All Answers 358514 Answers

Thanks guys for catching my mistakes today!!! :)

I have not been feeling my 100% best today :'(

Theoretically, it could be any positive number as X and Y are undefined and no negative can be under a square root.

BOOOOOOOOOOOM!!!!!

\(14x-7y<-21\)

You do not specify if you want to solve for x or solve for y so I will solve for both

Solve for x

add 7y to both sides

\(14x<-21+7y\)

divide 14 from both sides

\(x<-21/14 + 7y/14\)

reduce the fractions

\(x<-3/2 +y/2\)

Solve for y

subtract 14x to both sides

\(-7y<-21-14x\)

divide both sides by -7

\(y>21/7+14x/7\)

reduce the fractions

\(y>3+2x\)

14x-7y<-21    →    7x - y < - 3  →  y > 7x + 3

This is an inequality graph........seen here.....    https://www.desmos.com/calculator/apkrshjmo1

For future reference, just type it into google, will give you a faster answer.

It is 0.166666667

0.166666667

:)

All the calculations needed to answer the questions in this revised version, have already been answered in the previous questions. No extra calculations are needed.

OMMGG, My tummy hurts just lookin' at that!

Correct me if i'm wrong.. but isn't it 18271?

Haley, he/she asked how many Danny has right?

when they say "twice as many" They want you to add.

So..

18271 + 18271

= 36542

:)

OH GOD

COMPLETELY FORGOT ABOUT SYNTHETIC DIVISION

YOU JUST SAVED MY EXAM GRADE

Thanks CPhill

X^4+3X^3-12X^2-6X+20

This might be difficult to factor directly.......we can use the Rational Zeros Theorem to [possibly] reduce the polynomial to one of a 2nd or 3rd degree which might be more easily factored

The possible factors are all the factors of 20  divided by all the factors of 1

1/1  = 1   is not a factor  because it does not produce 0  when substituted into the polynomial

-1/1  = -1    is not a factor for the same reason

2/1 = 2   is a factor because we get a 0 when we substitute it into the polynomial

So   using synthetic division, we have

2  [ 1   3     - 12       -6       20   ]

           2       10       -4      -20

     -------------------------------------

      1   5      -2        -10       0

So, this reduces the polynomial to

x^3 + 5x - 2x  - 10       which factors as

x^2 ( x + 5)  - 2(x + 5)  =

(x^2 - 2) ( x +5)

So.....the factorization is

(x - 2) (x + 5) (x ^2 - 2)

If the company decides to delay the expansion for 1 year, then this means that the whole of reserve fund will be invested for 1 full year at 5.2% comp. quarterly.

This would come to $2,737,859.32 - $2,6000,000=$137,859.32 This is additional cash that the company has earned in 1 year. This new cash will continue to earn interest for another 4 years, which will be worth $169,506.86. This is in addition to the surplus calculated in question #3.

From the calculations here and in the previous question, the last payment will increase from a $1,000,000 to $1,100,000, which will be subtracted from the final amount.

Since the payments are delayed for 1 year, then their PV, which we calculated in question #1 will be projected into 1 year from now at the assumed rate of 4.5% comp.S.A., which will come to $2,612,928.15.

Ohhhhh myyy...

*face plame*

I didnt see the Y!!

^ Haley, how you get rid of Y?

What i would do is set this up into a system of equations.

1st, find Y

14X-7Y>-21

-7Y>-14X-21

Y<2X+3

Then Plug in for Y in previous equation

14X-7(2X+3)>-21

14X-14X-21>-21

Simplify

0>0

False

Are you ready for my amazingness??

14x-7y<-21

     +7    +7

------------------

14x=-14

x=-1

:)

Assuming you're wanting a proportion, ? = 18.75 satisfies the proportion.

5*30/8 = 18.75

are you kidding me?! everyone knows how to do that!! jk i have no idea what you are talking about 

Baby steps!!!

-4+56(45-645)-534=6745

Add -4+56..

52(45-645)-534=6745

Then times 52 by 45, 645 

2340-33540-534=6745

Subtract 2340 from 33540..

-1014..

subtract -1014 from 534 then devide by 6745..

And youre answer will be...

-0.22919751258

:)

\({10}^{-3} = \frac{1}{{10}^{3}} = \frac{1}{1000} = 0.001\)

10^-3 = 0.001

Hope this helps.

o get rid of negative exponents you have to make the equation in to a fraction. 
10^-3 becomes 1 over (or divided by) 10^3. 
10^3 is 1000, and 1 divided by 1000 = 0.001

:]

Of the reserve fund of $2,600,000, the first payment of $300,000 is due now and must be subtracted from the reserve fund, which would leave you with $2,300,000. This amount will be invested for 5 years at the rate of 5.2% comp. quarterly. It is assumed that this investment in not "locked in" and that the company can withdraw the needed payments as they come due.

If this assumption is right, then the $2,300,000 will be worth $2,421,952.48 in one year from now. From this you have to subtract the $700,000 due. That leaves you $1,721,952.48. This amount will continue to earn to earn interest for another year, at which time it will be worth $1,813,255.25. From this amount you will have to subtract $800,000 due in 2 years, which will leave you with $1,013,255.25. This amount will continue to earn interest for another 2 years, which comes to $1,123,555.23. Now, from this amount you have to subtract $1,000,000 due in the 4th year, which will leave you with $123,555.25. This amount will continue to earn interest for another year, which comes to $130,106.47 at the end of the 5th year.

From these calculations, you can easily answer their questions.

f(x) = sinx + cosx         take the derivative and set to 0

f ' (x)   = cosx  - sinx   = 0

So

cosx  = sin x        an this happens at    pi/4 and 5pi/4  on 0≤x≤2(pi)

Take the second derivative

f " (x)  = -sinx - cosx

Substituting in the critical points we have

-sin(pi/4) - cos(pi/4)   =   negative.....       so  we have a  relative max at pi/4

And

-sin (5pi/4)  - cos (5pi/4)   =   positive.......    so we have a relative minimum at 5pi/4

So the function is increasing on    [0, pi/4], decreasing on [pi/4, 5pi/4]  and increasing again  on [ 5pi/4, 2pi]

Here's a graph  [ in degrees]...........https://www.desmos.com/calculator/r1e6o1daoa

it was yesterday (the 14th)