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Answers by Philip P.

V(t) = 10ekt   In 2002, t = 2002 - 1975 = 27:   V(27) = 10e27k 20 = 10e27k 2 = e27k ln(2) = 27k ln(2)/27 = k   This is the exact answer.  If you want an approximate answer, use your calculator to compute the value of ln(2)/27.

In all of these types of problems, you need to draw a diagram and find the right triangle.  In this case: One leg of the triangle runs horizontally from the boat to the base of the cliff and equals 128 feet The other leg runs vertically from the base to the top of the cliff, so it's...

You don't get the same answer because multiplying 0.23 by 50 is not the right procedure.  If you turn 23 into 0.23, you need to divided it by 0.50:   23/50 = 0.23/0.50 = 0.46 = 46%   Another way to think of it is that 0.5 = (1/2):   0.23/0.5 = 0.23/(1/2)...

Assuming the temperature remains constant, you can use Boyle's Law:   P1V1 = P2V2 P1 = starting pressure = 20 atm V1 = starting volume = 500 ml P2 = final pressure = 14 atm V2 = final volume = ? ml   Plug in the numbers and solve for V2.

Let x = the length and x-4 = the width:   Area = (length)(width) 96 = x(x-4) 96 = x2 - 4x 0 = x2 - 4x - 96 0 = (x-12)(x+8)   x = 12 and -8.  Since you can't have a negative length, x = 12.   Perimeter = 2(length) + 2(width) Perimeter...

16x2 - 64x + 7y2 = 48   Complete the square on the x terms:   16(x2-4x+4) + 7y2 = 48 + 16·4 16(x-2)2 + 7y2 = 112   Divide by 16·7 (=112):   (x-2)2/7 + y2/16 = 1   This is the equation of an ellipse centered...

x3 + 3x2 = 4 x3+ 3x2 - 4 = 0   To factor, we want three factors of -4 that add to +3:  Answer: 2·2·(-1) = -4, 2+2+(-1) = 3.   (x+2)(x+2)(x-1) = 0 (x+2)2(x-1) = 0 x = -2 and x = 1   Since you can't have a negative...

y = 4x · x2   y = eln(4^x) · x2   y = ex ln(4) · x2    [Log Property: ln(ab) = b ln(a)]   Use the Product Rule to find the derivative.  Remember that ln(4) is just a constant.   https://www.wyzant.com/resources/files/454985...