It takes Caroline 1 hr to ride the train to some place and 1.5 hr to ride the bus. Every​ week, she must make at least 8 trips to the​ place, and she plans to spend no more than 9 hr in travel time. If a train trip costs ​$6 and a bus trip costs ​$5​, how many times per week should she ride each in order to minimize her​ cost? She should ride the train for ___ trips and the bus for ___ trips in order to minimize her cost.

She should ride the train for 6 trips and the bus for 2 trips in order to minimize her cost.

Step-by-step explanation:

Let x represent the number of times that she travels using the train and let y represent the number of times she travels using the bus. Since she makes at least 8 trips to the place, hence:

x + y ≥ 8

Also, she plans to spend no more than 9 hr in travel time. Hence:

x + 1.5y ≤ 9

x ≥ 0, y ≥ 0.

Plotting the above equations on geogebra online graphing tool, the solution is (6, 2), (8, 0) and (9, 0).

If a train trip costs ​$6 and a bus trip costs ​$5, The cost equation (C) is:

C = 6x + 5y

At point (6, 2): C = 6(6) + 5(2) = $46

At point (8, 0): C = 6(8) + 5(0) = $48

At point (9, 0): C = 6(9) + 5(0) = $54

Therefore the minimum cost is at (6, 2). She should ride the train for 6 trips and the bus for 2 trips in order to minimize her cost.

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