ElectricPavlov

Spring constant    F =  kx      and we know (or should know)  F = ma (Newtons)   and   ONE joule = ONE Newton-Meter

Stretch distance = 1.25 - .75 = .5 m

100 j = 100 N-m

F= 100 N-m / .5 m = 200 N

F=  kx

200 = k(.5)

200N / .5m = k = 400 N/m  ??????      Hmm...... second time today that I got an answer that does not match your variable choice answers..........I do not know what to think..... At what answer did YOU arrive???

ANYONE???

d/dx of  2 x^2  = (2) 2x^(2-1) = 4x

d/dx of a constant is '0'                     so f'(x) = 4x

Just substitute in for 'x
 

-3 (-1)^3 + 2 (-1)^2 = -3(-1) + 2(1) = 3 + 2 = 5

-3(1/2)^3 + 2(1/2)^2 = -3(1/8) + 2 (1/4) = -3/8 + 2/4 = 1/8

Hmmmmm.... I don't get ANY of those answers......Are the charges separated by AIR or something else?????

Use Coulomb's Law   F = k Q1Q2 / d^2      Where k=Coulomb's constant 9.0 x 10^9 N M^2/C^2  (for AIR)

=  9 x 10^9  (2 x 10^-6)(44 x 10^-6) / (5 x 10^-3)^2       (the distance between the charges is 5mm per pythagorean theorem)

= 792 x10^-3 / (25 x 10^-6)  = 31.68 x 10^3 N

Hmmmm....    I think the charges must be in something besides AIR which changes the value of 'k'

# 8     Using Pythagorean theorem (to find the resultant distance from the starting point)

  a^2 + b^2 = c^2

250^2 + 575^2 = c^2     c= 626.99 meter      626.99 meters/ (45 + 55)seconds = 6.27 m/s average from her starting point(as a RESULTANT)  

Her ACTUAL average speed is  (250 + 575)/(45+55) = 8.25 m/s

4 a   R = 16 + 12  +  (60 x 40)/(60+40) = 52 ohms

  b  V = I R  = .25 x 52 = 13 volts

  c   Voltage drop across R1 =  .25 (16) = 4

                                        R4 = .25 (12) = 3         13 - 4 - 3 = 6V across R2  (AND R3)

  d Current through R2 = V/R =  6/60 = .1 A     Power = I^2 R    or VA  =  .6 watts

11. cuts       (318 ft = 3816 inches)

1 cut = 4 inches

2 cut = 8 inches

3 cut = 16 inches

4 cut = 32 inches

5 cut = 64

6   = 128

7  = 256

8= 512

9 = 1024

10 = 2048

11= 4096

The base rectangle is 11 + 11 + 3 + 3 = 28 cm

the additional two squares on top add 4 sides of 2cm = 8 cm     28 + 8 = 36 cm 

 (I don't think you should add the 2cm on TOP of the squares as they are counted in the LOWER rectangle perimeter).

As Alan said : arrange in numerical order

2  3  4  4  4  5  7  7  18     the number in the middle is the MEDIAN----

  '4'   has four numbers below it and four above it.

Hey Melody..... kinda just figured that one in my head  (I do not think you can find two other values for a and b that add to 17 with a hyp of 13 ....try)        ....here is the method:

a+b =17     so b = 17-a   (1)

Pythagorean theorem:    a^2 + b^2 = c^2 = 13^2= 169    Substitute (1) into this

                                        a^2 + (17-a)^2 = 169

a^2 +a^2 - 34a + 289 = 169

 2 a^2 -34a + 120 = 0

a^2 -17a +60 = 0    Use Quadratic formula to get  (17+- sqrt49)/2    results in  12 and 5  

12-5-13 triangle    area = 1/2 a x b = 1/2   x 12  x 5 = 30 sq units