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Usually we cover both subject knowledge and exam technique, although that can change depending on each individual student. Then we go through diagrams, and they ask questions, and we go from there.

Lots of students say that the classes are too big in school, or that they don't have time to ask teachers after Online Lessons. In my Online Lessons, we take time to explore things in a little in a bit more detail.

I always look up the board my students are taking so the Online Lessons are really relevant. Then we go through past papers or set texts, whatever the student finds helpful.

I use the shared whiteboard. We make diagrams together and label them, and often the student prints it off because they know it's right and they completely understand it.

After tutoring one girl went and told all her friends the new explanation I gave her. And she was so excited about what she wrote in the exam she emailed me immediately afterwards.

There was one girl who had her exam on Monday. She wanted tuition on Friday, Saturday and Sunday beforehand. It was very intense, but she said the exam went well.

Step 1: Multiply both equations together so that the multiples of one of the unknown terms are the same or the negative of that number. This will allow you to add/subtract the two equations to eliminate one of the unknowns. Remember you are multiplying the whole of the equation so each term must be mutliplied.
Step 2: once you have eliminated one of the unknown terms (e.g. y) you can easily solve the equation to find the other unknown term (e.g. x) by rearraning the equation to make it the subject .
Step 3: Once you have found one of the unknowns, you can substitue your answer into one of the equations, and solve the equation to find the answer to the other unknown.

Answered by Matthew K.

Studies MBBS at Kings, London

x=4
y=3

Specific heat capacity does tell you how much energy a substance needs to increase their temperature and so substances with a low specific heat capacity (SHC) will increase in temperature more rapidly than those with a higher specific heat capacity.
Another way of thinking about it is that low SHC substances have less capacity in their thermal energy store per degree than substances with a higher SHC. It takes less energy to fill it but that means they contain less thermal energy at the same temperature than something with a higher SHC. Because they contain less thermal energy they will also cool faster than something with a higher SHC.
The reason metals often feel colder than non-metals is due to the transfer of thermal energy. Because of their atomic structure (metallic bonds) metals contain free electrons. These free electrons transfer thermal energy very rapidly. This means that when you put your hand on a metal surface it is able to quickly transfer the energy away from your hand making it feel colder than if you place your hand on a wooden surface, because it can’t transfer the thermal energy away as quickly.

Answered by Thomas-William M.

Studies Optical and X-ray Studies of the Accretion Flow in Black Hole Binaries at Durham

Firstly, let's rewrite each of these equations as the equation of a line i.e. in terms of y. So we have:
(1) y = 4x/3 - 11/3
(2) y = 2 - 3x/2
Draw line (1) on a graph. The (x,y) co-ordinates of any point on this line represent a pair of values for x and y which solve the equation y = 4x/3 - 11/3. Draw line (2) on the graph. Like with (1), the (x.y) co-ordinates on this line solve the equation y = 2 - 3x/2 . The __intersection__ of these points is the point where __both__ equations are solved. In this case, it is the point (2, -1), so our answer is x = 2 and y = -1

Answered by Daniel L.

Studies Actuarial Science at LSE

Pythagoras' theorem states that the square of the hypoteneuse is equal to the sum of the squares of the other two sides of a right angled triangle. The main usage of Pythagoras' theorem is to work out the length of an unknown side of a triangle. The formula we use is a^2 + b^2 = c^2. Where a and b refer to the shorter sides of the triangle, 'opposite' and 'adjacent' and c refers to the hypoteneuse which is the longest side of a triangle. If we use an example question: There is a ladder against a wall, the wall is 6m high and the distance between the bottom end of the ladder and the wall is 4m. Work out the length of the ladder. If we use pythagoras' theorem, we know that a^2 + b^2 = c^2, therefore 4^2 + 6^2= c^2. This comes to: 16 + 36 = c^2 -> 52= c^2. In order to solve this, takes a basic understanding of algebra; square root the 52 to get, 7.21111 to 2 d.p (decimal points) we get 7.21m.

Cosx-3sinx =R(CosxCosa-SinxSina)
1=Rcosa
R^2=1^2+3^2 r=(10)^0.5=(approx)3.16
a=1.249
3.16Cos(x+1.249)=4 has no solution as 4<3.16 so as cos(theta) has maximum value of 1, there are no solutions

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