Grade 12 math sheet please help solving it

full algebraic solutions and a final statement are required for all questions all calculations should use as exact values, only round final answers to three decimal places this assessment will be marked as a level, see rubric below 1. The position of a particle as it moves horizontally is described by: s(t) = sin?t - 2 cost Where's' is the displacement in metres and 't' is the time in seconds, where 0 S t $ 5 a) Determine when the particle has a velocity of 2m/s. b) Determine the acceleration of the particle when t = 4s. c) Is the particle moving towards or away from the origin when t = 4seconds? Justify your answer. 2. A right triangle has a hypotenuse of 20cm. Determine the angles that will maximize the perimeter of the triangle. 3. A dog chases a squirrel at a speed of 4m/s. The squirrel dashes up a tree at a rate of 2m/s. Find the rate of change of distance between the squirrel and the dog at the instant when the dog is 4m from the base of the tree trunk and the squirrel is 1.5m up the tree. 4. A non-uniform metal chain hangs between two walls. The height above ground level of this chain is given by the equation: h(x) = e-Zx + ex,0 s x s 2 Where 'x" is the distance along the ground from the left wall. Height and distance are both measured in metres. How close to the ground will the chain get? 2 m 5. An inverted conical tank has a depth 2m and a radius at the top of 0.8m. If water runs out of the tank at a rate of 2m'/min, how fast is the water level descending when its depth is 1.5m? 6. An open rectangular box with a square base is made from two different materials. The material for the bottom costs $3/m' and the material for the sides costs $2/m'. Find the dimensions of the box with the greatest volume and a total cost of $120. 7. A train leaves a station at 10:00 and travels due North at a speed of 100km/h. Another train has been heading due west at 120km/h and reaches the same station at 11:00. At what time were the two trains closest together