Tutor profile: Robbie M.
Subject: Applied Mathematics
Solve for x: x^2 - x - 12 = 0
Because this is of the type : x^2 +mx+c We know that it's a quadratic equation We have an x^2, a multiple of x (-1) and an integer (-12). Because of this our equation will look like : (x+a)(x+b) where a and b are integers. Let's have a look: We need a * b to equal -12 and a+b to equal -1. Which numbers add together to make -1 and times together to make -12? -4 and 3 Let's check if that works: (x-4)(x+3) = x^2-4x+3x-12 = x^2-x-12 It's correct You could also use the quadratic equation to solve this question, though it would probably take longer
Complete the balanced equation for the overall reaction in a hydrogen fuel cell. _____ H2 + _____ --> _____H2O
This is a simple explanation of the answer, not just the answer. This equation is showing that the reactants (on the left of the arrow) react to form the product (right hand side of the arrow). Since atoms never simply disappear in a reaction, there must be the same number of Hydrogen and Oxygen atoms on the left hand side of the equation as there are on the right. Therefore we have to balance the equation. Looking at the right hand side, we see that there is an Oxygen atom. Therefore there must be at least one O atom on the left hand side.. _____ H2 + O2 --> _____H2O Now there's two Oxygen atoms on the left, so we have to increase the number of O atoms on the right to match it. We are making H2O so we can't just add another O to make it H2O2 as that's not what happens in the reaction. We must increase the number of H2O molecules to 2 instead: _____ H2 + O2 --> 2H2O Now we have 2H2O on the right, how many H atoms do we have there? It's 2*2 = 4. We have 4 H atoms on the right. Now we must make the left hand side equal to 4 as well. 2H2 + O2 --> 2H2O Now we have 4 H atoms on the left (2H2) and 4 on the right. We have 2 O atoms on the left and 2 O atoms on the right. We are all balanced and have solved the problem.
Gas in a tube is compressed. If the gas is compressed quickly the temperature of the gas increases. Explain how the temperature increase would affect the pressure exerted by the gas. 4 marks
Pressure is the force per unit area (f/a). The temperature increase will increase the kinetic energy of the gas particles so they will be moving faster. Because the particles are moving faster, they collide with the walls of the container more frequently, so they exert a greater average force on the walls of the container. Because the particles are moving faster, each individual collision with a wall of the container will exert more force. The faster and more frequent collisions exert a greater pressure (force/area) of the inside of the tube. (I have simulations which I can share that show this happening)
needs and Robbie will reply soon.