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Saw this presented the other day as

0 = 1 000 000  * .9^t

    This is just not possible to ever equal zero.....   . 9^t    will never equal 0

             in approx 131 days   (for  't' ) the value is  1      after that, as the value of 't increases the vlaue of f(t) is below one....but never ' 0 '

                  in 200 days the value is .000705              but it never reaches  ' 0 '   no matter how many days you put in for 't'

3 out of 5 elements in the given set are prime; they are 2, 3, and 5.  So you are in reality counting the number of subsets of the set {2, 3, 5}, which has \({2}^{3}\)subset, including the empty set. Taking that set out, leaves us with 7subsets. Can you list them? (Hint: there are 3 with only one element, 3 with exactly 2 elements and 1 with three elements.)

Find  the  slope of the  second line

(  8  - 0 )   / ( 7 - - 9)   =     8  / 16   =   1/2

Using  ( -9, 0)   the  equation of this  line  = 

y  =  (1/2) ( x  - - 9)

y   =   (1/2)x  + 9/2

Set  the y's  equal

2x -10  =  (1/2) x  +  9/2         multiply  through by 2

4x  - 20   =  x  + 9

3x  =  29

x  =  29/3

And y   =  2 ( 29/3)   -10  =   28/3

(a , b) = ( 29/3 , 28 /3)

(a + b)  =     29/3  + 28/3  =   57 / 3    =    19

The probability is 17/160.

Multiply  the  first  equation  through  by  -  30    and we  have

- 150 t   -  6s   =    -90              add this  to  the  second equation  and we  get

-147t  =   -81

t  =   -81 / -147  =    27/49  

To  find  s

3(27/49)  +  6s   =   9

81 / 49   +  6s   =   9

6s   =  9   -   81/49

6s   =   360 /49

s =  360  / (49 * 6)   =   60 /  49

(s , t)   =   ( 60  / 49   ,   27  /  49)

I think the image above (drawn on GeoGebra) summarizes the situation in your problem. I leave it to you to decide which way you rotate (clockwise or counterclockwise) and by what angle. Good luck.

Yep...I mis-read it, MWH.....your answer is  correct  !!!!

A "Best Answer"  fer shure   !!

wait u put 8 as the height but the problem says 6

the lateral area of a cylinder is \(2πrh\)

so \(2\pi r\cdot 6=48\pi\) and \(r=4\)

so the volume is \(96\pi \)

CPhill got something different so i'm not sure

Lateral surface area =    2pi *  r * h

So

48 pi   =   2 pi  * r  *   8

48  =   2 *  8  *  r

48  = 16  r

r =  48  /16     =   3  cm

Volume     =    pi * r^2  * h  =

pi * 3^2  *  8  =

72  pi    cm^3

Volume   of   the  12 cylinders =    12  *  pi  *  4^2  * h  =    192 pi * h

So

192  pi  * h    =    N  *   pi  *  ( 8^2)  *  h           divide out  h  and pi   and simplify

192  =     N *  64

192 /  64   =  N

3  =  N   =  the  number  of new  containers   needed

2  feet  = 24 in

So

20  /  24   = 

5 /   6

a^2  -  b^2    =100

(a + b)  ( a - b)   =  100

Factors  of  100  =    1 , 2 , 4 , 5 , 10 , 20 , 25  , 50  ,  100

a + b =  100

a -  b  =    1

2a  =  101

a not an integer

a  +  b =   50

a  -  b  =   2

2a   = 52

a   = 26

b  =  24

a + b   =  25

a - b    =    4

2a   =  29

a not  an integer

a + b =  20

a  - b   =  5

2a   = 25

a not an integer

a + b  =  10

a  - b   =  10

2a  =  20

a = 10

b =   0    (not a positive integer)

So

(a , b)  =     (26,24  )   

I think this problem is stated incorrectly and that is why no one has answered it yet.There is an x missing in the expression for \({f}^{-1}(x)\). It should be\({f}^{-1}(x)=\frac{ax+b}{cx+d}\).

j, k  >   8

Let  8  =z

Let  j =   z +  a

Let k  =  z +  b

So we  have

1/ ( z + a)    +   1 /  ( z + b)   =     1/z

(2z + a + b)  / (  z^2 + az  + bz + ab)   =   1  /z            cross-multiply

z ( 2z  + a  + b)  =  z^2  +  az  + bz   +  ab

2z^2  +  az   +  bz    =    z^2  + bz +  az  +  ab

z^2   = ab

So

8^2   =  ab

64   = ab

Factors   of  64     =  1, 2 , 4 , 8 , 16 , 32 , 64

So

a    b           =      (z + a)   (z + b)     =   j    ,  k    

64  1          =          72         9              72      9

32  2         =           40       10              40 ,  10

16  4          =          24       12              24 ,  12

 8   8          =          16       16              16 ,   16

Depending on  our  choice for  k     the  sum of all possible  values = 

(72  + 9  +  40  + 10  +  24  + 12  +  16)    =    183

The total number of outcomes is C(100, 7). The number of outcomes wherein there are 3 friends and 4 non-friends is C(12, 3) times C(88, 4). So the probility of having 3 friends selected is

                                                                                                     \(\frac{C(12, 3)\times C(88,4)}{C(100, 7)}\).

[942!  +  120!] mod 60^n ==0

The largest n == 28

Since the only condition is that no 2 trues are consecutive aren't there more than 4 ways to arrange them? 

I always feel good  when my answer  matches up with heureka's   !!!!!!

2x  +  8y   =   21

8y   =   -2x  + 21

y  = (  -2/8)x  +  21/8

y = (-1/4)x  +  21/8

Slope =   -1/4

So

(17 -  -9 )                1

________  =   -   _____               

( j -  2)                    4

26  /  ( j -2)  =   -1/4                cross-multiply

4 * 26   =    -1  ( j  -2)

104  =  2   -  j

j   =  2 - 104   =   -102

We must have \({x}^{4}+a{x}^{3}+b{x}^{2}+cx+d=2x+3\) at x =1, x=2, and x=3. Substituting we get

                                                                         a + b + c +d = 4                                             (1)

                                                                        8a + 4b + 2c + d = - 9                                     (2)

                                                                       27a + 9b + 3c +d = - 72                                   (3)

Subtracting (1) from (2) and (2) from (3) gives

                                                                       7a +3b + c = -13                                              (4)

                                                                       19a +5b +c = - 63                                            (5)

Subtracting (4) from (5) results in

                                                                        12a + 2b = - 50                                               (6)

We are asked to find

                                                           f(0) + f(4)= d + 256 + 64a + 16b + 4c + d 

                                                                         = 256 + 64a + 16b + 4c + 2d                         (7)

Solving (2) for 2c + d we get

                                                                           2c + d = - 9 - 8a - -4b                                   (8)

Substituting (8) in 7 gives

                                                           f(0) + f(4) = 256 +64a +16b +2(- 9 - 8a - 4b)

                                                                           = 256 +64a +16b - 18 -16a - 8b

                                                                           = 238 +48a + 8b

                                                                           = 238 +4(12a +2b)                                        (9)

Substituting for 12a +2b the value we found in (6) completes the lengthy computations:

                                                             f(0) + f(4) = 238 + 4(-50) = 38.

Unless I am in error, no ther value of the function is needed.

Let a1, a2, a3, ... be an arithmetic sequence.
If a2/a4 = 3, what is a5/a3?

\(\begin{array}{|rcll|} \hline \dfrac{a_2}{a_4} &=& 3 \\ a_2 &=& 3a_4 \\ a_1+d &=& 3(a_1+3d) \\ a_1 + d &=& 3a_1+9d \\ -2a_1 &=& 8d \\ \mathbf{a_1} &=& \mathbf{-4d} \\ \hline \dfrac{a_5}{a_3} &=& x \\ a_5 &=& x*a_3 \\ a_1+4d &=& x*a_3 \quad | \quad \mathbf{a_1=-4d} \\ -4d+4d &=& x*a_3 \\ 0 &=& x*a_3 \\ x &=& \dfrac{0}{a_3} \\ \mathbf{x} &=& \mathbf{0} \\ \hline \end{array}\)

\(\dfrac{a_5}{a_3} = 0\)

a₂ / a ₄  =   3

So

a₄/ a₂  =   1/3

a₄  =  a₂ /  3

a₄  =   a₂  +  2d  =   a₂  / 3

So

a₂  +  2d  =  a₂  / 3

2d   =   -(2/3)a₂

d  =   -(1/3)a₂

a₃   =    a₂  +  d   =   a₂  -  (1/3)a₂ )   =    (2/3)a₂

a₅   =  a₂   +   3d   =   a₂  +  3( -(1/3)a₂)   =    a₂  -  a₂  =  0

So

a₅ / a₃     =     0

On February 21, a 61-year-old man who had gone to work in Italy disembarked in Brazil, more specifically in the city of São Paulo. After presenting the symptoms of the new coronavirus (fever, sore throat, runny nose and cough), he went to the hospital, where the first case of the disease in the country was confirmed through tests. From then on, we quickly had an explosion in the number of cases due to the exponential growth in the number of infected. Making a mathematical approximation through the disease progress function we were able to arrive at the following function representing the number of cases by the time in days of the first case. f(x) = Xi * R^t where : f(x) is the number of cases in a given time t Xi is the initial number of cases in a population R or Rt is the rate of spread, that is, to how many people an infected person transmits the disease on average t - Time measured in days. Calculate: If, when we reach 1,000,000 cases, our Rt rate drops to 0.90 ( Rt = 0.90 ) , how long would it take to zero the number of daily cases. (f(x) = 0 and Xi = 1,000,000 ).

uh here's the translation

i honestly don't know how i would do this one

it's way too wordy and it's confusing me.