Respuesta :
Answer:
The quadratic equation in terms of v is v² + 2 v + 180 = 0
Step-by-step explanation:
Given as :
The distance between house to the school = d = 6 km
The uniform speed = v km/h
So, Time = [tex]\dfrac{\textrm Distance}{\textrm speed}[/tex]
or, t = [tex]\dfrac{\textrm d}{\textrm v}[/tex]
Or, t = [tex]\dfrac{\textrm 6}{\textrm v}[/tex]
Now, Again
The speed is increase by 2 km/h
i.e speed = (v + 2) km/h
So, Time taken = t' = (t - [tex]\dfrac{4}{60}[/tex])hours
i.e t' = (t - [tex]\dfrac{1}{15}[/tex])hours
Now, Time = [tex]\dfrac{\textrm Distance}{\textrm speed}[/tex]
So, (t - [tex]\dfrac{1}{15}[/tex]) = [tex]\dfrac{\textrm d}{\textrm v}[/tex]
Or, (t - [tex]\dfrac{1}{15}[/tex]) = [tex]\dfrac{\textrm 6}{\textrm (v + 2)}[/tex]
Or , [tex]\dfrac{\textrm 6}{\textrm v}[/tex] - [tex]\dfrac{1}{15}[/tex] = [tex]\dfrac{\textrm 6}{\textrm (v + 2)}[/tex]
Or , [tex]\dfrac{\textrm 90 - v}{\textrm 15 v}[/tex] = [tex]\dfrac{\textrm 6}{\textrm v + 2}[/tex]
Or, (90 - v) × (v + 2) = 6 × 15 v
Or, 90 v - 180 - v² - 2 v = 90 v
Or, v² + 2 v + 180 = 90 v - 90 v
Or, v² + 2 v + 180 = 0
So, The quadratic equation in terms of v
v² + 2 v + 180 = 0
Hence The quadratic equation in terms of v is v² + 2 v + 180 = 0 Answer
