blackjack

Second part:

Draw a vector from the origin to the point (3, -1). That is vector a. Then draw a vector from the origin to the point (2, 2). That is vector b. Then complete the parallelogram from these two sides. The diagonal of the parallogram that goes from the origin to the opposite corner is the vector a + b

From the origin, go right 3 units and down 1 unit. Draw a vector from the origin to this point. That is vector a.

From that point, go left 1 unit and down 4 units. Draw a vector from the point (3, -1) to this point. That is vector b.

The red vector is the vector a + b

5

After that you can always put a pack of 4 into the cart and take out a pack of 3 resulting in the addition of 1 tennis ball OR (if there are no packs of 3 left in the cart) take out two packs of 4 and put in 3 packs of 3 resulting in the addition of 1 tennis ball.

To find the angle, we need to do:

arctan( -648 sqrt(3) / -648 ) = pi / 3

But our point is in the third quadrant, so we need to add pi to that angle to get it into the third quadrant.

pi/3 + pi = 4pi / 3

Let  x  be the number of pennies they each had to start with.

A month later, Kenny has 2 + 3x pennies while Linny has 4x - 7 pennies.

4x - 7 = 8 + (2 + 3x)

4x - 7 = 10 + 3x

x = 17