1. Two straight walls meet an an angle T/4. A straight piece of fencing PQ of length 10 metres is used to create an enclosure APQ as shown. a) Show that the area of APQ is given by 50-2 sin(-" - (). [T -5 ] 10 m b) If the angle is varied, using differentiation or otherwise find the value of o which maximizes the area of triangle APQ. [T -5]1. Explain two different ways to solve for the derivative of $(0) = 200cos'0 - 100. [C - 4] 2. Explain the steps you would take to find the derivative of f(x) = (1)e-3x +tan(3x-5) [C - 4]1. Determine the equation of the normal line to f (x) = eat x =- 1. [A -5] 2. A radioactive substance decays so that after t years, the amount remaining, expressed as a percent of the original amount, is A (t) = 100(1.2)". [A - 5] a) What is the half-life for this substance? Round to 2 decimal places. b) Determine the rate of decay after 5 years. Round to 2 decimal places. 3. The value of an investment in Canada Savings Bonds is compounded continuously at 3.75% per annum. At what rate, correct to 2 decimal places, is the investment growing at the time when its value has doubled? [A -5]