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Philip P.'s Resources

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f(x) = x³ - 4x² - 3x + 4   To find the extrema, compute the first derivative, f'(x), set it to zero and solve for x:   f'(x) = 3x² - 8x - 3 0 = 3x² - 8x - 3 0 = (3x+1)(x-3)   x = -1/3 and 3   To determine whether the extreme points...

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Solve for t:   h = -(1/2)gt² + k h-k = -(1/2)gt² 2(k-h)/g = t² √(2(k-h)/g) = t   tearth = √(2(400-75)/9.8) = √(325/9.8) = ____? tmoon = √(2(400-75)/1.6) = √(325/1.6) = ____?   How much longer = tmoon - tearth

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If (-2,-5) is the minimum, it is the vertex of the parabola.  Use the vertex form y = a(x-h)2+k where (h,k) is the location of the vertex = (-2,-5):   y = a(x-(-2)) + (-5) y = a(x+2)² -5   To find a, plug in the given point (1,4):   y =...

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You don't know what the two numbers are, so they are the unknowns you are trying to find.  Label one of the numbers as x, the other as y.  Now translate the words to math.  When you have two unknowns (x and y), you will need two equations to solve the problem.   The sum...

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KE = (1/2)mv2 m = mass in kg = 40 kg v = speed in m/s = 5 m/s   Plug in the numbers and compute the answer.  The units of KE are "joules".

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what's dilation (answer)

Dilation changes the size of the object while keeping the object shape.  Dilating by a factor of 2 makes an object twice as big.  It's a two step process:   First, subtract the point of dilation (P = (0,-1)) from each point on the triangle:      A"...

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