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Differentiate this equation: xy^2 = sin(3x) + y/x

y² + 2xy dy/dx = 3cos(3x) + 1/y - x/y² dy/dx thereforedy/dx = (3cos(3x) + 1/y - y²) / (2xy + x/y²)

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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

Perimeter= 72Ratios are 3:4:5In total, you can think of there being 3+4+5=12 "portions".This means that in the perimeter includes 12 portions. 72/12=6 so each portion is worth 6cm.
Now we c...

Answered by Natasha A. • Maths tutor

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Can you please explain how to expand two brackets, eg. (3x-7)(5x+6)

When I am expanding brackets I use the acronym FOIL and simplify. You begin by multiply the first term (F) in each bracket, followed by multiplying the outside terms (O), then the inside terms (I) and fin...

Answered by • Maths tutor

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Given that cos(x) = 1/4, what is cos(2x)?

cos(2x) = 2cos²(x) - 1 This is the identity. Therefore we can substitute in 2[cos²(x)] to be 2 multiplied by (1/4)².Therefore cos(2x) = 2(1/4)(1/4) - 1 = 2/16 - 1 = 2/16 -...

Answered by Bhumi K. • Maths tutor

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