Answer:
The required IVP is;
u'' + 196u = 0
where;
u(0) = 0 and
u'(0) = -10
Explanation:
See the attached for explanation
If the velocity is constant then the acceleration of the object is zero.

Thus when we apply the equation

It remains

or equivalent
Answer:
F = - 1,598 10⁻³ N
Explanation:
Electic strength is given by Coulomb's law
F = k q₁ q₂ / r²
Where k is the Coulomb constant that is worth 8.99 10⁸ N m²/C², q₁ and q₂ are the charges and r is the distance that separates the electric charges
In this case the charge of the two spheres is the same and of a different sign since when you remove the charge of a sphere that was initially neutral, it is left with that charge removed but of the opposite sign
q₁ = q₂ = 2.50 10¹³ electrons = 2.50 10¹³ 1.6 10⁻¹⁹
q₀ = 4.0 10⁻⁶ C
Let's calculate
F = - 8.99 10⁸ (4.0 10⁻⁶)² / 0.30²
F = - 1,598 10⁻³ N
A carbide ion is an anion of carbon atom with two carbon atoms with a triple bond connected to each other. Since this carbide ion is a negatively charged ion, in order to convert carbide ion to its neutral carbon atom, it has to give up/remove four electrons.
Answer:
Rectangular path
Solution:
As per the question:
Length, a = 4 km
Height, h = 2 km
In order to minimize the cost let us denote the side of the square bottom be 'a'
Thus the area of the bottom of the square, A = 
Let the height of the bin be 'h'
Therefore the total area, 
The cost is:
C = 2sh
Volume of the box, V =
(1)
Total cost,
(2)
From eqn (1):

Using the above value in eqn (1):


Differentiating the above eqn w.r.t 'a':

For the required solution equating the above eqn to zero:


a = 4
Also

The path in order to minimize the cost must be a rectangle.