The Johnstown Inclined Plane in Pennsylvania is one of the longest and steepest hoists in the world. The railway cars travel a distance of 896.5 feet at an angle of approximately 35.4°, rising to a height of 1693.5 feet above sea level. (see figure in the website). (Round your answers to two decimal places.)
(a) Find the vertical rise of the inclined plane. (in feet)
(b) Find the elevation of the lower end of the inclined plane.(in feet)
(c)The cars move up the mountain at a rate of 300 feet per minute. Find the rate at which they rise vertically. (in ft/min)

a. 519.35 ft b. 1174.15 ft c. 173.78 ft/min

Explanation:

a. Since the length of the incline = 896.54 ft, and the angle of the incline = 35.4°. Let h be the vertical rise of the incline. From trigonometric identities,

sin35.4° = h/896.54 ⇒ h = 896.54sin35.4° = 519.35 ft

b. Since the top of the incline is 1693,5 ft above sea level, and the vertical height of the incline is 519.35 ft, the elevation of the lower end of the inclined plane is 1693.5ft - 519.35ft = 1174.15 ft

c. The cars move up the mountain at a rate of 300 ft/min along the inclined plane. The rate at which they rise vertically is the vertical component of the velocity = 300sin35.4° ft/min = 173.78 ft/min

elly's long hair:

a. if the salon only takes cash, then this isn't the problem. it doesn't matter how much she has in her checking account.   she can't get a haircut until she has the cash.

b. if she has overdraft protection, then there's no problem.   she can go ahead and write a check that her account can't cover, then sometime later, pay the bank some outrageous usury for loaning her a few bucks for a few days, but with beautiful hair.

c. if elly has some principles, and doesn't want to write a bad check, then now she has a problem.   her desire for the new hairstyle is in conflict with her honesty and integrity.

d.   if the bank will not process a check she writes, then even if she had a million $$ in her account, she couldn't use any of it.   the amount she has in her account is not the problem.   and if i may suggest, she might as well close her checking account, and put the money where it'll work for her.   it's not doing her a bit of good in a checking account, since she can't write any checks.

justin can't pay the full balance:

a. he can't even handle the credit limit he has now.   under no circumstances should he ask for a higher limit.

b.   he can ask for the grace period to be extended.   but that's no solution, the bank will almost certainly refuse anyway, and there are much better options.   he knew the rules of his credit card when he started using it.

c.   he definitely should pay the interest on the balance, plus as much of the balance as he can cover at the same time.

d.   he definitely should pay the minimum otherwise they could shut down his card.   he should also pay as much more as he possibly can.   he should also remember the awkward situation he's in, stop buying stuff on credit that he can't afford, and avoid adding any more debt.

i'd say that justin's best best option isn't on this list of choices.   what he has to do:   pay as much as he can at least the minimum payment plus as much more as he can and then avoid adding more debt.

15.3 cos 65 degrees trig