Before a battle there were the ratio of captains to soldiers was `2 : 7`. During the war 25 captains and 100 soldiers were martyred. The new ratio of captains to soldiers became `3 : 10`. What is the number of soldiers after the war?

In a regiment, the ratio of number of officers to the number of soldiers was 3 : 31 before a battle. In the battle 6 officers and 22 soldiers were killed. The ratio between the number of officers and the number of soldiers now is 1 : 13 . Find the number of officers and soldiers in the regiment before the battle.

In a certain experiments to measure the ratio of charge to mass of elementry particles, a surprising result was obtained in which two particle, a surprising result was obtained in which two particles moved in such a way that the distance between them always remained constant. It was also noticed that this two-particle system was isolated from all other particles and no force was acting on this system except the force between these two mases. After careful observation followed bu intensive calculation, it was deduced that velocity of these two particles was always opposite in direction and magnitude of velocity was 10^(3) ms^(-1) and 2 xx 10^(3) ms^(-1) for first and second particle, respectively, and mass of these particles were 2 xx 10^(-30) kg and 10^(-30)kg , respectively. Distance between them were 12Å(1Å = 10^(- 10)m). if the first particle is stopped for a moment and then released, the velocity of center of mass of the system just after the release will be

In a certain experiments to measure the ratio of charge to mass of elementry particles, a surprising result was obtained in which two particle, a surprising result was obtained in which two particles moved in such a way that the distance between them always remained constant. It was also noticed that this two-particle system was isolated from all other particles and no force was acting on this system except the force between these two mases. After careful observation followed bu intensive calculation, it was deduced that velocity of these two particles was always opposite in direction and magnitude of velocity was 10^(3) ms^(-1) and 2 xx 10^(3) ms^(-1) for first and second particle, respectively, and mass of these particles were 2 xx 10^(-30) kg and 10^(-30)kg , respectively. Distance between them were 12Å(1Å = 10^(- 10)m). Acceleration of the first particle was

In a certain experiments to measure the ratio of charge to mass of elementry particles, a surprising result was obtained in which two particle, a surprising result was obtained in which two particles moved in such a way that the distance between them always remained constant. It was also noticed that this two-particle system was isolated from all other particles and no force was acting on this system except the force between these two mases. After careful observation followed bu intensive calculation, it was deduced that velocity of these two particles was always opposite in direction and magnitude of velocity was 10^(3) ms^(-1) and 2 xx 10^(3) ms^(-1) for first and second particle, respectively, and mass of these particles were 2 xx 10^(-30) kg and 10^(-30)kg , respectively. Distance between them were 12Å(1Å = 10^(- 10)m). Acceleration of the second particle was

In a certain experiments to measure the ratio of charge to mass of elementry particles, a surprising result was obtained in which two particle, a surprising result was obtained in which two particles moved in such a way that the distance between them always remained constant. It was also noticed that this two-particle system was isolated from all other particles and no force was acting on this system except the force between these two mases. After careful observation followed bu intensive calculation, it was deduced that velocity of these two particles was always opposite in direction and magnitude of velocity was 10^(3) ms^(-1) and 2 xx 10^(3) ms^(-1) for first and second particle, respectively, and mass of these particles were 2 xx 10^(-30) kg and 10^(-30)kg , respectively. Distance between them were 12Å(1Å = 10^(- 10)m). Paths of the two particles was

100 mL of ozone (O_3) at STP were passed through 100 mL of 10 volume H_2O_2 solution. What is the volume strength of H_2O_2 after the reaction?

In a helium dilution refrigerator .^(3)He and .^(4)He are mixed in a special chamber to obtain extremely low temperature. A Bainbridge mass spectrometer is used to measure the ratio of the two isotopes (a) If the spectrometer were used with 100 V cm^(-1) between the plates and a magnetic field of 0.2 T, what would be the speed of an ion that can pass through the velocity filter? (b) If the velocity-filter exit slit were 1 mm wide, could this machine resolve the two isotopes ?

Anthropologists determine that new dwellings in an ancient farming community were constructed monthly as modeled by the function f(x)=2x+100, where x is the current month of the year and f(x) is the number of dwellings constructed by the end of that month. Additionally, they determine that the population grew exponentially each month, thanks to the discovery of more fertile land for farming. This growth is modeled by the equation g(x)=3^x , where g(x) represents the current population at the end of a given month. What is the smallest integer value of x, with 1 representing the end of January and 12 representing the end of December, at which the population surpasses the number of dwellings built?