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Solve the ODE y' = -x/y.

we have dy/dx = -x/y , so we treat the differentials as fractions and write y dy = -x dx. Now integrating the left side with respect to y and the right side with respect to x, we have y 2 /2 = -x 2 /2 + C. W...
JM
3696 Views

On the line of centres between the Earth and the Moon, there is a point where the net gravitational force is zero. Given that the distance between the two is 385,000 km, and that the Earth has a mass 81x that of the Moon, how far is this point from Earth?

Here, we must consider Newton's Law of Universal Gravitation. This states that the gravitational force acting between two bodies is proportional to the masses of each body and inversely proportional to the s...
PR
Answered by Phil R. • Physics tutor
8130 Views

How do I multiply and divide indices?

First you need to understand what an index (or power) is. It’s just a compact way of writing a number multiplied by itself a number of times. For example: 3 4 = 3x3x3x3 and a 2 = axa. If two indices have the...
SM
Answered by Sarah M. • Maths tutor
14225 Views

I've been told that I can't, in general, differentiate functions involving absolute values (e.g. f(x) = |x|). Why is that?

When you differentiate a function which has only one parameter, like f(x), you are finding a new function, f'(x), which gives the gradient of your original function at every point. You'll probably remember t...
RW
Answered by Richard W. • Maths tutor
3456 Views

What will make my personal statement stand out?

Universities get a huge amount of applications each year. Each one will contain a person trying to explain to them why they should be let into that specific university. What they are really interested to see...
DT
2698 Views