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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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find the roots of the equation 7x^2+11x-2=0 in exact form

since the values are too difficult to calculate from factorising, we use the quadratic formula ((-b)±(b^2-4ac)^(1/2))/(2a).putting the values in as (ax^2+bx+c=0) we find the roots in exact form are;(-11+(177...
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Answered by Matthew P. • Maths tutor
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what is differentiation for?

When differentiating you find the gradient of the function/line, this means how fast does the function goes up or down.
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Answered by Richard B. • 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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