Centerville is the headquarters of greedy cablevision inc. the cable company is about to expand service to two nearby towns, springfield and shelbyville. there needs to be cable connecting centerville to both towns. the idea is to save on the cost of cable by arranging the cable in a y-shaped configuation.

centerville is located at (8,0) in the xy-plane, springfield is at (0,7), and shelbyville is at (0,- 7). the cable runs from centerville to some point (x,0) on the x-axis where it splits into two branches going to springfield and shelbyville. find the location (x,0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. justify your answer. to solve this problem we need to minimize the following function of x:
f(x)=
we find that f(x) has a critical number at x=
to verify that f(x) has a minimum at this critical number we compute the second derivative f''(x) and find that its value at the critical number is , a positive number.
thus the minimum length of cable needed is

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.  

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

step-by-step explanation:

a and d