ElectricPavlov

Bruce rate  100m/15 s =  6 2/3 m/s

   Allen was there 3 seconds before Bruce who still had to run   3 sec x 6 2/3 m/s = 20 meters

The roots of x^2 - 34x + 34 = 0      are  17 + sqrt 255     and    17 - sqrt 255

then   (a + 1)(b + 1)   =   (18 + sqrt255)(18-sqrt255)       Can you calculate the answer from here?

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WolframAlpha.com  says 10500    but I do not know how to get there !     Let's see what Melody has to say.....

This Q has been asked before.....do a search for it....

Impulse = change in momentum

100 N = m * change in v

100N = 20 kg * change in v

5 m/s = change in velocity  

if the impulse is applied in line with the direction of travel, the object will now be travelling 55 m/s

if the impulse is applied OPPOSITE to the direction of travel , the object is now traveling 45 m/s

7t + h = 67

5t +h  = 49      subtract bottom eq from top

2t = 18      t = 9

5(t) + h = 49

5(9) + h = 49

45 + h = 49

h = 4                                 Edited for mistake Guest pointed out to me...Thanx !

1 3/4  x 3/4 = 21/16

1 3/4 - 21/16 =   28/16 - 21/16 = 7/16

2^8 is 256 , so this is equivalent to:

2^8(x-2) =2^{(-x-7)    Now equate the exponents}

8(x-2) = -x-7

8x-16 = -x-7

9x = 9

x=1

9^(3-x) = 9^2(4-2x)

equate the exponents

3-x = 8-4x

3x = 5

x = 5/3

Another way:

If you take the LOG of both sides you will get this:

(3-x) Log 9   = (4-2x) log 81

(3-x)/(4-2x) = log81/log9

(3-x)/(4-2x) = 2

3-x = 8-4x

-5 = -3x

x = 5/3