-.1 Vusi sets out for a 40 kilometre run. After he runs for two hours he injures
his ankle. He takes an hour to walk the rest of the way. If he injured
himself after he had run 16 kilometres, he would have taken four hours to
complete the distance. Determine the average speed in kilometres per hour
at which Vusi ran.

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

On traditional maps, earth is represented in a flat plane, or by euclidean geometry. however, a globe is a more accurate model that comes from elliptical geometry.how does a globe represent the fact that there are no parallel lines in elliptical geometry? the equator is not parallel to any other latitudinal lines. the north and south poles are never connected by a geodesic. the geodesics connecting the north and south poles never intersect. the geodesics connecting the north and south poles intersect at both of the poles.

Which description is represented by a discrete graph? kiley bought a platter for $19 and several matching bowls that were $8 each. what is the total cost before tax? the temperature at 9 a.m. was 83° f and is heating up at an average rate of 6°f per hour. what is the temperature x hours later? juan ate an egg with 78 calories and some cereal with 110 calories per serving for breakfast. what is the total amount of calories he consumed? a bottle contained 2,000 ml of liquid and is being poured out at an average rate of 300 ml per second. how much liquid is left in the bottle after x seconds?