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The equation for continually compounded interest is:  A = Pert, where   A = final amount, P = principal invested, r = rate in decimal, and e is the constant.   Since you want to double your investment, let A = 2p.   Thus makes the equation 2P = P e.08t   So:...

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related rates (answer)

So, V = (1/3)πr2h,  and h = 14 m., when d = 6.5 m. = 13/2 m.,  which means r = ½d = 13/4 m.   dV/dt = (-0.008 + k) m3/min  (leaking 0.008 and increasing by a constant,m k) at the time when h = 2.5 m. and dh/dt = +.28 m/min.   I would stat by finding...

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let y = -sin(x+5) - 9.   exchange y and x.   x = -sin(y+5) - 9   Solve for y:  sin(y+5) = -x - 9.   How do you solve this?  Try using the inverse sin of each side.   Good luck.

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If sin-1x = π/6, remember what the notation say.  It says "the angle whose sine is x, equals  π/6."   Therefore, this becomes:  sin π/6 = x.   Using the special triangle (30-60-90) says that x = ½.

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Sin(A - B) = sinAcosB - cosAsinB   (sinAcosB - cosAsinB)/sinAcosB = sinAcosB/sinAsinB - cosAsinB/sinAsinB.   There is a start.  Can you finish?   (hint: Look for common factors)

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Remember the double angle formula?   cos(2θ) = cos2θ - sin2θ = 2cos2θ - 1 = 1 - 2sin2θ.   Since your equation has a sin2θ, let's use the last one.   That makes the equation 1 - 2sin2θ + 6sin2θ = 2.   Subtract 1 and combine terms:  4sin2θ...

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OK, Irene.  I believe your equation is:  2/(w+2) - 3/w + (w+10)/(w2-4).   If this is correct, the LCD (least common denominator) is w(w-2)(w+2).   The first term only has (w+2) and therefore, needs to be multiplied by w(w-2)/(w)(w-2).   The...

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6x6x6=63, and (6x6x6)6 means 63x61 = 64.   Now, if you mean (6x6x6)6 then you have (63)6.  The rule here says to multiply the exponents:  618.    

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I see you have the factors.  Great.  Not that there is a pair that are equal.  If these are divided out, we get:        f(x) = −5(x + 7)                   ...

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Let's use synthetic division.  f(x) / (x - c).     In dividing by x + 4, to find c, let x + 4 = 0.      This makes x = -4,   so c = -4.       Use the c, and the coefficients, 1, 1, and -12.  We will...

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It means that somewhere between the values x = 2, and x = 3, the graph of f(x) = 0, or crosses the x axis. since the signs of f(x) change from a positive number to a negative number.   In other words, the zero of the function f(x) is between 2 and 3.  It appears that it may cross...

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Note that this is still a rectangle, and the length of the fencing is still 600 ft.                                         ...

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OK.  So f(x) = x2-5, and g(x) = √(x+5).   f(4) = 16 - 5 = 11, and g(4) = √9 = 3.   So (f/g)(4) = 11/3.   Since the only restriction on x on the function (f/g)(x) occurs when g(x) ≠0, the domain of this function is x>-5 (since the radical must be...

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