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Answers by Michael F.

Adding acid? (answer)

.5×7 + x = the acid in the final soloution 7+x is the amount of the final solution (3.5+x)/(7+x)=.7 3.5+x=.7(7+x) 3.5+x=4.9+.7x .3x=1.4 x=14/3=4 2/3 gal Note:3 1/2 + 4 2/3 = 8  1/6  total acid after addition of acid 7+4...

x6-19x3-216=0 Let y=x3 and have y2-19y-216=0 which may be factored as (y-27)(y+8)=0 which gives that y=27, y=-8 and so that x=3 or x=-2

The number of successes is 12C10 = 12C2 choose 10 face cards from the 12 in the deck. The number of ways to choose 10 cards from the deck is 52C10. The probability is 12C2/52C10 The calculation gives (12×11/2)/((52×...×43)/10!)=4.171927873E-09 as the probability

[sec(π/4)cos(2π/3)]/[tan(π/6)/csc(3π/4)]. =cos(2π/3)/[cos(π/4)tan(π/6)sin(3π/4)] =-.5/[(√2/2)(√3/3)√2/2)]=-3/√3=-√3 The only tricky parts are finding the reference angles for 2π/3 and 3π/4

D. x=sin2y dx=2sinycosydy √x/√(1-x)=siny/cosy integrand is (siny/cosy)2sinycosydy=2sin2ydy at x=0 y=0 and at x=1/2 y=π/4 ∫2sin2ydy from 0 to π/4

word problems (answer)

Original fraction 5d/d. Adjusted fraction  (5d+12)/(d+12)=2 5d+12=2d+24,  3d=12, d=4 20/4 original fraction, 32/16 when 12 added to both numerator and denominator

Probability (answer)

a.       4C2/52C2=1/221  two aces out of four/choose 2 cards from deck   b.      48C2/52C2=188/221  two cards not aces/choose 2 cards from deck  

Distance= Rate times time and so time=Distance/Rate time=85/√10,800 if you like rational denominators time=85√10,800 /10,800

5x^2 + 7x = 6 (answer)

The quadratic equation 5x2+7x-6=0 has discriminant 72-4(5)(-6)=49+120=169, it has both its roots real. Since we are so near the solution, the quadratic formula gives x=(-7±13)/10=-2, 6/10 N.B. 5×4+7×(-2)-6=0 as does 5×(3/5)2+7×3/5-6=5×9/25+21/5-6=0