A summer camp has 400 ft of float line with which to rope off three adjacent rectangular areas of a lake for swimming? lessons, one for each of three levels of swimming ability. A beach forms one side of the swimming areas. Suppose that the width of each area is x feet. Answer parts? a) through ?c). Three rectangles each with a vertical side of length 'x' but with varying horizontal lengths are situated adjacent to each other.

a) A = x*(400 - 4*x)

b) domain of function A(x) is ( 0 , 100 )

c) dimension of swimming section x = 30 ft maximizes area.

Step-by-step explanation:

Given:

- Total length of float-line used L = 400 ft

- Inner sections length x

Find:

a) Express the total area A as a function of x

b) Find the domain of the function

c) Using the graph, find the dimensions that leads to largest area

Solution:

- The amount of side length of the rectangle can be calculated from the total length given y:

                                 y = L - x - x - x - x

                                 y = L - 4*x

                                 y = 400 - 4*x

- The area of a rectangle is as follows:

                                 A = x*y

- Replace y with the expression derived first:

                                A = x*(400 - 4*x)

- To find the domain of the function we know that A >= 0:

                                 400*x - 4x^2 > 0

                                 x(400 - 4x) > 0

                                 x > 0 , 400 - 4*x < 0

                                 x < 100

- Hence, the domain of function A(x) is ( 0 , 100 )

- From the graph given, we can see that Area is maximum when x = 30 ft. Denoted by the turning point of the graph.

- Hence, the dimension of swimming section x = 30 ft maximizes area.

1 x=22.52

2: 65/39=604+39x

65x-39x=604

26x=604

x=604/26

×=23.23

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !