this is for math please answer asap clealry

Q1

\fAcceleration of a Falling Object During the construction of an office building, a hammer is accidentally dropped from a height of 1024 ft. The distance (in feet} the hammer falls in t sec is s = 16:2. What is the hammer's velocity when it strikes the ground? :I fuse: What is its acceleration? Emma Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. (Enter your answers using interval notation. If an answer cannot be expressed as an interval, enter EMPTY or o.) f ( x ) = 5 5 x2 3 2 increasing decreasingDocking a Boat A boat is pulled toward a dock by means of a rope wound on a drum that is located 6 ft above the bow of the boat. If the rope is being pulled in at the rate of 2 W5, how fast (in ft/s) is the boat approaching the dock when it is 26 ft from the dock? (Round your answer to one decimal place.) Air Pollution According to an Air Quality Management District, the level of nitrogen dioxide, a brown gas that impairs breathing, present in the atmosphere on a certain May day in a busy downtown city is approximated by A(t) = 0.0330: 7)4 + 55.3 (o 5 ts 7) where A(t) is measured in pollutant standard index (PSI) and t is measured in hours, with t = 0 corresponding to 7 am. At what time of day is the air pollution increasing, and at what time is it decreasing? (Enter your answers using interval notation in terms of t.) increasing decreasing Consider the following function. 900 = x2 + 5X+ 3 Find the first and second derivatives of the function. 9 '(X) g "(X) Determine where the function is concave upward and where it is concave downward. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) concave upward concave downward The owner of the Rancho Grande has 3,008 yd of fencing with which to enclose a rectangular piece of grazing land situated along the straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area he can enclose? What is this area? We are given the description of an enclosure that has fencing on 3 sides and can use 3,008 yards of fencing. We are to nd the dimensions that will maximize the area contained within the fence. 3' G) Let y represent the length of fence that is opposite the river and x represent the length of each length of fence perpendicular to the river. As there are 3,008 yards of fencing available, the sum of the lengths of the sides of the enclosure results in the following equation. (:)x+y=3,008 Solve this equation for y. y=3,008(|:])x Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does not exist, enter DNE.) g(x) = x2 + 2x2/3 on [-7, 8] maximum minimum