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Need the diagram ....

x^2+10x+y^2+16y   = k        now complete the square for x and y

(x+5)^2     +  ( y+8)^2   = 25 + 64  +k      the red part = r^2    ( which = 6^2 = 36) 

r^2 = 89 + k    = 36    solve for k

         k = -53

Gather 'like' terms and you will find the second one is the answer

The solution will then be where the two graphs intersect.

n takes the following values:

n ==2,  8,  10,  32  and  98

Therefore, the largest n==98

Check: [98^3 + 100] mod [98 + 1] ==0

3^{11} + 5^7 + 1 ==255,273

255,273 = 3 * 85091 [The smallest prime factor is 3]

Area = 11 + 12√2

[ABCD] = 13 square units

urw! 

Area = 2(36pi - 72)

Find r^2+s^2.

Hello Guest!

\(3x^2+4x+12 = x^2 - 5x + 7\\ 2x^2+9x+5=0\\ x^2+4.5x+2.5=0\\ x=-2.25\pm \sqrt{5.0625-2.5}\)

\(r^2=14.8285\\ s^2=0.4215\)

\(r^2+s^2=15.25\)

  !

What is the smallest prime divisor of 3^{11} + 5^7 + 1?

Hello Guest!

\( 3^{11} + 5^7 + 1=255273\)

I think three.        Or one?

  !

waitwaitwait.

\(\sqrt125\)

\(5\sqrt5\)

oops. um...

By division we find that 𝑛3+100=(𝑛+10)(𝑛2−10𝑛+100)−900n3+100=(n+10)(n2−10n+100)−900.

Therefore, if 𝑛+10n+10 divides 𝑛3+100n3+100, then it must also divide 900. Since we are looking for largest 𝑛n, 𝑛n is maximized whenever 𝑛+10n+10 is, and since the largest divisor of 900 is 900, we must have 𝑛+10=900⇒𝑛=890n+10=900⇒n=890

The largest 𝑛 is therefore 890

ok so the n3 and n2 is just \(n^3 or N^2\)

Entire area = 10 x 10 = 100

   less    2   *  2*6        less   2 *2

100 - 24 - 4  = 72 units²

8 *  1.33    * 1/5 = ................

=== 1/b³  = b^-3

[4 C 2] * 5^2 ==150

The probability is: 150 / 6^4 ==150 / 1,296==25 / 216==11.574%

2^2×3^3×4^4×5^5×6^6

The smallest number==3 x 5 ==15

2^2  x  3^4  x  4^4  x  5^6  x  6^6==60,466,176,000,000

Sqrt(60,466,176,000,000) ==7,776,000

Let the amount of money Nell have = N,

And the amount of money David have = D

                              Nell         David

           Initiallly          N             D

           Case 1          N - 16      D + 16

           Case 2          N + 9       D - 9

Case 1 --> When Nell gives David $16,

         Then both have the same amount.

           So, N - 16 = D + 16

                     N = D + 16 + 16 = D + 32

Case 2 --> When David gives Nell $9,

            Nell and David's amount will be in

              The ratio 6:1.

                  (N + 9)/D - 9 = 6/1

                   N + 9 = 6D - 54

                   N = 6D - 63

After equating the equations from both cases,

We will get          N => D + 32 = 6D - 63

                                      32 + 63 = 6D - D

                                            95 = 5D

                                            D = 95/5 = $19

     And, N = D + 32
 Nell have $51 and David have

 $19. Together they have $(51 + 19)

                                        = $70

For Part A:

     Average change = -15/5 = -3°C/1 week

For Part B: 

     expression =  △T = -3°C/week

     It means that the temperature falls down 3°C per week

The area of the polygon is 8 + 15*sqrt(2).

The smallest possible average is 12.

The area of the region is 68.