Balance the reaction for the combustion of octane: __C8H18 + __O2 ---> __H2O + __CO2
First, balance the carbon atoms. 1*C8H18 + __O2 ---> __H2O + 8*CO2 Next, balance the hydrogen atoms. 1*C8H18 + __O2 ---> 9*H2O + 8*CO2 Finally, balance the oxygen atoms. 1*C8H18 + 12.5*O2 ---> 9*H2O + 8*CO2 We can't have a decimal in front of the oxygen molecule, so multiply all of the coefficients by 2. 2*C8H18 + 25*O2 ---> 18*H2O + 16*CO2 The answers are 2, 25, 18, 16.
Integrate the following equation from 0 to pi: y = cos(x) + 4x + 5
The antiderivative of the sum is equal to the sum of the antiderivatives. Since the derivative of sine is cosine, the antiderivative of the function above is: Y = sin(x) + 2x^2 + 5x + C To get the answer, calculate Y(pi) - Y(0) = 2*(pi)^2 + 5*pi The numerical answer is approximately 35.45
A person holding a gun is standing on a frictionless sheet of ice. The person and the gun together have a mass of 75 kg. The person then shoots the gun. The bullet with mass 15 g leaves the barrel at 1000 m/s. How fast will the person holding the gun be moving backward after the shot?
Using conservation of momentum: Bullet: (15/1000 kg) * (1000 m/s) = 15 kg*m/s Person: (15 kg*m/s) / (75 kg) = 0.2 m/s