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Hi guest, we want to find the perimeter of 4 semicircles and the formula for a circle's perimeter $2(pi)(r)$, since the perimeter is cut in half the formula is $(pi)(r)$.

Now we need to find the radius, since the side of the square and the diameter of the circle are tangent and equal, we know the radius, the formula for radius is $d=2r$.

the diameter is 2/pi, therefore making the radius 1/pi, using the formula 1/pi * pi = 1, so the perimeter of 1 semi circle 1, the perimeter of 4 semicircles is:

$4$

Please put your questions in the question space.

The title could have been

"Infinite sum of a series"

-3x^2   + x  - 4

-5x^2  + 3x  -8

 6x^2   - 7x  -3

_____________

-2x^2  -3x  -15

( -3x^2-5x^2 + 6^x^2)  + ( x + 3x-7x) + ( -4-8-3)      simplify from here

1650 - 20 m = 570 + 20m   solve for m

1080 = 40 m

m = 27 mins

For simplicity  say      f(z) = z^3

                                   g(z) = z^2

z^3  *  z^2 =  z⁽³⁺²⁾  = z⁵          5 is the largest possible degree for integer exponents

(a) The sum of the numbers in the first row is 1/(1 - a).

The sum of the numbers in the second row is ab/(1 - a).

The sum of the numbers in the third row is (a^2 b^2)/(1 - a).

So, the sum of the numbers in the rows form a geometric sequence, which adds up to

1/(1 - a) + ab/(1 - a) + (a^2 b^2)/(1 - a) + ...  = 1/((1 - a)(1 - ab)).

(b) Since the colors of the chessboard alternate white and black, the sum of the numbers on the black squares is equal to the sum of the numbers on the white squares, except for the numbers that are on every other white square, and every other black square.

The sum of the numbers that are on every other white square is a/((1 - a)(1 - ab)), and the sum of the numbers that are on every other black square is b/((1 - a)(1 - ab)), so to find the sum of the numbers on the black squares, we take half the difference, which gives us a sum of

1/((1 - a)(1 - ab)) + 1/2*a/((1 - a)(1 - ab)) + 1/2*b/((1 - a)(1 - ab)) = (a + b + 2)/(2(1 - a)(1 - ab)).

4⁴ miles / 4² miles =   4 ^4-2 =  4²  times longer

Unit cost     175 cents / 5 apples = ........ cents per apple

100 cents / (175 cents/5 apples ) = .........  apples for 100 cents ($ 1 )

Expand

2/5 d - 4 - 2/3 d -4

6/15 d  - 10/15 d  - 8

-4/15 d - 8

If you had 8 equal bags with exactly 500 coins, then each bag would have 62.5 coins.  

But you can't have half a coin, so you're going to have to have 63 coins in each bag. 

63 coins/bag times 8 bags is 504 coins.  Subtract the 53 coins you discovered, and

you would have had 451 coins before your lucky discovery.  

https://web2.0calc.com/questions/need-help-fast-please_1

Well neither is a calculator. Me giving answers is the same as looking for answer on a calculator, right? Not trying to be mean, but I don't think it's a good idea to write an entire article on webcalc. Long division isn't hard, I think. But I'm not really supposed to teach them something that already has many articles about it and/or their teacher taught them. Can they not ask their teacher? I'll give a short summary of long division then. However, a calculator, like CPhill said, is a good tool for double-checking! :)

Long division is division but longer. Here are the steps for it:

1. Divide the tens column dividend by the divisor.

2. Multiply the divisor by the quotient in the tens place column.

3. Subtract the product from the divisor.

4. Bring down the dividend in the ones column and repeat.

Hope this somewhat helps! :))))

If 3^(x + y) = 81 and 81^(x - y) = 9 then what is the value of the product xy? Express your answer as a common fraction.     

3⁴ = 81 so (x+y) must equal 4  

81^–2 = 9 so (x–y) must equal –2  

                                                                x + y  =  4  

                                                                x – y  =  –2  

Add those two equations and obtain       2x       =  2     therefore x =1  

Sub 2 back into one of the equations       1 + y  =  4     therefore y=3  

                                                                 x • y  =  1 • 3  = 3   

I suppose, to comply with the terms of the                                3  

problem, the answer should be expressed                     xy  =  ––  

as a fraction.                                                                             1  

its c

I'll solve #5 

4*(4+x) = 6²

16 + 4x = 36

4x = 20

x = 5

#6 is similar to #5

#7 and #8 --- just multiply radii by 2 and then multiply by 3.14

x+(2+x)+(x-1)=11

x=3.33333333333 sliver

gold=2+3.33333333333=5.33333333333

bronze=3.33333333333-1=2.33333333333

3.33333333333+2.33333333333+5.33333333333=11

We can maximize the number of roots by taking the prime factorization of 42, i.e. (x + 2)(x + 3)(x + 7).  So the maximum number of integer roots is 3.

222.43 right ?

f(3) = f(2*1+1)=f(1)+1=2

f(7)=f(2*3+1)=f(3)+1=3

f(15)=f(2*7+1)=f(7)+1=4

You are correct!!!!!! Thanks for answering my question

The conjugates will also be  roots

So.....the  polynomial is

P(x)  =  a [x - ( 1+ 2sqrt (3))]  [ x - (1 - 2sqrt (3)) ]  [ x - (3-sqrt (2))] [ x - ( 3 + sqrt (2)) ]  =

(I used WolframAlpha to expand this  )

a (x^4 - 8 x^3 + 8 x^2 + 52 x - 77)

Since  f(0)  = -154

Then

a (-77)  = -154

a =  -154/-77  =   2

So....the polynomial  is

2 [ x^4 - 8 x^3 + 8 x^2 + 52 x - 77 ]  =

2x^4  - 16x^3 + 16x^2  + 104x - 154

And  we  just need to  add all the  coefficients plus the  constant term to get f(1)   =

2 - 16 + 16  + 104  - 154   = 

-48

Revenue  = 1.50c

Expenses  = 14

Profit ...   P  =     1.50c  -14

19.5  cups isn't  viable  (nobody buys  ,5  =   1/2  cup of lemonade )

5%   =   .05

So

5%  of  234.14 =  (.05)(234.14)  ≈  $11.71   = discount

So.....the bill = 234.14  - discount  =

234.14 - 11.71  =????

You should be able to finish this  now

Thanks for trying but the answer is 24