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(c)

-9x^2 = 30x + 25   rearrange as

9x^2 + 30x + 25 = 0        we can factor this    !!!

(3x + 5) ( 3x + 5) = 0

Setting either factor to 0 and solving for x produces     x =  - 5/3

Please if you are going to say stuff like that please put it in off topic!

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b )  x^2 + 41 = -8x

x^2 + 8x  =  -41      complete the square on x

x^2 + 8x + 16  =   -41 + 16

(x + 4)^2 =   - 25      take both roots

x + 4 =  ±√-25

x + 4 = ± 5i      subtract 4 from both sides

x =   - 4 ± 5i

1 pound = 453.592.37 gm

453 .59237 / 2.016  = 224.996 =~~225 moles     ( =  225 x 6.022 x 10^23  molecules  = 1.355 x 10^26 molecules)

135 lbs x  0.45359237 kg / 1 lb   x  0.5 mg / kg   x  ml /120 mg   ≈   0.255 ml  

-x^2+4x-13 = 0

x^2 - 4x + 13 = 0      Use quadratic formula  

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)       a = 1  b  = -4   c = 13

Sustituting yields       4 +- sqrt( 16- 4*1*13)   /  2     =    2 +-sqrt (-36)/2    =  2 +-  3i

Think you can try the others?

Let's use consistent units     .75 l = 750ml

Density = mass/volume  =  765 gm / 750 ml  = 1.02   gm/ml

Urine density can change by the kindneys increasing the concentration....by excreting more salt ...or re-absorbing more water.

                                                            or decreasing the concentration by holding salt and excreting more water....

a)    1/x + 1 / 3x  = 6

        3/3x + 1/3x  = 6

        [ 4] / 3x = 6  multiply both sides by 3x

         4 =  18x       divide both sides by 18

         4/18 = x

         2/9 =   x

b)     1/x + 1 /x+1  = 3

         [ x + 1 + x ] / [ x ( x + 1) ] = 3

         [2x + 1 ] =  3 [ x ( x + 1) ]

         2x + 1  = 3 [ x^2 + x]

         2x + 1 =  3x^2 + 3x          rearrange as

         3x^2  + x - 1 = 0

Use the quad formula

x = [ -1 ±√ [ 1 - 4(3)(-1) ] / {2 * 3 ]

x =   [ -1 ±√13] / 6

c)   ( x +3 ) / ( x - 1)   -  x / (x + 1)  =    8 / [ (x + 1) ( x - 1) ]

Multiply through by  (x + 1) ( x - 1)

(x + 3)(x + 1)  - x(x - 1) =  8       simplify

x^2 + 4x  + 3  - x^2 + x = 8

4x + 3 + x = 8

5x + 3 = 8

5x = 5

x = 1

However....this makes a denominator = 0...so no solution exists

The first four ' - ' signs cancel out and you are left with

-10x = -5

x = 1/2= 0.5

135 lb  x   1kg/2.2lb  x  .5 mg/kg   /  120 mg/ml  = 0.256 ml

Why don't you do it yourself?

\(\sum \limits_{n=0}^\infty ~\alpha^n = \dfrac{1}{1-\alpha}\\ \text{here }\alpha = \dfrac 1 2\\ \text{and thus the sum is equal to }\dfrac{1}{1-\dfrac 1 2}= 2\)

Yes it all makes sense. thank you

help, so 5 kg*m/s was transferred?

okay sorry

when did you get so smart and where did you get so much knowledge?

x^5, a^3

Maybe right 

Not sure about this 

a)  t is the  time elapsed since the egg was dropped

b)  h(t) is the height at some time, t

c)  When it hits the ground, h(t) = 0

So....we can solve this

-16t^2 + 50 = 0  

-16t^2 = -50       divide both sides by -2

8t^2 =  25         divide both sides by 8

t^2 =  25/8  take the square root

t = √[25/8]  ≈ 1.77    sec

(d)  At 1 sec  the height is  -16(1)^2 + 50   =  34 ft

At 1.5 sec the height is  -16(1.5)^2 + 50   = 14 ft

So....it falls  34 -14   = 20 feet  in this time interval

In your previous posting, you stated how fast the 5 kg object was traveling after the collision.   We need that info here to solve this....if it is travelling at 20 m/s , I already answered this in the previous posting   

The conservation of momentum, means that before and after the collision, the momentum totals are the same...

original momentum    5 kg * 25 m/s = 125  kg -m/s

After collision             5      *20 =          100 kg-m/s

this means that the 1 kg object has the remainder of the momentum   and is traveling at 25 m/s