Answer:
The vector equation of the line is

Parametric equations for given line are

Explanation:
The vector equation of the line is given by

r₀ = (7, -8, 3)
v = (1, 6, -13)
At these points the vector equation for this line is:

Parametric equations for given line are

Answer:
The solution(s) are in order with respect to the attachments
Joules ; 5. Adding the same amount of heat to two different objects will produce the same increase in temperature ; 2. Same speed in both ; 2. A
Explanation:
Diagram 1 ( Liquid Nitrogen ) : So as you can see, we want our units in Joules here, and can therefore multiply the mass of gaseous nitrogen and the latent heat of liquid nitrogen, to cancel the units kg, and receive our solution - in terms of Joules. Let's do it.
q ( energy removed ) = mass of nitrogen
latent heat of liquid nitrogen,
q = 1.3 kg
2.01
10⁵ J / kg =
=
=
=
Joules =
kiloJoules = 2.613
10⁵Joules is the energy that must be removed
Diagram 2 : The same amount of heat does not necessarily mean the same increase in temperature for two different objects. The increase in temperature depends on the specific heat capacity of the substance. Therefore your solution is 5 ) Adding the same amount of heat to two different objects will produce the same increase in temperature.
Diagram 3 : The temperatures in both glasses are the same, and hence the molecules have the same average speed. Therefore your solution is 2 ) Same speed in both.
Diagram 4 : Glass A has more water molecules, and hence has more thermal energy. Your solution is 2 ) A.
Answer
D) burning a candle
Explanation
When burning a candle no new substance is form.
We have both physical and chemical change occuring.
Physical part: Melting of the solid wax and evaporation of the liquid forms the physical change.
Chemical part: burning of the wax vapour forms the chemical change.
Answer:
The options are not shown, so let's derive the relationship.
For an object that is at a height H above the ground, and is not moving, the potential energy will be:
U = m*g*H
where m is the mass of the object, and g is the gravitational acceleration.
Now, the kinetic energy of an object can be written as:
K = (1/2)*m*v^2
where v is the velocity.
Now, when we drop the object, the potential energy begins to transform into kinetic energy, and by the conservation of the energy, by the moment that H is equal to zero (So the potential energy is zero) all the initial potential energy must now be converted into kinetic energy.
Uinitial = Kfinal.
m*g*H = (1/2)*m*v^2
v^2 = 2*g*H
v = √(2*g*H)
So we expressed the final velocity (the velocity at which the object impacts the ground) in terms of the height, H.