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Simplify 7 × e × f × 8

Always do the numbers first before dealing with the letters. We move the numbers to one side , and the letters to the other. (7 x 8) x e x f -> I have enclosed the numbers in brackets in order to separate...
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Solve the integral int(sin^2(x))dx

Knowing that 1-2sin 2 (x) = cos(2x), substitute sin 2 (x) as: sin 2 (x) = (1-cos(2x))/2Use the linearity of the integral to split it into: Int(1/2) - Int(cos(2x)/2)dxWhich is in the end:0.5x - 0.25 sin(2x) +...
MM
Answered by Maks M. • Maths tutor
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Solve the simultaneous equations x^2 +8y=20 and y=x+4

To begin you must substitute the value of y provided into the first equation. The would change the equation into the following form:x^2+8(x+4)=20. Now expand the bracket so that the equation becomes:x^2+8x+3...
AM
Answered by Anthony M. • Maths tutor
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Differentiate y=x^x with respect to x.

y=x^x, taking natural log of both sides ln(y)=ln(x^x), using laws of logs ln(y)=xln(x), using product rule and implicit differentiation dy/dx 1/y=ln(x)+1 dy/dx=(ln(x)+1)y dy/dx=(ln(x)+1)x^x
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Solve the following simultaneous equations. x^2 + 2y = 9, y = x + 3

x^2 + 2y = 9y = x + 3 x^2 + 2y = 9x^2 + 2(x+3) = 9x^2 + 2x + 6 = 9x^2 + 2x - 3 = 0(x + 3)(x - 1) = 0x= -3, x = 1 when x = -3y = x + 3y = (-3) + 3y = 0 when x = 1y = x + 3y = (1) + 3y = 4
JF
Answered by John F. • Maths tutor
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