Calculus question!!! see below...?

Question

A dune buggy is on a straight desert road, 40 km north of Dustin City. The

vehicle can travel at 45 km/h off the road and 75 km/h on the road. The

driver wants to get to Gulch City, 50 km east of Dustin by another straight

road, in the shortest possible time. Determine the route he should take.

Answer 1

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.. C

.. |\ angle ACP = z.

.. |-\

w|--\

...|----\

.. |-----\------

..A. x P ...B gulch city

...<---- y --->

let dist. to dustin city = w (40 km)

speed ratio regular road: desert road = k (5/3)

dist. over desert = w•sec z,

dist. over regular road = y - w•tan z

time taken ∞ k•sec z +(y - tan z)

dT/dz = k•secz•tan z - sec^2 z

= (ksin z - 1) / cos^2 z

for minima, sin z = 1/k

which yields x = w /√(k^2 - 1)

plugging in,

x = 40/√((5/3)^2 - 1)

ans: x = 30 km

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note that the optimal value of angle z is solely dependent on k !

Answer 2

Its (eleven+five)/(eleven+15) =sixteen/26 = sixty one.538% roughly. (Note: I'm assuming that it entails those who're freshman "and" feminine. So, if thats now not the case, my reply is flawed then. Sorry.)