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Let  h  =  the  height of  both

Let  the  radius of the cylinder  =  R    and  that of the  cone =  2R

So   for the cylinder

1  = pi * R^2  * h

And  for the cone

V = (1/3) pi ( 2R)^2 *h    =   (1/3)pi  * (4 R^2) * h   =  (4/3) pi R^2 *h

But

pi R^2 * h  =  1

So....the volume of  the  cone  = 

(4/3) (1)  =    4/3

The  center of the circle =   (-3, 4)

Using   the formula  for the  distance  from a point to a line we have  that

l  3(-3)  - 4(4)  + 5  l              l  -20  l

________________    =     ________   =     20   / 5   =    4

    sqrt ( 3^2 + 4^2)              sqrt 25

Adding the radius  (6)  to  this gives us  the  greatest distance from  a point on the  circle to the line =   10

CORRECTED  !!!....thx  Shibu   !!!

104 right?

Thanks!

Thank you so much

I  think  there  might  be  some "formula" for solving this in an easier fashion, but, I believe  the Law of Cosines  might also work

Note  that angles  DCB  and DAB  are supplemental   so     cos ( DCB)   =  -cos (DAB)

Using the Law of  Cosines we have this system    (and subbing  -cos (DAB) for cos (DCB)  )

DB^2   =  3^2  + 2^2   - 2 ( 3 * 2)  (-cos DAB)

DB^2   =  1^2   + 4^2  - 2 ( 4 * 1)   (cos DAB)

DB^2  =  13  +  12 cos DAB

DB^2  =  17   -   8 cos DAB

Multiply  the  first equation  by     8    and the  second  by    12

8 DB^2   =  104  + 96  cos DAB

12 DB^2  = 204  -  96  cos DAB               add  these

20 DB^2  =   308

DB^2  =  308  / 20     =    15.4  

We find the first multiple of 9, start with 99999, add a 9 to get 100008

100008 to 100179, they are both mutlpies of 9, now count, we can't just give the answer. 
 

keep adding 9 from 100008 to 100179, see how many time you can add, that's how many multiples there are.

If tan C  = 2.4     then  we  can let   AB  =  2.4    and  we can let  BC  =  1

So      AC   =  sqrt  (  2.4^2  + 1^2)  =  sqrt ( 5.76  + 1)  =  sqrt ( 6.76)  = 2.6

Cos A   =   BC /  AC    =     1  /  2.6  =  1 /( 26/10)  =  10/26  =  5/13

Awww, thank you. :))

=^._.^=

Very  nice  on  number 3 , catmg.....I wouldn't have  noticed  that  "trick"  !!!!!

x  +  y   +   3z    =  10

-4x   +  3y   +  5z  =  7

  kx  +  z  =   3

Multiply  the  first  equation  through by  -3

-3x  - 3y   - 9z  =  - 30

Add this  to the second equation  producing

-7x   - 4z  =   - 22

Multiply the third given equation  through  by   -4   producing

-4kx  - 4z  =  -12

So   notice  that  if      -7  =  - 4k  ,    k   =   7/4      we eill have  no solutions  because  the  system  then becomes

-7x  - 4z  = -22

-7x  -  4z  =  -12         The  left side cannot  simulataneously  give  different results on the right

So....no solutions when  k = 7/4

The side lengths of a cyclic quadrilateral ABCD are provided in the diagram. Find BD^2.

x = sqrt(7 - sqrt(13)) - sqrt(7 + sqrt(13))

x^2 = 7 - sqrt(13) + 7 + sqrt(13) - 2*sqrt(36)

x^2 = 14 - 2*6

x^2 = 2

x = sqrt(2) or - sqrt(2)

However, sqrt(7+sqrt(13)) > sqrt(7-sqrt(13)), so x is a negative number. 

x = -sqrt(2)

=^._.^=

2. 

a + b = 14

ab = 46

(a+b)^2 - 2ab = a^2 + b^2

Take it from here. :))

=^._.^=

See  if  this  helps

Find  the  area  of  rectangle  EFGH

Then   subtract  the  areas of  right triangles   EBA , AHD, BFC   and  CGD

This will give you the area  of  ABCD

(Remember  that  the area  of a right triangle  =   product of leg lengths  /  2    )

Let me know if you get stuck  !!!!

     A                  C

                  O

       D                   B

DOB  and  COB   are  supplemental

So

5COB  + COB  =  180

6COB  =  180

COB  =  30

And AOD  is  a  vertical angle  to  COB  so  it also   =   30  (degrees)

Factoring x² + 7x + 12 ≤ 0, we get (x + 3)(x + 4) ≤ 0, so -4 ≤ x ≤ -3. Probaby not the right way to do it, but I then plugged in -4 and -3 to see which resulted in a higher value, and -4 gets us 16 - 20 + 6 = 2, and -3 gets us 9 - 15 + 6 = 0, so the answer is 2.

thanks!

                    C

        4sqrt 2                      4sqrt 3

A     60                                           B

Using the Law  of Sines

sin A  /BC   =  sin B /  AC

sin 60  / (4sqrt (3) )  =  sin B   / (4sqrt 2)

sqrt (3) / 2          sin B

________  =     ______  

   4sqrt 3            4sqrt 2

(1 / 8)   =   sin B / 4sqrt 2

(1/8)   =  sin B  / 4sqrt 2

4sqrt 2

______   =   sin B

    8

sqrt (2) / 2  =   sin B

B  =  45°

First  one

(a)

(a  + 1/a)^2    =   a^2  +  2a (1/a)  + 1/a^2    =    3^2

a^2   + 2  +  1/a^2   =  9

a^2  + 1/a^2   =  7

(b)  

a^4  +  1/a^4

(a^2  + 1/a^2)^2    =   a^4  +   2 a^2 (1/a^2)  +  1/a^4     =  49

a^4  + 2  +  1/a^4   =  49

a^4  + 1/a^4    =   47

(c)

a^3   +  1/a^3    =   (a  + 1/a) ( a^2   -  a(1/a)  + 1/a^2)   =

(3)  ( a^2  + 1/a^2   -  1)   =

(3)  ( 7 - 1)  =

18

The  nth  term  in  the  Lucas series  is  given by  :

Phi ^n    -  (-phi)^n

Where   Phi  =    ( 1 + sqrt (5) )  / 2        and phi  is  (sqrt (5) - 1))  /2

So....the  100th term  =

[ (1 + sqrt (5))/2) ] ^100  +  [  ( sqrt (5) - 1)  /2  ]^100   =  792070839848372253127

792070839848372253127 mod 20   =   7

Here  :  https://web2.0calc.com/questions/help-plz_8534

Here's my  take

We  would  have  to draw    all    the  red  and  green balls  in the  first  7 draws

The probability of  this  is      (7/12) (6/11) (5/10) ( 4/9) ( 3/8) ( 2/ 7) ( 1/ 6)   =    1/ 792

Identifiable   arrangements   = 

Number  of  Letters !                  8!

___________________   =    ______   =    3360  identifiable  arrangements

any repeated  letter(s) !          2!  * 3!

Actually I just need the first and third one

There are 4 possible values of X + Y.