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Given y(x+y)=3 evaluate dy/dx when y=1

y(x+y)=3,yx +y 2 =3,Differentiating with respect to x,y+x(dy/dx) +2y(dy/dx)=0when y=1, x=3-1=2 (from original equation)1+2(dy/dx) +2(dy/dx)=0,dy/dx=-1/4
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Answered by Leto P. • Maths tutor
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How do I rewrite 2 cos x + 4 sin x as one sin function?

This question makes use of the sin addition formula. It may be stated as sin (A + B) = sinA cosB + sinB cosA . We want to rewrite 2 cosx + 4 sinx in the form R sin (x + a), so firstly work out what R sin(x +...
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Answered by Sara S. • Maths tutor
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show that f(x)=cos(x) is even and what is its graphical property

If the function is even, f(x) = f(-x).cos(-x) is the same value as cos(+x) therefore the function is even. Its graphical property is that it is symmetrical about the y axis as all even functions are.
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Answered by Matthew P. • Maths tutor
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Differentiate: ln((e^x+1)/e^x-1))

Chain rule: First resolve the log differential, then resolve the fraction integration either by knowing the formula for it or by writing (e^x+1)/(e^x-1) as (e^x+1)(e^x-1)^(-1) and applying chain rule againLe...
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Answered by Mihai V. • Maths tutor
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A machine is used to manufacture custom spoilers for two types of sports car( Car A and Car B0. Each day, in a random order, n are produced for Car A and m for Car B. What is the probability that the m spoilers for Car B are produced consecutively?

First we look at the probability of producing a total ensemble which is 1/(n+m)!. This is in any random order and any part either m or n To further see what is going on let’s take some example let’s have 6 n...
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Answered by Mihai V. • Maths tutor
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