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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)]

HF
Answered by Henry F. Maths tutor
2867 Views

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  ...

HF
Answered by Henry F. Maths tutor
4599 Views

Solve 9x +1> 2x +3

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

SG
Answered by Suruthi G. Maths tutor
3206 Views

Describe how carbon dioxide helps maintain temperature on Earth

Carbon dioxide allows radiation of short wavelengths to pass through the atmosphere to the Earth and absorbs any outgoing radiation that has long wavelengths.

SG
Answered by Suruthi G. Chemistry tutor
7685 Views

How can I get above 40 in my literature and film essays?

Getting above 40 at first can seem like a difficult task, but is more than possible. Regarding a literature response, if possible short and simple quoting can be helpful however not vital. A simple quote ...

DO
Answered by Dea O. Spanish tutor
1901 Views

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