Alan

Assuming a(t) is acceleration, then

velocity is:  v(t) = t³/3 - t² + 6t + k₁     where k₁ is a constant

position is:  s(t) = t⁴/12 - t³/3 + 3t² + k₁t + k₂  where k₂ is another constant.

The two constants are found from:

s(0) = 0:    0 = k₂

s(1) = 20:   20 = 1/12 - 1/3 + 3 + k₁ + k₂

.

A more pictorial approach! 

This wouldn't be so good for much bigger numbers though!

.

This should help (though I've left some work for you to do!):

.

"Serena is wearing a pendant that was made by inscribing a square ruby in a sterling silver circle. The distance from the center of the pendant to its edge is 5.3 centimeters. Find the area of the pendant that is not covered by the ruby. Round to the nearest hundredth"

radius of circle: r = 5.3cm

Area of circular part of pendant;  A1 = pi*r² so A1 = pi*5.3² cm²

r is half the diagonal of the square ruby so the side length of the square is 2r/sqrt(2) → r*sqrt(2) 

Area of square ruby is:  A2 = (r*sqrt(2))² or A2 = 2*5.3² cm²

Area not covered by ruby:  A1 - A2 = (pi - 2)*5.3² cm² →    32.07 cm²

.

Examples:

.

Melody,

The first group of Wolfram Alpha results ( e.g. 80.c1) give values that make x1 and x2 not only equal, but equal to zero, when c1 is an integer.  The second group (e.g. 6.3662(6.28319.c1 - 0.82757 ) ) give values that make x1 and x2 equal (but not equal to zero) when c1 is an integer.  

However, the Wolfram Alpha expressions don't seem to include all possible solutions as far as I can see.  In particular they don't give the 5.268s result!

.

"1288e^(-60x)-549e^(-30x)-739=0"

Because 1288 = 549 + 739 the solution is x = 0

.

Yes, this is correct!

.

Search for information on the Simplex method.

.

Calculate:  (length² + width² + height²)^1/2

.

.