## Philip P.'s Resources Twice y (2y) is at most (≤) 16:   2y ≤ 16 y ≤ 8 Assuming a direct variation relation, the ratio x/y is the same for any x, y combination.  Hence:   24/30 = x/90   Solve for x. 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... 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 A product is a multiplication, so the product of 5 and -4 is (5)(-4).  Eight less than that is (5)(-4) - 8 = -20 - 8 = -28. g(x) = 6x-3 g(5) = 6·5 - 3 g(5) = 27   f(x) = 2x + 5 f(g(5)) = f(27) = 2·27 + 5 = 59 average speed = distance/time = (3 km)/(6+7+7 min) = ___? km/min Compute the time to drop 200 m.   h = (1/2)gt²   2h/g = t² √(2h/g) = t √(2·200/9.8) = t 6.4 sec = t   It takes the supplies 6.4 sec to drop to the ground, so drop them 6.4 sec before you get directly overhead. 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 =... OK, I've figured out what you meant.  It's not "m is greater than s is 64", it's "the measure of angle s (m∠s) is 64.  What is the measure of angle t (m∠t)?"  Since s and t are complementary, they sum to 90°.   m∠s + m∠t = 90°   The... It's an incomplete definition.  The complete definition would be:   An angle bisector splits an angle into two equal parts; that is, into two congruent angles tan(t) = sin(t)/cos(t)   1/sec(t) = cos(t)   tan(t)/sec(t) = sin(t)·cos(t)/cos(t) = ? 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... "Making u the subject" means getting u by itself on one side of the equation and everything else on the other side.  So we need to move all of the non-u terms to the other side of the equation.   s = ut + ½ at²   Subtract ½ at² from both sides:   s... 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". Numbers have place value.  The 5 in 634,952 is in the tens place, so it's value is 5×10 = 50.  The 5 in 43,597 is in the hundreds place, so its value is 5×100 = 500.  So the 5 in 634,952 is only 50/500 = 1/10 as big as the 5 in 43,597. 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"... angle 1 = 4x + 12 angle 2 = 2(4x+12) = 8x + 24   Since they are supplementary:   angle 1 + angle 2 = 180° 4x + 12 + 8x + 24 = 180 12x + 36 = 180   Solve for x, then plug the value of x into the angle 1 and angle 2... 180° - 105° = 75°   The two remaining angles of the triangle sum to 75°.  The are in a part to part ratio of 4:11.  The part to whole ratio for each angle is 4:15 and 11:15.  So one angle is:   (4/15)(75°) = _____?   and the other angle is:   (11/15)((75°)... f(x) = -6x + 7 when f(x) = 61   61 = -6x + 7   Subtract 7 from both sides:   54 = -6x   Divide both sides by -6:   -9 = x   Done