Answer :
Answer:
% change in stopping distance = 7.34 %
Step-by-step explanation:
The stooping distance is given by
[tex]T = 2.5 x + 0.5 x^{2}[/tex]
We will approximate this distance using the relation
[tex]f (x + dx) = f (x)+ f' (x)dx[/tex]
dx = 26 - 25 = 1
T' = 2.5 + x
Therefore
[tex]f(x)+f'(x)dx = 2.5x+ 0.5x^{2} + 2.5 +x[/tex]
This is the stopping distance at x = 25
Put x = 25 in above equation
2.5 × (25) + 0.5× [tex]25^{2}[/tex] + 2.5 + 25 = 402.5 ft
Stopping distance at x = 25
T(25) = 2.5 × (25) + 0.5 × [tex]25^{2}[/tex]
T(25) = 375 ft
Therefore approximate change in stopping distance = 402.5 - 375 = 27.5 ft
% change in stopping distance = [tex]\frac{27.5}{375}[/tex] × 100
% change in stopping distance = 7.34 %