Solve the following pair of linear equations by using cross multiplication.
@^
\begin{aligned}
&u x - v y = w \\
&v x - u y = 1 - w
\end{aligned}
@^
A.
^@ x = \dfrac { v } { (v - u ) ( v + u ) } - \dfrac { w } { v - u } \text{ and } y = \dfrac { u } { (v - u ) ( v + u ) } - \dfrac { w } { u - v } ^@
B.
^@ x = \dfrac { - v } { (v - u ) ( v + u ) } - \dfrac { w } { (u + v) } \text{ and } y = \dfrac { u } { (v - u ) ( v + u ) } + \dfrac { w } { ( u + v ) } ^@
C.
^@ x = \dfrac { v } { (v - u ) ( v + u ) } - \dfrac { w } { (u - v) } \text{ and } y = \dfrac { u } { (v - u ) ( v + u ) } + \dfrac { w } { ( u - v ) } ^@
A vertical stick which is ^@ 24 \space cm^@ long casts a ^@21 \space cm^@ long shadow on the ground. At the same time, a vertical tower casts a ^@80 \space m^@ long shadow on the ground. Find the height of the tower.
From a point ^@ P ^@ outside a circle with center ^@ O ^@, tangents ^@ PA ^@ and ^@ PB ^@ are drawn to the circle. The line segment formed by joining the points ^@ A ^@ and ^@ B ^@ intersect the line segment ^@ OP ^@ at ^@ M ^@. What is the measure of ^@ \angle BMP ^@ ?
Bashir cut a cylindrically shaped solid pipe, having a diameter and height as ^@ 4 \space cm ^@ and ^@ 20 \space cm ^@ respectively, into ^@5^@ equal parts. He then took a piece and rolled it into ^@4^@ similar balls. What would be the diameter of the ball^@?^@
A tent is in form of a right circular cylinder and cone as shown in the picture. The radius of cone and cylinder is 4 meters. The height of cylinder and cone are 11.5 meters and 3 meters respectively. Find the outer surface area of the tent. (Assume π =
UAE
