A football is thrown across a field and lands on the grass. while a disappointing throw, it can be modeled by using the function f(v) = -0.3(v+6.2)(v-30), where V represents the distance thrown (in yards) and f(v) is the height of the ball (in feet) at each distance, V. A) find the zero (horizontal intercepts) of the function, and describe their meaning within the context of the problem ( be sure to use untits) if a point has no meaning say no. B) write F(v) in standard form C) find the vertical intercept of the function, and describe its meaning within the context of this problem (be sure to use untits)  D) Describe the end behavior of f(v), as v → ±∞

The height of a hot air balloon, in feet, m minutes after takeoff is modeled by the function f(m) = 16m. b. Another balloon takes off 5 minutes later and rises at the same speed. Write an equation for the function g(m), where g is the height, in feet, of this balloon in terms of m. g (m) =

A farmer wants to fence an area of 24 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. Let y represent the length (in feet) of a side perpendicular to the dividing fence, and let x represent the length (in feet) of a side parallel to the dividing fence. Let F represent the length of fencing in feet. Write an equation that represents F in terms of the variable x. F(x) = Find the derivative F'(x). F'(x) = Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) X = What should the lengths of the sides of the rectangular field be (in ft) in order to minimize the cost of the fence? smaller value ft larger value ft Submit Answer

A rectangular parcel of land has width, w feet. The length of the diagonal, d, between opposite corners is 18 feet more than the length of the parcel. Note that d is lowercase. (a) Express the length, L, of the parcel as a function of d. (b) Express the width, w, of the parcel as a function of d. (c) Express the area, A, of the parcel as a function of d. L = W = A = (d) Suppose a fence is to be built around the perimeter of the rectangular parcel of land. The fencing material will cost $25 per foot. Express the total cost, C, of fencing the parcel as a function of d. C =

The amount of water in a tub increases at a constant rate. After 5 minutes of filling, the amount of water in the tub is 18.75 gallons. After 14.2 minutes of filling, the amount of water in the tub is 33.93 gallons. A) Determine the function f that models the amount of water in the tub with respect to the number of minutes that tub has been filling. Define any variables used. B) Evaluate f (11.2) and explain the meaning in the context of the problem. C) Determine the vertical intercept and explain the meaning in the context of the problem. D) Determine the horizontal intercept and explain the meaning in the context of the problem. E) Assuming the tub has a capacity of 40 gallons, determine the practical domain and range of the function. f) Determine the formula for the inverse function f ^-1. g) Evaluate f^-1 (11.2) and explain the meaning in the context of the problem.

The worldwide sales in millions of hand-held PCs can be modeled by the function P(x) 1.85(x 1998) + 4 where x is the year. Use the function to determine the year when sales reach $25 million.

A 1000-square-foot rectangular plot of land is going to be divided into three equal-sized, adjacent playgrounds (see diagram). Find the number of feet of fencing required as a function of x. (Note: there is only one fence between the playgrounds, not two.) Answer: