Your target variable is δf, the magnitude of the difference in frequency between the waves emitted from the sonar device and the waves received by the device after reflecting off the whale. write an expression for δf in terms of the relevant frequencies using the subscript notation introduced above.

  f´ = f (v ±v₀) / (v ⁻₊ v_{s})

Explanation:

This is a doppler effect exercise that is the change of frequency by the relative speed of the emitter and receiver of sound

For the first part, the sound comes out of the sounding device, which is generally removed, so the speed of the emitter is vs = 0 and the receiver (the whale) is moving, so the equation is

               f ”= f ((v ± v₀) / v)

where the sign plus (+) corresponds to the observer moving towards the source that is at rest, f is the frequency emitted by the probe and f” the frequency received by the whale.

In the second part, the waves are reflected by the whale, which becomes the emitter and the receiver that is the probe remains at rest, so the expression is

               d´ = d ”(v / (v ⁻₊ ))

where the least succor for the source moving towards the observer,

Therefore, the frequency received by the probe (f´) is

              f´ = f ((v ±-v₀) / v) (v / v⁻₊ v_{s}))

              f´ = f (v ±v₀) / (v ⁻₊ v_{s})

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.