 ==> sin(x) = 1/3 ...

Answered by Henry F. • Maths tutor

4916 Views

Solve 9x +1> 2x +3

9x - 2x> 3-17x > 2x > 2/7

Answered by Suruthi G. • Maths tutor

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You are told that y is proportional to x^2 and that y=75, x=5. Find a formula for y in terms of x.

You know that y is proportional to x², so let y=kx² . You also know that y=75 and x=5. Substitute y=75 and x=5 into the equation y=kx² . Therefore: 75=k multiplied by 5

Answered by Anna G. • Maths tutor

3123 Views

How do I find the maxima and minima of f(x) = e^(x^2)?

When dealing with maxima and minima points, there are two ways to go, one of these is to first compute the first derivative of the function, check when this function is zero, and then study its sign; the ...

Answered by Jacob A. • Maths tutor

3373 Views