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How would I identify and translate a purpose clause?

A purpose clause explains why an action is done and so can be considered the motivation behind the verb. It is constructed with 'ut' + a subjunctive verb and is translated in English as 'in order to' or simp...
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Answered by Victoria P. • Latin tutor
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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) +...
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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...
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Answered by Anthony M. • Maths tutor
3468 Views

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
Answered by • Maths tutor
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Explain the concept of internal economies of scale and the three stages of returns that can occur when firms increase their factors of production? Graphs maybe used in your answer

Internal economies of scale are centred around the relationship of a firm increasing its factors of production ie. its inputs and how this affects the average cost of producing goods. The general concept is ...
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Answered by Colm K. • Economics tutor
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