Answer:
Therefore the required solution is
Explanation:
Given vibrating system is
Consider U(t) = A cosωt + B sinωt
Differentiating with respect to t
U'(t)= - A ω sinωt +B ω cos ωt
Again differentiating with respect to t
U''(t) = - A ω² cosωt -B ω² sin ωt
Putting this in given equation
Equating the coefficient of sinωt and cos ωt
.........(1)
and
........(2)
Solving equation (1) and (2) by cross multiplication method
and 
Therefore the required solution is
The area of the top and bottom:
2πr²
Cost for top and bottom:
2πr² x 0.02
= 0.04πr²
Area for side:
2πrh
Cost for side:
2πrh x 0.01
= 0.02πrh
Total cost:
C = 0.04πr² + 0.02πrh
We know that the volume of the can is:
V = πr²h
h = 500/πr²
Substituting this into the cost equation to get a cost function of radius:
C(r) = 0.04πr² + 0.02πr(500/πr²)
C(r) = 0.04πr² + 10/r
Now, we differentiate with respect to r and equate to 0 to obtain the minimum value:
0 = 0.08πr - 10/r²
10/r² = 0.08πr
r³ = 125/π
r = 3.41 cm
Answer: The property that will best provide evidence that the samples are solid includes:
--> if the substance has a definite shape,
-->if the substance has a definite volume
--> if it's tightly packed.
Explanation:
According to the kinetic theory of matter, every substance consist of very large number of very small particles called molecules. These molecules, which are made up of atoms that are the smallest particles of a substance that can exist in a free state.
Matter can exist in the following states:
--> Solid state
--> liquid state or
--> Gaseous state.
The general property of a substance that is in gaseous state includes:
--> Definite shape: A substance can be grouped as a solid if it's shape is fixed that is, it doesn't depend on the shape of other materials.
--> Definite volume: A substance can be grouped as a solid if it occupies its own shape. This is due to the force of cohesion among its molecules.
--> Tightly packed: A substance can be grouped as solid if the molecular movements of the particles are negligible.
From the samples under observation by Juan and kym, if the sample that possesses the above described qualities, it is a solid rather than liquid or gas.
I’ve answered this before so I know the question is missing an
important given and that given is: <span>1 has an
empty trailer and the other has a fully loaded one.
So, it would be the fully loaded trailer that would take a longer distance to
stop because a lot of weight is being pulled, and when the brakes are started,
the fully loaded trailer is more like pushing against the truck.</span>
Explanation:
According to Dalton's atomic theory, all the atoms are individual, all the atoms of the same element are identical in properties and mass, the compound is formed from two or more kinds of the atoms, all the matter is made up of small atoms and the chemical reaction is a rearrangement of the atoms.
The discoveries which contradicts the components of Dalton's atomic theory from the given discoveries are:
Nuclear reactions can change an atom of one element into an atom of another element.
Atoms of a given element can have different numbers of neutrons.
Atoms contain smaller particles: protons, neutrons, and electrons.
