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 } { (u - v ) ( u + v ) } - \dfrac { w } { (u + v) } \text{ and } y = \dfrac { u } { (u - v ) ( u + v ) } - \dfrac { w } { ( u + v ) } ^@
B.
^@ x = \dfrac { - v } { (u - v ) ( u + v ) } - \dfrac { w } { (u - v) } \text{ and } y = \dfrac { u } { (u - v ) ( u + v ) } - \dfrac { w } { ( u - v ) } ^@
C.
^@ x = \dfrac { - v } { (u - v ) ( u + v ) } + \dfrac { w } { v + u } \text{ and } y = \dfrac { u } { (u - v ) ( u + v ) } + \dfrac { w } { v + u } ^@
Wei required ^@ $2280 ^@ after ^@ 11 ^@ weeks to buy a watch. He saved ^@ $110 ^@ in the first week and increased his weekly savings by ^@ $10 ^@ every week. Find whether he will be able to buy a watch after ^@ 11 ^@ weeks.
A vertical stick which is ^@ 33 \space cm^@ long casts a ^@30 \space cm^@ long shadow on the ground. At the same time, a vertical tower casts a ^@50 \space m^@ long shadow on the ground. Find the height of the tower.
Tony drew the following figure in his mathematics notebook. In which ^@AB^@ and ^@BC^@ are co-initial tangents drawn from an external point ^@A^@ to the circle ^@OB^@ and ^@OC^@ are the radii of the circle. Then what is always true ^@?^@
To warn ships for underwater rocks, a lighthouse throws a red colored light over a sector of angle ^@ 90^\circ ^@ to a distance of ^@ 4.9 \space km^@. Find the area of the sea over which the ships are warned. ^@ \bigg( ^@ Use ^@ \pi = \dfrac { 22 } { 7 } \bigg)^@
A drinking glass is in the shape of a frustum of a cone of height ^@20 \space cm^@. The diameters of its two circular ends are ^@13 \space cm^@ and ^@10 \space cm^@. Find the capacity of the drinking glass.(Use ^@ \pi = \dfrac { 22 } { 7 } ^@)
In this diagram, the triangle represents women, the square represents accountants and the circle represents employed. Find the number of women who are accountants and employed.
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