All Answers 356741 Answers

First, you have to convert the interest rate of 7.6% from compound annually to compound monthly.

1.076^1/12 =1.0061228738...- 1 =.0061228738 x 1200 =7.34745% compounded monthly.

Then you would use this formula to find out his accumulated retirement fund:
FV=P{[1 + R]^N - 1/ R}
FV = 750 x {[1 + 0.0061228738]^(30*12) - 1 / [0.0061228738]}
FV =$980,250.96 - This is the balance of his acct. at age 60.

Then you would use this formula to calculate his monthly retirement payments:
PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}
PMT =980,250.96 x 0.0061228738{[1+0.0061228738]^300 / [1+0.0061228738]^300 - 1} 
PMT = $7,146.98 - This is the monthly payment that he will receive for 25 years or 300 months.

The editing label depicting LaTex is a misnomer. This forum doesn’t use LaTeX . It uses TeX

Despite the French sounding name, the “La” in LaTex (probably) comes from (Leslie B. Lamport), the initial developer who wrote advanced scripted algorithms that augmented Donald Knuth’s TeX typesetting program to a more advanced markup and layout program used for publishing.

Translating LaTex into TeX, requires only a slightly higher intelligence than the machine you are using. 

\(\text{Find } a+b+c, \text{given that } x+y\neq -1 \\ \text{ and }\\ \begin{align*} ax+by+c&=x+7,\\ a+bx+cy&=2x+6y,\\ ay+b+cx&=4x+y. \end{align*} \)

GA

When the number begins with 4, then there are 4! =24 permutations for 2, 3, 5, 6

Half of them, or 12 would be even, and the other half or 12, odd.

When the number begins with 5, then there are 4! =24 permutations for 2, 3, 4, 6

3/4  x  24 =18 would be even, and 1/4 x 24 =6 would be odd.

When the number begins with 6, then there are 4! = 24 permutations for 2, 3, 4, 5

Half of them or 12 would be even, and the other half or 12 would be odd.

So, 24+24+24 =72 numbers over 40,000, and:

12+18+12 =42 would be even, and:

12 + 6+ 12=30 would be odd. 

Just as Melody found !!

Just saying 4-46= -42 not -44.

Thank you!!!

If c = 2*10^6 and y = 2*10^5 
w^2 = c*y/c-y 
Work out the value of w. Give your answer in standard form.

w^2 =[2*10^6] x [2*10^5] / [2*10^6  -  2*10^5]

w^2 =[4*10^11] / [1.8*10^6]

w^2 =222,222.22......

w = sqrt(222,222.22...)

w ~ =+,- 1,000sqrt(2)/3 =+,- 471.40....

 6n+3=2

n         result  of  6n + 3

-2             -9

-1             -3

0               3

So......  6n + 3    must equal 2 when n  is between     -1 and  0

[ The actual solution is that n  = -1/6 ]

When n=3, your equation becomes: (6*3) + 3  = 21

When n=4, your equation becomes: (6*4) + 3  = 27

Not sure what you mean by "modulus" !! It has many uses and meaning in Math and Physics:

Read it about here: https://en.wikipedia.org/wiki/Modulus

I don't understand??

"n" can take the values of: 3 or 4 ONLY, when it =21 and  27.

Does not translate into LaTex !!.

If $x + y =2$ and $xy = 23$, then what is $x^2 + y^2$?

x + y  = 2    square both sides

x^2 + 2xy + y^2  =  4

x^2 + 2(23) + y^2  = 4

x^2 + 46  +  y^2   =  4     subtract 46 from both sides

x^2  + y^2  =  -42

Thanks to the guest for spotting my error !!!

CPhill Sep 29, 2017

Q1)  u+2=4     subtract 2 from both sides

u  = 2

Q2)   6= x+2/3       multiply through by 3

18  = 3x  + 2   subtract 2 form both sides

16  =  3x      divide both sides by 3

16 / 3  = x

Q3)   13+w/7=18   multiply through by 7

91  + w =  126       subtract 91 from both sides

w  =  35

Q4)    17= -13-8x      add13 to both sides

30  =  -8x     divide both sides by -8

30 / -8   =   15 / -4   =  x

(522, 1322) and (9000, -1337)

Distance  =   sqrt [  ( 9000- 522)^2  + ( -1337 - 1322)^2 ]  ≈  8885.199 units

This forms a right triangle....

tan B  = AC /AB = 12/9 =   4/3

So

arctan (4/3)  = B ≈  53.13°

 y = 4x - (5a)x^(-5)  

dy / dx  =  4 + (25a)x^(-6)

Possible derivation:
d/dx(-(5 a)/x^5 + 4 x)

Differentiate the sum term by term and factor out constants:
 = -5 a (d/dx(1/x^5)) + 4 (d/dx(x))

Use the power rule, d/dx(x^n) = n x^(n - 1), where n = -5: d/dx(1/x^5) = d/dx(x^(-5)) = -5 x^(-6):
 = 4 (d/dx(x)) - (-5)/x^6 5 a

Simplify the expression:
 = (25 a)/x^6 + 4 (d/dx(x))

The derivative of x is 1:
 = (25 a)/x^6 + 1 4

Simplify the expression:
= 4 + (25 a)/x^6

LOL!!!!!

Doesn't every poster have to accept our answers at their own peril ????

6826.25/1.25 = 5461 bushels can be held

1 + 3/4 times larger  = 1.75  .....so......

6826.25 (1.75) =  11945 +  15/16  cubic feet 

6826.25 (1.75) / 1.25  = 9556.75 bushels can be held with the increase in volume

2x+30= -4(5x-2)  simplify the right side

2x + 30  =  -20x + 8   add  20x to both sides, subtract 30 from both sides

22x  =  - 22      divide both sides by 22

x =  -1

Using the digit 2,3,4,5,6 without repition. How many

a) numbers greater than 40000 can be formed?

the first digit can be 4, 5, or 6 and the others can be any.  So that is

3*4*3*2*1  = 72 ways

b) even numbers greater than 40000 can be formed?

The last can be 2 or 4 or 6 and the first can be 4 or 5 or 6

If the last on is 4 or 6 then there is    2*2*3*2*1 = 24

If the last digit is 2 then there is         1*3*3*2*1  = 18

You have to add those two result together to get the total number.   42 ways

c) odd numbers greater than 40000 can be formed?

The last can be 3 or 5 and the first can be 4 or 5 or 6

If the last on is 3 then there is            1*3*3*2*1  =  18

If the last digit is 5 then there is         1*2*3*2*1  =   12

You have to add those two result together to get the total number.     30 ways

Accept my answer, or anyone elses, at your own peril.     

Yep....if you have a right triangle and you know two sides, you can use the Pythagorean Theorem to find the remaining side.....just remember...

hypotenuse  =   sqrt [ ( leg 1)^2  +  ( leg 2)^2 ]

leg  =  sqrt [ hpotenuse^2 - other leg^2 ]

Simplify the following:
2 (-2 (2 - 6) + 3) + 1

2 - 6 = -4:
2 (3 - 2-4) + 1

-2 (-4) = 8:
2 (8 + 3) + 1

3 + 8 = 11:
2×11 + 1

2×11 = 22:
22 + 1 = 23

 to simplify

(8x^-15 + 8y^-15)/((x^5+y^5)*y^-4)

Hello Guest!

\(\large \frac{8x^{-15}+8y^{-15}}{(x^5+y^5) y^{-4}}\) 

\(\large =(8x^{-15}+8y^{-15})\times \frac{y^4}{x^5+y^5}\)

\(\large =(\frac{1}{x^{15}}+\frac{1}{y^{15}})\times \frac{8y^4}{x^5+y^5}\)   \(More\ is\ not\ possible.\)

  !