Alan

This would be 3*(0.8^2810) = not much wood left!

Approximately 95.45% falls within 2 standard deviations of the mean.

This is true of any normal distribution, irrespective of the actual values of the mean and standard deviation.

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1 mile = 1760 yards

1 square mile = 1760^2 square yards

1 township = 36 square miles = 36*1760^2 square yards

3.5 townships  =  3.5*36*1760^2 square yards = 3.902976x10^8 square yards

Did you mean to put f(x) = 3x  so f(2) = 3*2 = 6

h(x) = 2x - 7 so h(f(2)) = h(6) = 2*6 - 7 = 5

21000 = a + 100b                    (1)

126000 = a + 450b                  (2)

Subtract (1) from (2)

105000 = 350b

Divide by 350

b = 300

Put this back into (1)

21000 = a +100*300

a = -9000

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Let the number be n

Then  5n - 6 = 7n

Subtract 5n from both sides

-6 = 2n

Divide both sides by 2

-3 = n  (or just n = -3)

Since area = pi*radius^2 then radius = (area/pi)^(1/2)  or radius = square root of (area/pi)

The vertex is where df(x)/dx = 0

df(x)/dx = -(2/3)x-5

This is zero when x = -15/2, at which point f(x) = -(1/3)(15/2)^2 - 5*(-15/2) + 2 = 83/4

so the vertex is at (-15/2, 83/4)

Something like this?

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When x → 0, sin(2x) → 2x and e^(2x) → 1 + 2x so (g(x)*sin(2x) + e^(2x) - 1)/x → (5*2x + 1 + 2x - 1)/x → 12x/x → 12