A total x feet of fencing is to form 3 sides of a level rectangular yard. What is the maximum area of the yard in term of x?
A) x^2/9
B) x^2/8
C) x^2/4
D)x^2
E)2x^2
Please, help

- Loser66

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- freckles

oops meant to write x

- freckles

one sec

- freckles

\[2L+W=x \\ A=LW=L(x-2L)\]

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## More answers

- freckles

So we want to find A' here

- Loser66

yes, then??

- freckles

x is a constant I believe
\[A=Lx-2L^2 \\ A'=x-4L \\ A'=0 \implies x=4L \\ A=L(x-2L)=L(4L-2L)=L(2L)=2L^2 \\ \]
I think you can find A in terms of x now since x=4L

- freckles

still processing?

- Loser66

Yes. Thanks a lot. I got the right answer. It is not test, just practice exam with the answer sheet. But I want to know logic.

- freckles

Why are you doing calculus 1 problems?

- Loser66

oh, is it calculus problem??

- freckles

Yes it is an optimization problem

- Loser66

Question: why do you link to derivative?

- freckles

because it say to maximize

- Loser66

I assume it is an algebra problem and get no outlet

- freckles

usually those in the cal problems I have seen they actually gave a number instead of saying x

- Loser66

I am prepare for my GRE test for maths major students. ha!!!

- freckles

http://tutorial.math.lamar.edu/Classes/CalcI/Optimization.aspx
this example one here is pretty similar

- Loser66

My tough one is English, not math.

- freckles

except as I said they say 500 feet instead of x feet

- Loser66

Any tips for GRE math practice?? I have only 1. :)

- freckles

there was a question
and I think it was on the gre
it was my favorite question to
give me a sec and I will remember it

- freckles

solve for x+y
\[x^2+y^2+2xy+2x+2y=-1 \]

- freckles

there was a similar question on the gre or it might have been on another standard test
can't remember which standard test

- Loser66

hihihi... I have time. I will study carefully before taking the test. But you know, I am old. hahaha..... I am slow!!

- freckles

that question isn't too bad
did you want me to show you how to do it
or did you want to try it first

- Loser66

show me, please

- freckles

\[x^2+2xy+y^2+2x+2y+1=0 \\ (x+y)^2+2(x+y)+1=0 \\ (x+y+1)^2=0 \\ x+y+1=0 \\ x+y=-1 \]

- freckles

I turned it into a quadratic in terms of (x+y)

- Loser66

What if we let x+y =t??

- Loser66

oh, yea, we met there

- freckles

good luck on your gre
if i could figure out anything to tell you to help you I will
I probably should have studied for it back in the day more than I did

- Loser66

Sure. Again, thanks for the help.

- freckles

np

- Loser66

What is the units digit in standard decimal expansion of the number 7^(25)
I don't get what it mean

- Loser66

since \(7^{25} = 1.34106862 *10^{21}\)
hence the number of digits after decimal point is 8 but it is not one of the options which are 1,3,5,7 or 9

- Loser66

@freckles

- Loser66

To this problem, if I don't have calculator, how can I find out the answer?

- freckles

so you are trying to find out the length of the number 7^(25) ?

- Loser66

problem 14 https://www.ets.org/s/gre/pdf/practice_book_math.pdf

- freckles

on

- freckles

oh*

- freckles

the units digit is the ones digit

- freckles

answer is 1

- Loser66

total??

- Loser66

nope, answer is 7

- freckles

wait standard notation is not scientific notation is it ?

- Loser66

I am not sure.

- freckles

there was need to write in scientific notation
because standard notation is different from scientific notation

- freckles

7^(25) mod 10 will give you number in 1's digit

- freckles

or aka units digit

- freckles

\[4^2=16 \text{; 16 is standard notation for } 4^2 \\ 4^2=1.6 \times 10 \text{ is sceinfict notation }\]

- freckles

I missed the word no in
there was need to write in scientific notation
there was no need to write in scientific notation*

- Loser66

to this http://mathcentral.uregina.ca/QQ/database/QQ.09.06/tyrone1.html
they said that the units digit is the last digit of the number in standard form
in decimal form, the unit digit of 7^25 is the last one, which is 2, not 7 : (

- freckles

\[7^{2} \mod 10=9 \\ 7^4 \mod 10 =9 \cdot 9 \mod 10=81 \mod 10=1 \\ 7^{4(6)+1} \mod 10=(7^4)^6(7) \mod 10=1^6(7) \mod 10 =7 \\ 7^{25} \mod 10=7 \]

- freckles

the units digit is the first number
it is the one's digit
that is what that picture above says also

- freckles

for example 61
do you call 1 the first digit because I do
and 6 is the last digit
1 is in the one's place (or the units place)
6 is in the ten's palce

- freckles

oh I think I see where you are getting confused

- freckles

\[7^{25} = 1.34106862 *10^{21} \]
you think this equality is exact when it is not

- freckles

and even if it was exact you would say the units digit is 0
but it is not the case because this equation is not exact

- freckles

like you still need to move that decimal to the right like 21 times

- freckles

2 is not in the one's digit

- freckles

http://www.wolframalpha.com/input/?i=7%5E25+

- freckles

the number where it says result is the number in standard notation

- Loser66

oooooooooooooooooh!! got you

- freckles

a mod 10
should always give you the units digit of a

- Loser66

modular method help me out
7^0 -----1 last digit
7^1 -----7 last digit
7^2 -----9
7^3 -----3
7^4-----1
hence the cycle is 4,
25 = 4*6 +1, hence \(7^25 = 7^24 *7 , but the last digit of 7^24 is 1 then *7 =7

- freckles

yah

- Loser66

Thanks a ton. :) I do appreciate.

- freckles

np

- freckles

interesting practice exam
I think they have made changes to it seen I last took the gre
I feel like that was 8 years ago or something :p

- freckles

I don't remember linear algebra or number theory on it

- freckles

but maybe there was some

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