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derivation of sin(3x)/(1+x^2) (answer)

Quotient rule: "low d'high - high d'low, square the denominator and away we go"   This essentially means "[ (bottom function)*(derivative of the top function) - (top function)*(derivative of the bottom function) ] / (bottom function)2   Applying the quotient...

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What are the roots of the equation (answer)

You have to use the quadratic equation to solve this problem.   The general formula for the quadratic equation is x = {-b +- sqrt [ b2 - 4(a)(c) ]} / (2a)   Applying this formula to this problem, we get: {-(-7) +- sqrt [ (-7)2 - 4(2)(4) ]} / (2a)   From...

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3*(2x^2+6x+3) (answer)

This is actually pretty straight forward.  Just multiply 3 all the way through.   So, we get 6x^2 + 18x + 9.

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Find f(h(x)) (answer)

Awesome, thanks for posting an example.   So in this problem, we want to replace the x in f(x) with h(x).  That would give us f(12/x).  So in the function for f(x), where there is an x, we replace it with (12/x).   So, f(h(x)) becomes f(12/x) = (12/x)^2 +...

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Find the exact circumference (answer)

Hi Theresa,   Circumference =  2*pi*r and area = pi*r*r.   So, the circumference would be 2*pi*11cm = 22pi cm.   Furthermore, the area would be pi*11cm*11cm = 121pi cm2   Hope this helps.

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find the inverse (answer)

Hi Dalia,   To find the inverse of the function the first step is to solve for t.  To do this, get t by itself.   We get √(3t) = y - 2.   Squaring both sides, we get 3t = y2 - 4y + 4.   Dividing both sides by 3, we get t =...