Reed Bolton

01/05/2024 · High School

6 (a) Diberi \( y=x(5-x) \), ungkapkan \( y \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}+15 \) dalam sebutan teringkas. Given \( y=x(5-x) \), express \( y \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}+15 \) in its simplest form. (b) Luas segi empat sama dengan sisi \( x \mathrm{~cm} \) menokok pada kadar \( 3 \mathrm{~cm}^{2} \mathrm{~s}^{-1} \). Cari kadar perubahan sisi apabila luasnya ialah \( 9 \mathrm{~cm}^{2} \). The area of a square with side \( x \mathrm{~cm} \) increases at a rate of \( 3 \mathrm{~cm}^{2} \mathrm{~s}^{-1} \). Find the rate of change of its side when the area is \( 9 \mathrm{~cm}^{2} \). [2 markah] [2 marks]