CPhill

I assume this is

9^y =  3^( 5*9 / 27)

(3^2)^y = 3^(45/27)

3^(2y)  = 3^(5/3)          solve for the exponents

2y =  5/3      multiply both sides by 1/2

y = (5/3)(1/2) =  5/6

.05x=   16        divide both sides by 0.5

x = 16  / 0.5   =  32

100 / 18.75 =  5.33

I rounded to  the  nearest whole number

If we round up, the answer is  6

Here :

https://web2.0calc.com/questions/plz-help_3311

If 20 female Kodiak grizzly bears produce 50 cubs every 4 years, how many years will it take 30 female grizzlies to produce 100 cubs? Assume a constant rate of cubs per grizzly per year. Round up to the nearest whole number of years.

50  cubs every 4 years  =  50 / 4   =  12.5 cubs per year

So  each female (on  average)  produces   12.5  / 20   = .625 cubs per year

So  30 females  can  produce   30 * .625 =  18.75 cubs per year

So...it will take them

100 / 18.75    ≈ 5 years to produce 100

600 gallons of fuel was enough energy for the company to assemble 20 pipes in 10 days Then, 400 more gallons of fuel were added so that more pipes could be produced. How many pipes could they now produce in 11 days? Assume a constant rate of gallons per pipe per day. Round down to the nearest pipe.

20/10 =  2 pipes  per day could be produced by 600/10 =  60 gal of fuel

So....30 gal of fuel will produce one pipe every day

So when 400 gallons  of fuel are added we now have 1000 gallons

So........1000/11 =  the number  of gallons available in one  day

So   [ 1000 / 11 ]  / 30  =   3.03 pipes per day can  now be produced in one day

So   11 * 3.03  =    33.33  pipes can be produced in  11 days  =    33 pipes

(2n - 1)  + 2 ( 2n + 1) + 3(2n + 3)  =  34

2n - 1  + 4n + 2 + 6n + 9  =  34

12n + 10   =  34

12n  =  34 -10

12n =  24

n = 24 / 12  =  2

The integers  are

2(2) - 1   ,   2(2) + 1  ,  2(2) +  3

3  ,  5   ,   7

We need to use it  twice  [    derivative of numerator  /   derivative of  denominator ]

First time we get       [ 9x^2]  / [ 2x]

Second time we  get   [ 18x ]  / 2  =  9x 

So

lim          9x      =      inf              [   so....the limit doesn't exist ] 

x → inf

Rearrange  as

x^2  + 1x  =   -1

Take (1/2)  of 1  = 1/2

Square it   = 1/4  and add to  both sides

x^2 + x  + 1/4   -1 +  1/4                 factor the left side and simplify the right

(x + 1/2)^2  =  -3/4                       take both roots

x + 1/2 =    ± sqrt (-3 )  / 2

x + 1/2  =   ± sqrt (3) i   /   2

x =   -1/2    ± sqrt (3) i  / 2

x =   [ -1  ±  sqrt (3) i  ]   /   2

Write the equation of the line between  (15, 5)  and ( 9, 20)

Slope = (20 - 5) / ( 9 - 15) =  15 / - 6 =   -5/2

y =  -(5/2)(x - 9)  + 20

y =  (-5/2)x + 45/2 + 20

y =  ( -5/2)x + 85/2

When x =  11

y = (-5/2)(11) + 85/2  =  30 / 2  =  15

Let C = (11,15)

The ratio  is

AC  /   BC

sqrt [ (15 - 11)^2 + (5-15)^2 ]                   sqrt  [ 116]

_________________________   =        __________  = sqrt (116 / 29) =  sqrt (4) / 1  =   2  :  1

sqrt [ ( 9 - 11)^2 + ( 20 - 15)^2 ]               sqrt [  29 ]