ElectricPavlov

Acceleration is a change in velocity.

Let's break the electron's VELOCITY before and after the 3 seconds in to its x and y components.

vox = original x velocity  = 5.2 cos 36.8 = 4.164 m/s

voy =                                  5.2 sin 36.8 = 3.115

v1x = final x velocity      = 7.18 cos (-63.3) = 3.226 m/s

v1y =                                 7.18 sin (-63.3) = - 6.414

Now the CHANGE in velocities (x and y vectors)  is  

v1x-vox  and  v1y-voy

(3.226-4.164)  & (-6.414-3.115)    (these are x and y VECTORS so we cannot just add them together)

-0.938 m/s              -9.529          The RESULTANT change in velocity = sqrt (vx^2 +vy^2)

change in velocity  v delta= 9.575 m/s  @  -95.62 degrees 

This CHANGE in veocity happened over 3 seconds

Acceleration = change in velocity/change in time  = 9.575/3 = 3.192 m/sec^2  (absolute value)

   Note that the velocity change was negative for both x and y so the acceleration is - 3.192 m/sec^2

The 19 foot ladder forms the hypotenuse.

One leg is 5 ft     the other leg is the side of the wall

Pythagorean theorem (for right triangles ONLY)

a^2 + b^2 = c^2      where c = hypot    a  and b are legs

5^2 + b^2 = 19^2

b^2  = 19^2 - 5^2

b = height up the wall = sqrt(19^2-5^2) = 18.33 ft

Thanx! for the 'fix' !    I amke almost as mnay typos as I do math mistkaes

Hmmmmm.... Assuming no leading zeroes

1 0 4 6 8                     x     2 3 5 7 9   =  246 842 972

my guess

The first one    f(x) = y = 3-4x    solve for 'x'

y-3 = -4x

3-y = 4x

(3-y)/4 = x      now switch the x's and y's

f^-1 (x) =  (3-x)/4

The second one  y=3+4x

                            (y-3)/4 = x

f^-1 (x) =  (x-3)/4

Now add the two f^-1  (x) in red       (3-x)/4 + (x-3)/4    =  (x-x +3-3)/4 = 0

Deleted....

First one:

The formula for a sphere is 4/3 pi r^3

 if scale UP 'r' by a factor of 4.5     r^3   will yield a volume  (4.5)^3 larger  = 91.13 times larger

Second question:  

 The formula for the volume of a cone is  pi r^2  h/3

         if we scale it DOWN by 1/2      the   r^2 will be  1/4   and the h/3 will become  1/2 (h)/3

     so the volume will be ruduced to 1/4 x 1/2 = 1/8 of the original   1/8 (360) = 45 m^3

sin (x) = 0     where ?    at   x = 0 degrees

sin (0 degrees) =0

arcsin(sin (0 degrees)) = arcsin (0)
0 degrees = arcsin (0)

Guest troll visits some strange websites.

Do you know where   cos(x) = -1  ?    This is true at   pi radians (or 180 degrees ----same thing)

    so    cos (pi) = -1

    now arcos both sides

        arcos ( cos(pi) )  = arcos (-1)

                     pi = arcos (-1)

When you use the sin function, you 'undo' it when you use the sin inverse (also called the arcsin) function     so   if you start with theta

    then you use the sine function ,  sin (theta)     then    arcsin ( sin theta) = theta

Your equation:   sin(theta) = x/10      now    arcsin both sides

       arcsin(sin (theta))  = arcsin  (x/10)

                 theta = arcsin (x/10)