Abus and a train leave the same station at the same time and travel in the same direction along parallel routes. the train runs twice as fast as the bus. they are from 12 1/2 to 15 miles apart at the end of half an hour. find the smallest and largest possible value of each rate.

Smallest rate for the train is 50 mph and largest is 60 mph.

For the bus it is 25 and 30 mph.

Step-by-step explanation:

If the speed of the train is 2x then speed of the bus is x mph, and the train travels twice as far as the bus in a given time.

Distance = speed * time

For the largest rate:

d =  2x * 0.5   for the train

x = d

0.5d  =  x       for the bus

d - 0.5d = 15

0.5d = 15

d = 30

So the rate for the train =  30 / 0.5 = 60 mph.

In a similar fashion we can show that the smallest rate for the train is

25/ 0.5 = 50 mph.

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2

13

step-by-step explanation:

divide the cost of the total of sodas you bought by the cost of one soda, for example:

$24.57 divided by $1.89 is 13 which means you bought 13 sodas