Question

Suppose that you take out an unsubsidized Stafford loan on September 1 before your junior year for $4500 and plan to begin paying it back on December 1 after graduation and grace period 27 months later. The interest rate is 6.8%. How much of what you will owe will be interest?

Answer 1

i believe its $661.76

Answer 2

cantorset can we use induction on your problem? do you know what that is?.

Answer 3

yes we can

Answer 4

how did you find me, lol

Answer 5

i went to the homepage and you can see what everyone is doing

Answer 6

the chat program doesnt work for me

Answer 7

ok lets do this one
for all n>=5 , n^3 < 3^n

Answer 8

ok

Answer 9

for n=5, we have 5^3=125<243=3^5. Sold the inequality holds for n=5

Answer 10

right, basis case

Answer 11

now we should assume it is true for integers k>=5
Then we show it is true for k+1
the induction step is the hardest so let me think about it

Answer 12

it seems that you are going over logs so i'm pretty sure we may have to involved that somehow

Answer 13

hmmm, they may be unrelated though. here is what i got ,

Answer 14

that was a different question

Answer 15

is there a way to post without having to click my mouse on post?

Answer 16

no i guess not

Answer 17

show that (k+1)^3 < 3^(k+1)

Answer 18

k^3 + 3k^2 + 3k + 1 < 3^(k+1)

Answer 19

omg i got it

Answer 20

i got so excited i clicked out sorry.
so we have (k+1)^3<K^3+1^3=k^3+1<3^k+1

Answer 21

k ^3 + 3k^2 + 3k + 1 < k^3 + 3k^2 + 3k + 3k = k^3 + 3k^2 + 6k < k^3 + k^3 + k^3 = 3k^3 < 3*3^k = 3^(k+1)

Answer 22

(k+1)^3 = k ^3 + 3k^2 + 3k + 1 < k^3 + 3k^2 + 3k + 3k = k^3 + 3k^2 + 6k < k^3 + k^3 + k^3 = 3k^3 < 3*3^k = 3^(k+1)

Answer 23

i got excited ignore what i wrote

Answer 24

(k+1)^3<K^3+1^3=k^3+1<3^k+1 this is false

Answer 25

my proof isnt elegant, but i think it works, might have to do some side induction arguments for the intermediate steps

Answer 26

you are right i got excited

Answer 27

also you better use parenthesses :) more often

Answer 28

the log proof is A LOT easier

Answer 29

yep

Answer 30

what did you get?
log_3 n < n if n < 3^n , assuming we raise both sides to 3

Answer 31

or you can start, if we can show that n < 3^n , for n>=1, then taking the log base 3 of both sides we have our result.
what was your logic?

Answer 32

ok lets skip the case for n=1 that is easy to do and we know it holds. so assume for integer k, log3(k)<k (3is base)
now we want to show log3(k+1)<k+1
so we have ...

Answer 33

so that proof goes, 1 < 3^n,
assume k < 3^k then add 1 to both sides of that inequality we have k + 1 < 3^k + 1 < 3^k + 3 = 3^(k+1)

Answer 34

yea maybe we should base 3 on both sides to get rid of log

Answer 35

you mean exponentiate?

Answer 36

you cant get rid of log with log :)

Answer 37

can you help me with surface area of integral

Answer 38

surface area of a solid?

Answer 39

surface area of a torus

Answer 40

so you cant finish the proof with log, no problemo

Answer 41

one thing at a time

Answer 42

how do you find the question
i posted earlier

Answer 43

this website is so confusing

Answer 44

are you given the equation for the torus or is it a parametric curve/

Answer 45

Calculus question: surface area of a torus. it is

generated by circle with radius r , off center. Suppose

the circle is centered at (x - R)^2 + y^2 = r^2, and R> r. so the distance from (0,0) to the center of the

circle is (R,0) which has radius r.
Ok the integral i got is
int 2pi y sqrt [ 1+ (dy/dx)^2] = int 2pi sqrt ( r^2 - (

x-R)^2) [ 1 + (-2(x-R)/(2sqrt( r^2 - ( x-R)^2) ^2 ]

Answer 46

we are given a circle , and its going to generate the torus by revolving about the y axis

Answer 47

the final answer should be 4pi^2 R*r

Answer 48

so that last thing you have the square cancels the sqrt

Answer 49

ok im just going to do it on paper and scan it and you can open it give a few min

Answer 50

right, good :) ok here is what i got

Answer 51

integral 2pi y dS, remember ds can be sqrt 1 + dx/dy ^2 or sqrt 1 + dy/dx ^2

Answer 52

we need another pi in there somewhere

Answer 53

since are answer has pi^2

Answer 54

this is what i got using the integral you found we can get times another pi it would be correct

Answer 55

don't look at the name of the file. i know we are not finding volume

Answer 56

right, its surface area, here lets use twiddla

Answer 57

http://www.twiddla.com/521818

Answer 58

if you dont mind, we can draw on whiteboard