2020 SAJC P2 Q3
2020 SAJC P2 Q3 The variables $x$ and $y$ are related by the differential equation $frac{text{d}y}{text{d}x}=frac{x-y}{x-y+1}$. (i) Solve the differential equation, using the substitution $u=x-y+1$, and show that the general
2020 SAJC P2 Q3 The variables $x$ and $y$ are related by the differential equation $frac{text{d}y}{text{d}x}=frac{x-y}{x-y+1}$. (i) Solve the differential equation, using the substitution $u=x-y+1$, and show that the general
2020 TMJC P1 Q8 (i) Show that the differential equation $frac{text{d}y}{text{d}x}=5left( x-y right)$ may be reduced by the substitution $w=x-y$ to $frac{text{d}w}{text{d}x}=1-5w$. Hence find the general solution for $~y$ in
2020 RVHS P2 Q2 A particle moving in a liquid is such that after $t$ seconds, its velocity is $v$ ms$^{-1}$, $vne 0$. $v$ satisfies the differential equation $vfrac{text{d}v}{text{d}t}+2{{v}^{2}}=t{{text{e}}^{-2t}}$. (i)
2020 RI P1 Q3 (i) Prove that for $x>0$, the substitution $y=ux$ reduces the differential equation $left( y-x right)left( frac{text{d}y}{text{d}x}-frac{y}{x} right)={{y}^{2}}+2{{x}^{2}}$ to $left( frac{u}{{{u}^{2}}+2}-frac{1}{{{u}^{2}}+2} right)left( frac{text{d}u}{text{d}x} right)=1$. [2] (ii) Hence
HCI Probability Notes Example 24 A bag contains two red balls and three green balls. Three balls are drawn form the bag, one after another without replacement. Find the probability
ASRJC Permutation And Combination Tutorial 20 Q1 How many even numbers greater than $900$ but less than $1,000,000$ can be formed from the digits $0$, $1$, $3$, $5$, $7$, $9$
2018 SAJC P1 Q10 Albert and Betty each took a study loan of $$100,000$ from a bank on 1 January 2014 and both graduated on 31 December 2017. The bank
2014 HCI P2 Q5 [Modified] (i) A group of $5$ boys and $5$ girls are to be seated in a row of $10$ adjacent seats to watch a performance. Find
2023 DHS Promo Q7 (a) It is given that $sumlimits_{r=1}^{n}{{{r}^{2}}=frac{1}{6}nleft( n+1 right)left( 2n+1 right)}$. (i) Find $sumlimits_{r=1}^{n}{left( {{2}^{r+1}}+3r-{{r}^{2}} right)}$ in the form $Aleft( {{2}^{n}}-1 right)+text{f}left( n right)$, where $A$ is
2021 TMJC P1 Q9 The line $l$ passes through the point $A$ with coordinates $left( 1,-2,3 right)$ and is parallel to the vector $left( begin{matrix} 4 \ 0 \ -1