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Answers by Philip P.

logarithms (answer)

N(t) = 211e0.0109t   For 1980, t=0 and N(t) = 211.  This is the population in 1980.  We want to know when the population will be twice as big, so we want N(t) = 2*211.  Let's plug that into the population equation and solve for t:   2*211 = 211e0.0109t 2...

Exact Value (answer)

Cos and cos-1 are inverses of one another, so cos(cos-1(4/5)) = 4/5   Same for sin and sin-1.   (BTW, it's "pi" not "pie")

Logarithms (answer)

2log5(A) - log5(B) + (1/3)log5(C) - 5log5(D)   Log property: b*log(a) = log(ab)        log5(A2) - log5(B) + log5(C1/3) - log5(D5)   Rearranging:        log5(A2) + log5(C1/3) - (log5(B) + log5(D5))   Log...

0.45a - 0.35a - 0.9   Combine like terms:   0.1a - 0.9   That's the most you can do with it.

log16 √(x+1) = 1/4   log16 (x+1)1/2 = 1/4   (1/2)*log16 (x+1) = 1/4   log16 (x+1) = 1/2   161/2 = (x+1)   4 = x + 1   3 = x

P(t) = P0*(1 - r)t P(t) = Population at time t = 80% of P0 = 0.8P0 P0 = initial population = 10,000 r = rate of decrease = 3% = 0.03 t = years   P(t) = P0*(1 - r)t 0.8*(10,000) = (10,000)*(1 - 0.03)t 0.8 = (0.97)t log(0.8) = log(0.97t) log(0.8) = t*log(0...

Well if it's a 3/4" screw and one part is 3/4", then the "other two" parts are zero.  I'm guessing you meant one part is 3/16 of an inch, rather than 3/4 because it's the only way to get 9/16 as the answer for the sum of the other two parts:   3/4" - 3/16"...

The three angles add up to 180o.  So add them up and set them equal to 180:        2√(2x + 5 √(2x) + 2√(2x) = 180      9√(2x) = 180      √(2x) = 20      2x = 202     ...

algebra stuff (answer)

P(h) = P0*(1 - r)h/1000   Where: P(h) is the pressure at altitude h P0 = the pressure at sea level (h=0 m) = 9898 kp r = rate of decrease = 11.7% (?) h = altitude above sea level = 3000 m (?)   Plug the numbers into the equation and use your calculator to...