Calculate the following quantities:.
a) the angle (in radians) subtended by a circular arc that is 1.50 m long with a radius of 2.50 m
b) the radius of a circle that has an arc 14.0 cm long that subtends an angle of 128o
c) the length of an arc that subtends an angle of 0.700 rad on the circumference of a circle with radius 1.50 m

(a) 0.6 radians

(b) 6.27 cm

(c) 1.05 m

Explanation:

(a) The length of an arc is given as:

s = rθ

where r = radius of the circle

θ = angle subtended by the arc (in radians)

Therefore, the angle, θ, will be:

θ =

θ =

θ = 0.6 radians

The angle subtended by the circular arc is 0.6 radians.

(b) Using the same formula, we have that radius, r, is given as:

r = s/θ

But θ is in radians and the angle we have is in degrees (128°). Hence, we convert 128° to radians:

128° = radians = 2.234 radians

Therefore, r is:

r = 14/2.234

r = 6.27 cm

The radius of the circle is 6.27 cm.

(c) Using the same formula, we have that:

s = rθ

s = 1.5 * 0.7

s = 1.05 m

The length of the arc is 1.05 m.

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.