Find the acute angle, \theta between the lines 2 x+y-6=0 and 3 x-2 y+2=0.

A piece of wire of length l metres is cut into two pieces of length x metres and (l-x) metres. The former is bent into the shape of a square and the latter is bent into the shape of a rectangle of which the length is twice the width. Find the value of x in terms of l for which the sum of the areas of the two figures is a minimum or a maximum.

Find the equations of the lines l_1 and l_2 which pass through the point of intersection of the lines x-3 y=4 and 3 x+y=2, and are respectively parallel and perpendicular to the line 3 x+4 y=0.

A piece of wire of length l metres is cut into two pieces of length x metres and (l-x) metres. The former is bent into the shape of a square and the latter is bent into the shape of a rectangle of which the length is twice the width. Find an expression for the sum of the areas of these two figures.

A point P(x, y) moves such that the sum of the squares of its distances from the lines 3 x-2 y+6=0 and 2 x+3 y+4=0 is 13 \mathrm {~cm}. Find the locus of P.

A particle travels along the x-axis such that its velocity v metres per second from the origin after t seconds is v(t)=48t+7. What distance does it travel in the n t h second?

The angle at the point A of triangle A B C is always a right angle. If the sum of |AB| and |AC| is 6 \mathrm {~cm}, find the maximum area of the triangle.

The volume V of litres of petrol in a car’s tank is decreasing at a rate of \left (\frac {2}{5}-\frac {1}{50} x\right ) litres/ \mathrm {km} after travelling for x kilometres. If the volume is 4 litres when x=0, determine the number of kilometres the car travels until the tank is empty.

Family Stationery is the sole distributor of white board markers to the Computer Science department of KNUST. Knowing that under monopoly, the quantity sold and market prices are determined by the demand function, the company embarked on market analysis to determine its demand function. If the demand function for such a profit maximizing monopolist is p=274-q^2 and her marginal cost M C is given by M C=4+3 q, where p is price and q is quantity demanded, find the benefit enjoyed by consumers who are willing and able to offer more than the equilibrium price.

Which of the choices below is the general solution of the differential equation \frac {1}{y}\left (x^2+1\right ) \frac {d y}{d x}= \frac {2}{y} ?