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You have three keys in your pocket which you extract in a random way to unlock a lock. Assume that exactly one key opens the door when you pick it out of your pocket. Find the expectation value of the number of times you need to pick out a key to unlock.

Let X be the random variable for this question. P(X=x) = 1/3 for all x. When X=x, we have that it took x times for us to retrieve the correct key.Thus, we have the infinite sum 1/3 + 2 2/3 1/3 + 3*(2/3)^2 1/...
NO
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What's the best way to solve projectile problems in Mechanics?

Getting a complicated problem of a mass being projected at a weird angle can seem daunting at first but these problems can be solved easily by breaking them down into two simpler problems.Using trigonometry,...
OA
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Express (7+ √5)/(3+√5) in the form a + b √5, where a and b are integers.

(7+ √5)/(3+√5)Here, the denominator is not rational - (numbers like 2 and 3 are rational). A number with an irrational denominator isn't incorrect, it just isn't in the simplest form it can be in.To rational...
OG
19634 Views

Find the definite integral of f(x) = 12/(x^2+10x+21) with limits [-1,1]. Give your answer to 2 decimal places.

Factorising denominator of fraction: x^2 + 10x + 21 = (x+3)(x+7) 2) Partial fractions: f(x) = 12/(x+3)(x+7) ; let f(x) = A/(x+3) + B/(x+7) then equating the nominator: A(x+7) + B(x+3) = 12 From this we can s...
CG
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Solve the second order ODE, giving a general solution: x'' + 2x' - 3x = 2e^-t

First find an auxiliary equation, for the complimentary function:m^2 + 2m - 3 = 0, (m+3)(m-1)=0m=1 or m=-3So the complimentary function is: x= Ae^t + Be^-3tFor the particular integral (PI), let x = Ue^-tthen...
IF
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