What’s the length of the tunnel?

  3.40 km

Step-by-step explanation:

Given two sides and the angle between them, the Law of Cosines is useful for finding the remaining side of the triangle.

If we call the vertices of the triangle H, P, Y, then the Law of Cosines tells you ...

  HY² = HP² +YP² -2HP·YP·cos(P)

  HY² = 6² +7² -2·6·7·cos(29°) = 85 -84·cos(29°) ≈ 11.531944

  HY ≈ √11.531944 ≈ 3.40 . . . .  km

The length of the tunnel is about 3.40 km.

After 5 months, they would both have the same cost. If you were to cancel after 9 months, you would cancel $320 for the first option and $360 for the second option.

To solve this, you need to create an equation. You get $50+30x and let x=number of months. This would tell you how much you need to pay for option 1. In option 2, you would have $40x. This is because there is no setup fee and so there would only be the monthly cost.We then set thos equations both equal to each other because the first question asks for the options to be the same price. For the second question, you would need to substitute 9 for the x in those equations. That would have you find out which is more expensive.