CubeyThePenguin

The vertex of the parabola is at (2, 3), so the axis of symmetry is x = 2.

UTR is an equilateral triangle and RTS is isosceles.

UT = TR = RS 

x - 7 = 11

x = 18

The angles in triangle RTS add up to 180 degrees.

5y + 5y + 120 = 180

10y = 60

y = 6

Start by squaring the entire thing.

\(a^2 < 77 < (a+1)^2\)

Let's start with the first condition: a^2 < 77. From here, we know that a is equal to 8 or less.

Also, (8 + 1)^2 = 81, which works.

The integer a is 8.

(height of tree) / (shadow of tree) = (Andrea's height) / (Andrea's shadow)

Convert everything to inches beforehand.

(40 * 12)/(10 * 12) = x/15

x = 60 inches

Let the cubic be in the form f(x) = ax^3 + bx^2 + cx + d.

We have four points and four variables, so plug them in:

(3, -4) ==> 27a + 9b + 3c + d = -4

(-1, 2) ==> a - b + c - d = 2

(0, 0) ==> d = 0

(7, 5) ==> 343a + 49b + 7c + d = 5

Use WolframAlpha or a similar program to solve for a, b, c, and d.

= (120 - 20)/2

= 50 degrees

Here are the powers of i:

i^0 = 1

i^1 = i

i^2 = -1

i^3 = -i

i^x + i^y is a real number if: 

- x is divisible by 4 and y is 2 more than a multiple of 4

-x is 1 more than a multiple of 4 and y is 3 more than a multiple of 4

Thanks, I really needed that today.