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A = pi x radius squared

16 sqmm = 3.14 x r squared

r squared = 16 sqmm / 3.14 =  5.1 sqmm

r = square root of 5.1 sqmm = 2.26 mm

The homework is the profile pic...

By the way, is there any fast way to do this?

I'm sure you are correct Rom but I am with itsyaboi.

Talking about needing to go the long way around!

Jimmy first eats 2 cookies.

\(12 - 2 = 10\)

Next, he gives 1 to his mom.

\(10 - 1 = 9\)

Therefore, Jimmy has 9 cookies left.

Post your questions.....we'll see what we can do.....

7) Suppose b and c are positive integers. When b^2 is written in base c, the result is 121_c. When c^2 is written in base b, the result is 71_b. What is b+c?

121c  =  c^2 + 2c + 1   =  b^2      (1)

c^2  =  7b + 1  

c^2 - 1 = 7b

[ c^2 - 1 ] / 7 = b    ⇒   [c^2 - 1 ]^2  / 49 = b^2      (2)

Sub (2) into (1)

c^2 + 2c + 1  = [ c^2 - 1 ]^2 /49

49(c + 1)^2 = [ (c + 1) (c - 1) ] ^2 

49 =  (c - 1)^2

So....c = 8

And b =  [ c^2 - 1 ] / 7   =   [ 64 - 1 ] / 7 =  9

So

b + c  =    9 + 8   =   17

I wish it was that easy

We need some numerical  data......!!!!

The directrix lies above the focus.....so...this parabola opens downward

To find the vertex ....we have ( -3, (-4 + 1)/2 )   =  (-3, -3/2)  = (h, k)

The distance from the vertex to the focus = p   =    l -4 - (-3/2) l =   l -4 + 3/2l =  l -8/2 + 3/2] = l -5/2l = 5/2

We have the following form

4p ( y - k) = - (x - h)^2               fill in what we know

4(5/2) (y - (-3/2) )  =  - ( x -   -3)^2       simplify

10 ( y + 3/2 ) =  - ( x + 3)^2          divide both sides by  10

y + 3/2  =    - (1/10) ( x + 3)^2       subtract 3/2  from both sides

y =  - (1 /10) ( x + 3)^2   - 3/2

Have you looked at any of these?

6) There is a rectangular patio. If we increase both the length and width by 2 feet, the area of the patio will increase by 38 square feet. If we increase the length by 2 feet and decrease the width by 2 feet, the area of the patio will decrease by 2 square feet. What is the area of the patio?

Call the imensions of the patio L and W....so the area = LW

We know that

(L + 2) (W + 2) = LW + 38

LW + 2W + 2L + 4 = LW + 38

2(W + L) = 34

W + L = 17

L = 17 - W   (1)

And we also know that

(L + 2) (W - 2) = LW - 2

LW + 2W - 2L - 4 = LW - 2

2W - 2L =  2

W - L = 1

sub in (1) for L

W  - (17 - W) = 1

2W - 17 = 1

2W = 18

W = 9

And L = 17 - 9  =  8

So....the area is  LW = (8)(9) = 72 ft^2

oh okay! That makes more sense . Thank you 

5) Four positive integers A, B, C, D and  have a sum of 36. If A+2=B-2=C*2=D/2, what is the value of the product of A*B*C*D?

A+ 2 = B - 2    ⇒  A + 4 = B

and

A + 2 = C*2

[ A + 2 ] / 2 = C

and

A + 2 = D /2

2[ A + 2] = D

So     ... A + B + C + D   = 36            substituting

A + (A + 4) + [ A + 2] / 2 + 2[ A + 2] = 36      simplify

4.5A + 9 =  36

4.5A = 27

A = 6     B = 10    C = 4     D = 16

So

ABCD  =  3840

Nice job, itsyaboi !!!

tertre is correct

4 + 8 + 12 + 16 +.....+  400

3 + 6  + 9  + 12 +.....+  300

The difference in the series is

1 + 2 + 3 + 4 + ....+ 100   =  the sum of the first 100 positive integers =   100 (101) / 2  =  50 * 101 = 5050

1) - The smallest positive n! and (n + 1)! are: 10! =3,628,800  and  11! =39,916,800

2) 1991*1993*1995*1997*1999 = 31601836203377055

     0 + 5 + 5 = 10

3) 3) What is the remainder when (17^77) is divided by 35?

     17^77 mod 35 = 12

4)  Find the smallest positive multiple of 21 that has no digit larger than 1.

     481 x 21 =10,101.

If the directri is y = 4   and the focus is (0,0).....the vertex = (0, (0 + 4)/2 )  = (0, 2  )= (h, k)

In other words....the vertex is midway between the focus and the directrix

p  is the distance between the vertex and the focus = 2

And since the directrix is above the focus, the parabola opens downward

And we have the form

-4p ( y - k) = x^2

-4p(y-2) = x^2                (we use the " - " because the parabola opens downward )

- 4(2) (y -2) = x^2

-8(y - 2) = x^2

EDIT TO CORRECT AN ERROR

Don't know how to compute this without WolframAlpha

But....the exact sum is  

pi^6 / 960

C / S   =  5/3    ⇒    C = (5/3)S       (1)

[ C - 4] / [ S + 2]  =  8/7               (2)

Sub (1) into (2)

[ (5/3)S - 4 ] / [ S + 2 ]   =  8/7            cross-multiply

7 [ (5/3)S - 4 ] =   8[ S + 2 ]        simplify

(35/3)S - 28  = 8S + 16

(35/3)S - 8S =  16 + 28

(35/3)S - (24/3)S = 44

(11/3)S = 44

S =  (3/11) *44 =    12

So....the number of original clubs =  (5/3)S =   20

So....he has 20 - 12 =  8 more

That is correct: sum of 1 to 100 =5050.

x/y = 5/3

and

x-4/y+2 = 8/7

So, x = 5/3y

\(\frac{\frac{5y}{3}-4}{y+2}=\frac{8}{7}\)

Solving this, we should get that y=12 and x=20

So, Og has 8 more.

I believe this might be the second one

The sum of the interior angles of an octagon = 135 * 8  = 1080°

So....the remaining two angles must sum to   1080 - 2(115 + 125 + 135)  = 330°

So....since the opposite sides are parallel.....the largest remaining angles each measure 330/2 = 165°

The arithmetic sum formula shows that:

\(\text{sum} = 100(\frac{4+100}{2}) = 5200\)

\(\text{sum} = 100(\frac{3+100}{2}) = 5150\)

The difference is 5200 - 5150 = 50.

Compare the sums for a second: 

4+8+12+16+20+24

3+6+9+12+15+18

Sum of the first 100 positive integers, so 5050 or (D).