Question

an ornithologist studying the flight of birds measured the efficiency for parakeets flying at various speed in a descending flight pattern 0.18 at 12 mph, 0.23 at 22 mph and 0.15 at 30mph. the measurements suggest the efficiency E is a quadratic function of the speed s. find the quadratic function whose graph goes through the three given ordered pairs, and find the speed that gives the maximum efficiency for descending flight.

Answer 1

Step-by-step explanation:

Given:

1. when s = 12 mph     t =0.18  let   (s,t) or (a,b) = (12,0.18)
2. when s = 22 mph    t = 0.23 s     (s,t) or (a,b) =(22,0.23)
3. when s = 30 mph     t = 0.15 s     (s,t) or (a,b) =(30,0.15)

we know the general format of Quadratic equation to be

= ax²+bx+c=0

Step 1 :

when the birds pass through a,b (12,0.18) we cane give the expression as

= ax²+bx+c=0

= 12x² + 0.18x + c= 0

it can also be written as

s = ut + 1/2 at²  = 0.18t +( 1/2) a(0.18)²

step 2 :

through points (22,0.23)

= 22x² + 0.23x + c = 0

s = ut + 1/2 at²  = 0.23t + (1/2) a(0.23)²

Step 3 :

through points (30,0.15)

= 30x² + 0.15x + c = 0

s = ut + 1/2 at²    

= 0.15 u +(1/2)  a(0.15)²