Sue Pemberton Solutions for Chapter: Quadratics, Exercise 4: EXERCISE 1D

A cuboid has sides of length $5 \mathrm{cm}, x \mathrm{cm}$ and $y \mathrm{cm}$. Given that $x+y=20.5$ and the volume of the cuboid is $360{ \mathrm{cm}}^3$, find the value of $x$ and the value of$y$ .

The diagram shows a solid formed by joining a hemisphere, of radius $r \mathrm{cm}$, to a cylinder, of radius $r \mathrm{cm}$ and height $h \mathrm{cm}$. The total height of the solid is$18 \mathrm{cm}$ and the surface area is $205\pi {\mathrm{cm}}^2$. Find the value of $r$ and the value of $h$.

The line $7x+2y=-20$ intersects the curve $x^2+y^2+4x+6y-40=0$ at the points $A$ and $B$. Find the length of the line $AB$.

The line $7y-x=25$ cuts the curve $x^2+y^2=25$ at the points $A$ and $B$. Find the equation of the perpendicular bisector of the line $AB$.

The straight line $y=x+1$ intersects the curve $x^2-y=5$ at the points $A$ and $B$. Given that $A$ lies below the $x-$axis and the point $P$ lies on $AB$ such that $AP: PB=4: 1$, find the coordinates of $P$.

The line $x-2y=1$ intersects the curve $x+y^2=9$ at two points, $A$ and $B$. Find the equation of the perpendicular bisector of the line $AB$.

Split $10$ into two parts so that the difference between the squares of the parts is $60$.

Split $N$ into two parts so that the difference between the squares of the parts is $D$.