Math+Trail+Spring+2011+Solutions

=Solutions to our Math Trail Problems=

Solution Problem 1

It most closely resembles the family of sin and cosine. Below is the graph of what the derivative would look like.

Solution Problem 2

1) Count how many layers of bricks make up the wall (~14). Then estimate the height of one brick (~7.5in). Multiply the number of layers and the height of the brick (~105 inches = 8.75 feet). 2) Count the number of steps (~20 ). Then estimate the height of one step (~6.75in). Multiply the number of steps and the height on one step (~135 inches = 11.25 feet).

Solution Problem 3

Solution Problem 4

One wooden plank is estimated to be 15cm. 50.5 planks makes the hypotenuse of the triangle. (50.5)*15cm = 757.5 cm. There are squares that make up the longest leg of the triangle. The length of one square is equal to 7 planks. Seven squares make up the length of the leg. 7*15cm*7 = 735cm. The length of the hypotenuse is 757.5 cm and the length of a side is 735cm. By the Pythagorean theorem we can find out the last length of the triangle. The Pythagorean theorem states a^2 + b^2 = c^2. We have a^2 and c^2, so to find b^ we get b all by itself. b = (c^2 - a^2)^(1/2) = 183.25cm.