Paper 3 October/November 2004 MATHEMATICH (9709/3) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

In a chemical reaction, a compound $X$ is formed from two compounds $Y$ and $Z$. The masses in grams of $X$, $Y$ and $Z$ present at time $t$ seconds after the start of the reaction are $x$, $10 - x$, and $20 - x$ respectively. At any time the rate of formation of $X$ is proportional to the product of the masses of $Y$ and $Z$ present at the time. When $t = 0$, $x = 0$ and $\frac{{dx}}{{dt}} = 2$.
a) Show that $x$ and $t$ satisfy the differential equation
$\frac{{dx}}{{dt}}…