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A curve C has the following equation: x^3 + 3y - 4(x^3)*(y^3) a) Show that (1,1) lies on C b) Find dy/dx

a) Substituting the coordinate (1,1) into the left hand side of the equation for C we obtain: (1 3 ) + 3*1 - 4(1 3 )(1 3 ) = 1 + 3 - 4 = 0 = The right hand side of the equation, hence the equation is satisfi...
HW
Answered by Harry W. • Maths tutor
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show that tan(x)/sec2(x) = (1/2)sin(2x)

tan(x)/sec 2 (x) Sec(x) = 1/cos(x), therefore 1/sec(x) = cos(x). also tan(x) = sin(x)/cos(x).using substitution, tan(x)/sec 2 (x) = (sin(x)/cos(x)) * cos 2 (x) = sin(x)cos(x). sin(x+y) = sin(x)cos(y) + cos(x...
OO
Answered by Olaitan O. • Maths tutor
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A ladder 5.5m long is leaning against a wall. the foot of the ladder is 1.7m away from the wall. how far up the wall does the ladder reach?

This is a classic GCSE Pythagoras' Theorem question. The first thing we are going to do is draw a diagram. Once we sketch out a diagram, we can see that the ladder makes a triangle shape with the wall. If we...
AN
Answered by Annie N. • Maths tutor
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How do I work out the length of sides on a right-angle triangle?

Over 2000 Pythagoras discovered that when a triangle has a right angle (90 degrees), and squares are made for each of the three sides, then the biggest square has the exact same area as the two other squares...
AK
Answered by Amrita K. • Maths tutor
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Differentiate 5x^2 + 11x + 5 with respect to x

The simple rule of thumb applied to differentiation can be used in this example - 'Multiply each term by its power then reduce the power by one'. Doing this 5x^2 becomes 2 5x^(2-1)=10x. Repeating for 11x giv...
SL
Answered by Sam L. • Maths tutor
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