Answer:
Explanation:
According to the free-body diagram of the system, we have:
So, we can solve for T from (1):
Replacing (3) in (2):
The electric force (
) is given by the Coulomb's law. Recall that the charge q is the same in both spheres:
According to pythagoras theorem, the distance of separation (r) of the spheres are given by:
Finally, we replace (5) in (4) and solving for q:
Answer:
a) (0, -33, 12)
b) area of the triangle : 17.55 units of area
Explanation:
<h2>
a) </h2>
We know that the cross product of linearly independent vectors 
and 
gives us a nonzero, orthogonal to both, vector. So, if we can find two linearly independent vectors on the plane through the points P, Q, and R, we can use the cross product to obtain the answer to point a.
Luckily for us, we know that vectors 
and 
are living in the plane through the points P, Q, and R, and are linearly independent.
We know that they are linearly independent, cause to have one, and only one, plane through points P Q and R, this points must be linearly independent (as the dimension of a plane subspace is 3).
If they weren't linearly independent, we will obtain vector zero as the result of the cross product.
So, for our problem:
<h2>B)</h2>
We know that and are two sides of the triangle, and we also know that we can use the magnitude of the cross product to find the area of the triangle:
so:
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For many solids dissolved in liquid water, the solubility increases with temperature. The increase in kinetic energy that comes with higher temperatures allows the solvent molecules to more effectively break apart the solute molecules that are held together by intermolecular attractions.
Answer:
C. Decreasing the distance between the objects.
Explanation:
Gravitational force depends on mass and distance. The farther the objects are apart, the less gravitational force/pull they have.
