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Solve the following simultaneous equations: 3x + 5y = -4 and -2x + 3y = 9

Label the equations 1 and 2 We want to make it so the x are the same number - therefore we have to find a common multiple of 2 and 3 - this is 6 Therefore the equations turn into: 1) 6x + 10y = -8 2) -6x + 9...
KP
Answered by Krishnaa P. • Maths tutor
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What actually are sin, cos and tan?

This is a common question asked by my students when they first learn about trigonometry. First draw a unit circle on the plane and the graphs of sine and cosine next to it. The circle obviously has 360 degre...
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Answered by Leon P. • Maths tutor
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The point P (4, –1) lies on the curve C with equation y = f( x ), x > 0, and f '(x) =x/2 - 6/√x + 3. Find the equation of the tangent to C at the point P , giving your answer in the form y = mx + c. Find f(x)

First step is to understand all the notation, i.e. the prime for derivative. We then need to understand that the derivative is the gradient of the tangent at a point. In this case at the point P we can find ...
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Answered by Leon P. • Maths tutor
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Differentiate sin(x)cos(x) using the product rule.

The product rule states (assuming x' is the differential of x): (fg)​′​​=f​′​​g+fg​′​​ Substitute the values into the rule: (sin(x)cos(x))' = sin(x)'cos(x) + sin(x)cos(x)' (sin(x)cos(x))' = cos 2 (x) - sin 2...
MP
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i) Using implicit differentiation find dy/dx for x^2 + y^2 = 4 ii) At what points is the tangent to the curve parallel to the y axis iii) Given the line y=x+c only intersects the circle once find c given that c is positive.

I don't know how effectively I can communicate this answer via text without the whiteboard but I'll try. i) First implicitly differentiate with respect to x: 2x + 2y * dy/dx = 0. Rearranging gives dy/dx = -x...
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Answered by James D. • Maths tutor
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