Alan

There is a ceiling function (ceil(x)) if that's what you mean:

The horizontal distance as a function of time is given by x = v0*cos(60°)*t

The vertical distance as a function of time is given by y = v0*sin(60°)*t - g*t²/2    where g is gravitational acceleration.

The above assumes air resistance is negligible.

Use the proportion:  P/60 = 50/20  so P = 60*5/2 or P = 150 pounds of plums

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We can write  \(\frac{A}{x+2}+\frac{B}{x+4} \rightarrow \frac{(A+B)x+4A+2B}{x^2+6x+8}\)

For this to equal  \(\frac{5}{x^2+6x+8}\) we must have A+B = 0   (and 4A+2B = 5)

So A+B = 0

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t, the time, is the independent variable and f, the future value, is the dependent variable.

The 6 multiplies both terms within the brackets.  6(1 - x/2)   →   6*1 -  6*x/2   →   6 - 3x

So 2 + 3x - (6 - 3x)  →  2 + 3x - 6 + 3x  →  -4 + 6x

If this is greater than 0 then:   -4 + 6x > 0    →     6x >  4    →    x > 4/6  or  x > 2/3

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arclength = (30/360)*2*pi*7.4*10^8  →  3.9*10^8  This is correct to one decimal place.

 It is 4*10^8 to one significant figure.

The probability of missing any of 1 to 60 in 100 is 40/100 or 0.4, so the probability of missing this 9 times in a row is 0.4⁹ = 0.000262144

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Wolfram Alpha says it's unknown, but see http://mathforum.org/library/drmath/view/51617.html

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Because log_mn =  p  means m^p = n  then log₂(5*x+4)=-1  means  5x + 4 = 2^-1

5x + 4 = 1/2 

5x = -7/4 

x = -7/20