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A curve C has the equation x^3 + 6xy + y^2 = 0. Find dy/dx in terms of x and y.

By differentiating with respect to x, 3x^2+6x(dy/dx)+6y+2y(dy/dx)=0 So, dy/dx(6x+2y)=-3x^2-6y so dy/dx = -(3x^2+6y)/(2(3x+y))
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Answered by Mike H. • Maths tutor
4381 Views

Solve the quadratic equation X^2+3X+2=0 by factorisation.

There are different ways of solving quadratic equations but this one asks for you to solve by factorisation. This is where you take the equation on the left hand side and rewrite it into brackets - two bits ...
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Answered by Annabelle M. • Maths tutor
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Why does adding a constant to a function's input (as in f(x-a)) shift the plot of the function along the x-axis?

Imagine the function f(x) as a black box which takes in any value x and produces an output y. The black box acts on its input according to a rule which produces a unique value of y for a given x. If the blac...
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Answered by James H. • Maths tutor
7803 Views

Solve the following definite integral: f(x)=3e^(2x+1) for the limits a=0 and b=1, leaving your answer in exact form.

First set up integral. Do not forget dx! Int(f(x)) between 0 and 1 Optionally take out factor of 3 to simplify problem. Solve using substitution and the exponential rule. Integrated function should be (3/2)e...
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Answered by Fraser B. • Maths tutor
4822 Views

How do you convert between fractions, decimals and percentages?

For example, 7/10 is the same as 0.7 and 70%. Percentages are actually all fractions out of 100. 70% is 70/100, 50% is 50/100, etc. When these are written as fractions they should be simplified so the denomi...
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Answered by Elena D. • Maths tutor
4054 Views