Maxima and minima (1 Viewer)

[Roserox]

Two cars are travelling along roads that intersect at right angles to one another. One starts 200km away and travels towards the intersection at 80kmh^-1 (80km per hour to the power of negative 1) while the other starts at 120km away and travels towards the intersection at 60kmh^-1 ( 60km per hour to the power of -1).

Show that their distance apart after t hours is given by d^2 = 10000t^2 - 46400t + 54400 and hence find their minimum details apart!

Thank you for any help! I have seen a very similar question on bored of studies although it doesn't have negative powers in the average speeds given!

Again. Any help would be appreciated!

 

[InteGrand]

Two cars are travelling along roads that intersect at right angles to one another. One starts 200km away and travels towards the intersection at 80kmh^-1 (80km per hour to the power of negative 1) while the other starts at 120km away and travels towards the intersection at 60kmh^-1 ( 60km per hour to the power of -1).

Show that their distance apart after t hours is given by d^2 = 10000t^2 - 46400t + 54400 and hence find their minimum details apart!

Thank you for any help! I have seen a very similar question on bored of studies although it doesn't have negative powers in the average speeds given!

Again. Any help would be appreciated!

No, the negative powers of h in the speeds mean 'per hour'. So 60 km h^-1 means 60 kilometres per hour (or 60 km/h); the reason for this is that h^-1 just means 1/h, so km h^-1 means km/h.

 

[porcupinetree]

Two cars are travelling along roads that intersect at right angles to one another. One starts 200km away and travels towards the intersection at 80kmh^-1 (80km per hour to the power of negative 1) while the other starts at 120km away and travels towards the intersection at 60kmh^-1 ( 60km per hour to the power of -1).

Show that their distance apart after t hours is given by d^2 = 10000t^2 - 46400t + 54400 and hence find their minimum details apart!

Thank you for any help! I have seen a very similar question on bored of studies although it doesn't have negative powers in the average speeds given!

Again. Any help would be appreciated!

I think you're misunderstanding what kmh^-1 means: it is simply a different way of writing the unit of km/h (kilometres per hour), where kilometres (km) are divided by hours (h). Dividing by hours is the same as multiplying by hours to the power of minus one, hence the unit is kmh^-1.