State whether the statement is true (T) or false (F): When two quantities \(x\) and \(y\) are in inverse proportion, then \(\frac {x}{y}\) is a constant.___
State whether the statement is true (T) or false (F): When two quantities \(x\) and \(y\) are in inverse proportion, then \(\frac {x}{y}\) is a constant.___
Answer
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Solution
Given: \(x\) and \(y\) are in inverse proportion. So, \(x\propto \frac{1}{y}\) \(\Rightarrow\)\(x=\frac{k}{y}\) where, \(k\) is a constant. \(\Rightarrow\)\(xy=k\) \(\Rightarrow\)\(xy=\text{constant}\) So, the given statement is false.
State whether the statement is true (T) or false (F): If \(5\) persons can finish a job in \(10\) days then one person will finish it in \(2\) days.___
In a scout camp, there is food provision for \(300\) cadets for \(42\) days. If \(50\) more persons join the camp, for how many days will the provision last?
A tank is filled with water up to a height \(H\). Water is allowed to come out of a hole \(P\) in one of the walls at a depth \(D\) below the surface of water. Express the horizontal distance \(x\) in terms of \(H\) and \(D\)( )
Under the condition that the temperature remains constant, the volume of gas is inversely proportional to its pressure. If the volume of gas is \(630\) cubic centimetres at a pressure of \(360\;mm\) of mercury, then what will be the pressure of the gas if its volume is \(720\) cubic centimetres at the same temperature?