Alan

Multiply top and bottom by i to get    8i/i^2 →  -8i  →  0 - 8i

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sin takes values between 1 and -1, so there is no angle whose sin is 83/28

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Pressure head = p/(rho*g)

Use the following:

p_B + (1/2)*rho*v_B^2 = p_A + (1/2)*rho*v_A^2                   p_B = rho*g*h

v_A*Area_A =  v_B*Area_B

p_B + (1/2)*rho*v_B^2  =  p_C + (1/2)*rho*v_C^2  + (0.15/2)*rho*v_B^2

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v_C*Area_C = v_B*Area_B

Volume flow rate = v*Area

v is velocity,  p is static pressure

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To clarify:    cos(90° - x) = sin(x)

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x = sin^-1(0.2588) ≈ 15°

The cosine of the complementary angle to x is always equal to the sine of x.  (Complementary angles sum to 90°).

Use the online chi-squared calculator at http://stattrek.com/online-calculator/chi-square.aspx 

2*2*2*3*5 = 120

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ncr(n,k) calculates the number of combinations taken k at a time from n.

ncr(n,k)  = n!/(k!*(n-k)!)

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I assume the first term is meant to be (t-1)^2.  If so:

(t - 1)^2 + 12 = -7(t-1)

Add 7(t -1) to both sides:

(t - 1)^2 + 7(t - 1) + 12 = 0

This factors as

(t - 1 + 3)(t - 1 + 4) = 0

or (t + 2)(t + 3) = 0

so t = -2  or  t = -3

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