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- APPLICATIONS OF DERIVATIVES PROBLEM: An 80 cm piece of wire is cut into two pieces. One piece is bent into an equilateral triangle and the other will be bent into a rectangle with one side 4 times the length of the other side. Determine where, if anywhere, the wire should be cut to maximize the area enclosed by the two figures.The equation of a curve is y = x + 2cos x. Find the x co-ordinates of the stationary points of the curve for 0APPLICATIONS OF DERIVATIVES PROBLEM: A horizontal trough is 16m long, and its ends are isosceles trapezoids with an altitude of 4m, a lower base of 4 m and an upper base of 6m. Water is being poured into the trough at the rate of 10m^3/min. If the water level is decreasing at the rate of 25 cm/min when the water is 3m deep, at what rate is the water being drawn from the trough?
- x y-2 -1-1 0.50 01 0.52 -13 -13.54 -52 Find the quartic function that is the best fit for the data in the table below. Report the model with three significant digits in the coefficients.A linear second-order non-homogeneous equation models this scenario: People falling at a height of 100ft above the ground attached to a 100-foot rope into a pit that's 25 ft deep and 75 feet from ground level. Spring constant of the rope is 120 lbs/ft, and air resistance is 5 times the instantaneous velocity. M is mass of person and g is gravity. Note that the pit is actually 100 ft in height: 75 from ground level plus 25 ft deep. Write this scenario as an initial value problem in matrix form. The equation is my''+5y'+120y=mg