Draw the following scenarios. For all the drawings, you should include all appropriate markings. The figures should also be more or less “to scale.” Furthermore, in each scenario, M is a point on . [2 points each]
In Δ, ⊥ . ii. In Δ, = .
a) Draw a scenario where (i) is true, but (ii) is not.
b) Draw a scenario where (ii) is true, but (i) is not.
c) Draw a scenario where both (i) and (ii) are true.
d) Make a conjecture (hypothesis) about some feature of Δ that is true in (c) that is not true in either (a) or (b).
1. If two sides of a triangle are 7 and 12.
a. Find a range of values for the length of the third side of the triangle.
b. What is the probability that the unknown side is the longest side?
c. If it is known that the third side of the triangle is an integer length, what is the probability that the triangle is isosceles?
2. For each triangle below, determine if a triangle with the given dimensions is possible. If not, explain why not. [2 points each]
d.
e.
f.
g.
Kick It, Inc. manufactures soccer balls. To construct the covering for each ball, 20 regular hexagons and 12 regular pentagons cut from synthetic leather are sewn together. Since the polygons touch each other, each polygon has a side length of two inches.
a. What is the total area on the surface of the soccer ball? Round your answer to the nearest square inch. [4 points]
b. Using your answer from (a), find the radius of the soccer ball (assuming it is sphere-like). [2 points]
c. For easy shipping, the inflated soccer balls are placed in boxes. What is the volume of the smallest box that could hold one of these soccer balls? [2 points]
In the math office (L08), take one measurement on Mr. Osters’s STOP sign, and from that measurement alone, find the area of the STOP sign.
a. The measurement I took was: ______. (A word, not a number) [1 point]
I took this measurement because ______
[1 point]
b. Calculations [5 points]
(30 points) Pirate Robinson stole a box of gold from Pirate Mahoney. He decided to bury it in a parabolic trench 6 feet wide on a remote island and then retrieve it several years later. How deep must he dig the trench to bury a 2 ft cubical treasure chest (2 ft on all edges), 1 foot underneath the ground?
(By the way, Pirate Robinson measures the depth of his trench at the deepest point in the trench.)
5. Given the graph of the polynomial below, determine a possible equation taking the intercepts into account. You may leave your answer in factored form.
1. The 2016 Summer Olympics will be in Rio de Janeiro. Use Grapher to create the Olympic Rings.
The upper left ring has an equation of x2+y2=9, but shifted up 5. The circles on the same level have 1 unit separating them.
Once you have completed the task, write the equations of the five rings below.
______
______
Briefly explain the process you used to solve this problem.