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Given that sin(x) + cos(x) = 2/3, find cos(4x)

It is not clear what to do when starting, but we realise that by making both sides to the power of two, will lead to have an expression containing sin^2(x) + cos^2(x), which is equal to one (which will pr...

Answered by Felipe R. • Maths tutor

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Find the area enclosed between the curves y = f(x) and y = g(x)

Don't forget, in order to find the area under a curve y=f(x) between two values x=a and x=b we integrate f(x) between a and b.Thus to find the area enclosed between two curves y=f(x) and y=g(x) we simply ...

Answered by Matthew G. • Maths tutor

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Solve the two simultaneous equations X2 +2Y2= 18 and X - Y = 3

1) X² +2Y²= 182) X - Y = 3
Rearrange 2) in the form X=3-Y then substitute in to 1); (3-y)²+2Y²=18, this is your new equation 39+3Y+3Y+Y²+2Y^...

Answered by Rebecca C. • Maths tutor

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at a shop in the US tax is added onto the price of an item at the till. this shop adds 5.7% of the items value to the total cost. if you buy a ball priced as $15, how much will you have to pay ?

0.057 x 15 = 0.855 total = 15 + 0.988 = 15.855

Answered by Merlin B. • Maths tutor

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dy/dx = 6x^2 - 3x + 4 when y=14 x=2 Find y in terms of x

∫dy/dx = ∫6x^2 - 3x + 4y = (6/3)x^3 - ( 3/2)x^2 + 4x + cLet y = 14 and x = 214 = 2(2^3) - (3/2)(x^2) + 4(2) + c14 = 2(8) - (3/2)(4) + 4(2) + c14 = 16 - 6 + 8 + c14 = 18 + cc = -4therefore:y = 2x^3 - (3/2...

Answered by Lauren A. • Maths tutor

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