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Nice, Melody.....I always like these, too !!!!

Hi DS I shall give it a go.     I always like doing these.            

Sometimes humans can do better than calculators.  I do not know why ....

21 to the power of 953

\(y=21^{953}\\ log\;y=log\;21^{953}\\ log\;y=953\;log\;21\\\)

\(logy =1.2600749878814250929*10^3\\ y=10^{1.2600749878814250929*10^3}\\ y=10^{1260.0749878814250929}\\ y=10^{0.0749878814250929}*10^{1260}\\ y=10^{0.0749878814250929}*10^{1260}\\ \)

10^0.0749878814250929) = 1.1884690638742234

\(21^{953}=1.1884690638742234 \times 10^{1260}\)

3/9=1/3 of his life-Gabe did not live with his grandparents.

1 - 1/3=2/3 of his life lived with his grandparents. Or,

6/9=2/3 of his life lived with his grandparents-which is the same as above.

[3 x 10^8 ]   / [6.682 x 10^-7]   

We can write this as :

[3 / 6.682 ]  x [ 10^8 / 10^-7]  ≈

.449 x 10^15  ≈

4.49  x 10^14

Gabe is 9 yrs. old, has lived with grandparents since he was 3 yrs old, what is the percentage he lived with grandparents?

sin 30

Draw an equilateral triangle, side length  2 and then cut it in half.

Now read the answer off the pic

The total cost of producing x books is C(x)=50,000+2x dollars, and the total revenue generated by selling x books for R(x)=10x-0.0001x^2 dollars.

1) Find R'(x)

R(x)=10x-0.0001x^2

R'(x)=10-0.0002x

2)Find C'(x)

C(x)=50,000+2x

C'(x)=2

This means that each book costs $2

3)Find d/dx (r(x)-C(x))

d/dx (r(x)-C(x))=10-0.0002x-2

d/dx (r(x)-C(x))=8 - 0.0002x

4) When is the derivative positive, negative?

\(8-0.0002x>0\\ 8>0.0002x\\ 8\div 0.0002>x\\ x<8\div 0.0002\\ x<40000\)

5) To maximize total profits, how many books should be produced? What is the maximum total profit? Explain reason.

I won't keep going as I see CPhill has already answered it.

18 months =  1.5 years......so....

He didn't live with them for  1.5 / 7.5  = 1/5  = 20%  of his life

So......he must have lived with them the other 80%

We already know (1)  and (2)

3)   R(x)  - C( x)   =

10x - 0.0001x^2   - [ 50000 + 2x ]   =

-0.0001x^2 + 8x - 50000          this  the "profit" function

The derivative of this is

-0.0002x + 8

4)   Set the derivative to  0  and solve

-0.0002x  + 8  = 0

8  = 0.0002x      divide both sides by   0.0002

x = 40000    

.Here's the profit function graph : https://www.desmos.com/calculator/ejbztbmci4

The derivative will be positive from about  ( 6834, 40000) and negative from about (40000, 73,166)

5)   40000 books maximizes the profit......and, as the graph shows, the max profit  is $110,000

The maximum profit in this type of problem will always occur at the x value which makes the derivative = 0

I assume that you want to factor this????....if so, we have

x^2 - 4x + 4  =  (x - 2) (x -2)  =  (x - 2)²

Yes are cristi

Thanks Chris,

That is a very unexpected outcome :))

sqrt(7) = 2.6457513110645906, or ≈2.65

Same with you, Bree! (Man, I was so inactive...)

Omg yess!

Guys, this is a 21 Pilots song...

-Anon4338

910/3.5%x4

[910/.035] X 4 =104,000.

(4^5*6^-8)^0     =  1

Proof

[4^5]^0 * [6^-8]^0  =

[1024]^0 * [1/1679616]^0  =

[1] * [1]   =

1

[sqrt ( x + h + 2)  - sqrt( x + 2)]  / h  =         multiply top/bottom by [ sqrt(x + h + 2) - sqrt ( x + 2)]

[sqrt ( x + h + 2) - sqrt (x + 2)] [ sqrt( x + h + 2) + sqrt(x + 2)] / ( h * [sqrt(x + h + 2) + sqrt (x + 2) ] )

[ (x + h + 2)  - ( x + 2)] /  ( h * [sqrt ( x + h + 2)  + sqrt(x + 2)] )

h /  ( h * [sqrt ( x + h + 2)  + sqrt(x + 2)] )

1 / [ sqrt ( x + h + 2) + sqrt (x + 2) ]        let h →  0

1 [ sqrt ( x + 2)  + sqrt(x + 2) ] =

1 / [ 2 sqrt (x + 2)]

And f ' (2)  =

1/ [2 sqrt (2 + 2)]  =

1 [ 2 sqrt (4) ] =

1/ [2 * 2] =

1/4

Thank you, CPhill!

Greetings asinus :- )

(6x^2)^4 = 6^4 * x^(2 * 4)

= 1296 * x^8

:- )  !