Question 2. In this question you will explore the idea of \"pancake volume invariance\" which can be used to understand and explain various mathematical results. In particular you are going to prove a result about triangles you may have seen before. (1) Warmup. Think about the \"Marilyn Monroe towers\" in Mississauga.4 How difcult do you think it would be to compute the volume of these towers? Briey explain. (2) Warmup. If you have a stack of ve pancakes, does sliding some of the pancakes over change the total volume of the stack? Is \"ve\" special here, or does this work for any number of pancakes? Briey explain. (3) Warmup. If you have a stack of ve rectangles, stacked horizontally, does sliding some of the rectangles over change the total area of the stack? Is \"ve\" special here, or does this work for any number of rectangles? Briey explain. (4) Let B and H be positive real numbers (representing base and height), and let d be any real number (representing a horizontal shift). Let T1 be the triangle formed by the three points (0, 0), (B, 0), and (B, H). Let T2 be the triangle formed by the three points (0,0), (B, 0), and (B + d, H). (5) Method 1. Compute and compare the areas of these triangles using basic geometric formulas. (Is this result surprising to you?) (6) Method 2. Draw 5 stacked rectangles of the same height that cover T1. Compute their total area. Shift these rectangles horizontally to cover T2. What does this suggest to you about how the areas of T1 and T2 compare? How could you make your solution more accurate and have less error? (7) Method 3. For both triangles, set up an integral (with respect to y) that measures the areas of these triangles (call these integrals I1 and [2). Without computing the integrals, simplify T2 to show that it is equal to Il. (8) You have proved the result that \"any two triangles with the same base and height have the same area\". Hooray! Method 2 and method 3 are actually related. Briey explain why