Answer:
Explanation:
<u>Displacement
</u>
It's a vector magnitude that measures the space traveled by a particle between an initial and a final position. The total displacement can be obtained by adding the vectors of each individual displacement. In the case of two displacements:
Given a vector as its polar coordinates (r,\theta), the corresponding rectangular coordinates are computed with
And the vector is expressed as
The monkey first makes a displacement given by (0.198 km,0°). The angle is 0 because it goes to the East, the zero-reference for angles. Thus the first displacement is
The second move is (145 m , -15.8°). The angle is negative because it points South of East. The second displacement is
The total displacement is
In (magnitude,angle) form:
Einstein's...<span> theory of general relativity predicted that the </span>space-<span>time....</span>
Answer:
h'=0.25m/s
Explanation:
In order to solve this problem, we need to start by drawing a diagram of the given situation. (See attached image).
So, the problem talks about an inverted circular cone with a given height and radius. The problem also tells us that water is being pumped into the tank at a rate of 
. As you may see, the problem is talking about a rate of volume over time. So we need to relate the volume, with the height of the cone with its radius. This relation is found on the volume of a cone formula:
notie the volume formula has two unknowns or variables, so we need to relate the radius with the height with an equation we can use to rewrite our volume formula in terms of either the radius or the height. Since in this case the problem wants us to find the rate of change over time of the height of the gasoline tank, we will need to rewrite our formula in terms of the height h.
If we take a look at a cross section of the cone, we can see that we can use similar triangles to find the equation we are looking for. When using similar triangles we get:
When solving for r, we get:
so we can substitute this into our volume of a cone formula:
which simplifies to:
So now we can proceed and find the partial derivative over time of each of the sides of the equation, so we get:
Which simplifies to:
So now I can solve the equation for dh/dt (the rate of height over time, the velocity at which height is increasing)
So we get:
Now we can substitute the provided values into our equation. So we get:
so:
Answer:
A -TRUE
Explanation:
The mass, size, and shape of the object are not a factor in describing the motion of the object. So all objects, regardless of size or shape or weight, free fall with the same acceleration.
