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The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3 : 4 : 5. Work out the area of the triangle.

As we know the ratio of the sides is 3:4:5, label the sides x,y and z respectively. Side x is of length (3/12)*72, side y is of length (4/12)*72 and side z is of length (5/12) 72. Giving, x = 18cm, y = 24cm,...
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Answered by Viresh S. • Maths tutor
3193 Views

Find the turning points of the curve y = 3x^4 - 8x^3 -3

Differentiate to get:dy/dx = 12x^3 -24x^2Factorise and set equal to 0:12x^2(x-2) = 0Solve to get x = 2 and x =0.
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Answered by Daniel C. • Maths tutor
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How do you solve these simultaneous equations? 4x + 5y = 8; 2x + 3y = 5

By elimination:(eq1) 4x + 5y = 8(eq2) 2x + 3y = 5By eye you can see that 2x multiplied by 2 is 4x.If we multiply the whole of (eq2) by 2 we get:(eq2.1) 4x + 6y = 10(eq1) 4x + 5y = 8If we subtract the whole o...
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Answered by Wendy L. • Maths tutor
6035 Views

Integrate: xe^x

Integrate by parts once to obtain: xe^x - e^x + c
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Answered by Daniel N. • Maths tutor
4112 Views

Given y = x(3x+ 5)^3. Find dy/dx.

First we notice that y can be written as the product of two functions of x, u = x and v = (3x + 5)^3. This means we can use the product rule to differentiate which is dy/dx = uv' + vu'. We can plug our funct...
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Answered by Michael S. • Maths tutor
5018 Views