Helps needed with this diff qn

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a material decays at a rate proportional to its mass. there are 200mg of it initially, 5 hours later, it lost 10% of the original mass. let m denote the mass of remaining at anytime t. write the differential equation which describes the rate of change of m with respect to t, and solve the equation.
 
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miraclezdr said:
a material decays at a rate proportional to its mass. there are 200mg of it initially, 5 hours later, it lost 10% of the original mass. let m denote the mass of remaining at anytime t. write the differential equation which describes the rate of change of m with respect to t, and solve the equation.
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a material decays at a rate proportional to its mass. -> Is giving you the basic differential equation.

there are 200mg of it initially, 5 hours later, it lost 10% of the original mass. -> Tells you how they are proportional.

You've just got to learn how to read the problems^^
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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