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Write a short program to print all the even numbers 1 to 100

To begin with, we will need to make a loop which iterates (loops) 10 times, which we can use the for statement for:for value in range (1,101): // do something - this is a comment Note, here we use the range ...
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Answered by Sam P. • Python tutor
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Find the area under the curve y=xexp(-x)

first recognise ‘area under’ = integrationfunction is a product so by partsset x=u; exp(-x)=dv/dx integral(udv/dx)=uv-integral(vdu/dx) du/dx =1; v=-exp(-x)ans=(x.-exp(-x))-integral(1.exp(-x)dx)ans=-xexp(-x)+...
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Using z=cos(θ)+isin(θ), find expressions for z^n-1/z^n and z^n+1/z^n

We make use of De Moivre's Theorem which states that (cos( θ)+isin(θ))^n=cos(nθ)+isin(nθ). z^n-1/z^n=cos(nθ)+ isin(nθ)-cos(-nθ)- isin(-nθ)=cos(nθ)+ isin(nθ)-cos(nθ)+ isin(nθ) (by trig relationships)=2isin(nθ...
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Explain 2 Advantages of Using Die Casting over Sand casting for the manufacturing of a Metal Engine Block.

Options: (1 mark for 1 Advantage, 1 mark for 1 Explanation)Die casting has a better surface finish (1 mark). This Allows for a reduction of additional processes needed to finish the product which can make th...
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Prove that 2Sec(x)Cot(x) is identical to 2Cosec(x)

2 Secx = 2/CosxCotx = 1/Tan x = Cosx/SinxTherefore: 2SecCotx = 2/Cosx * Cosx/Sinx = 2/Sinx = 2Cosecx
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Answered by Ben S. • Maths tutor
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