Answer:
(a) 0.17 m
(b) 5.003 m
(c) 6.38 ×
N
(d) 7.37 ×
N
Explanation:
(a) The minimum value of
will occur when q3 = 0 m or at origin and q1, q2 are at 0.17 m so the distance between q3 and q1, q2 is 0.17 m, therefore the <em>minimum value of x= 0.17 m</em>.
(b) The maximum value of x will occur when q3 = 5 m because it is said in the question that 5 is the maximum distance travelled by q3. To find the hypotenuse i.e. the distance between q3 and q1,q2, we use Pythagoras theorem.

<em>Hence, the maximum distance is 5.002 m</em>
(c) For minimum magnitude we use the minimum distance calculated in (a)
Minimum Distance = 0.17 m
For electrostatic force= 

×
(d) For maximum magnitude, we use the maximum distance calculated in (b)
Maximum Distance = 5.002 m
Using the formula for electrostatic force again:
F = 
F= 7.37×
N
The 'net' force acting on the box is (9 - 3) = 6 newtons
in the direction that Carlos is pushing.
Force = (mass) x (acceleration)
6 = (3) x (acceleration)
Divide each side by 3 :
<em>2 m/s² = acceleration</em>
You don't need to worry about the 10 year bit with this question. Just grab a calculator and divide 100/2, then the answer to that (50) by 2 etc and keep dividing by 2 until you get down to 6.25.
The answer ends up being 4 half lives :)
If you don't understand what a half life is please let me know :)