Answer:
Option ‘a’ is the cheapest for this house.
Explanation:
Cheapest method of heating must have least cost per kj of energy. So, convert all the energy in the same unit (say kj) and take select the cheapest method to heat the house.
Given:
Three methods are given to heat a particular house are as follows:
Method (a)
Through Gas, this gives energy of amount $1.33/therm.
Method (b)
Through electric resistance, this gives energy of amount $0.12/KWh.
Method (c)
Through oil, this gives energy of amount $2.30/gallon.
Calculation:
Step1
Change therm to kj in method ‘a’ as follows:

$/kj.
Step2
Change kWh to kj in method ‘b’ as follows:

$/kj.
Step3
Change kWh to kj in method ‘c’ as follows:

$/kj.
Thus, the method ‘a’ has least cost as compare to method b and c.
So, option ‘a’ is the cheapest for this house.
Answer:
The temperature attains equilibrium with the surroundings.
Explanation:
When the light bulb is lighted we know that it's temperature will go on increasing as the filament of the bulb has to constantly dissipates energy during the time in which it is on. Now this energy is dissipated as heat as we know it, this heat energy is absorbed by the material of the bulb which is usually made up of glass, increasing it's temperature. Now we know that any object with temperature above absolute zero has to dissipate energy in form of radiations.
Thus we conclude that the bulb absorbs as well as dissipates it's absorbed thermal energy. we know that this rate is dependent on the temperature of the bulb thus it the temperature of the bulb does not change we can infer that an equilibrium has been reached in the above 2 processes i.e the rate of energy absorption equals the rate of energy dissipation.
Steady state is the condition when the condition does not change with time no matter whatever the surrounding conditions are.
Answer:

Explanation:
From the question we are told that:
Thickness 
Internal Pressure
Shear stress 
Elastic modulus 
Generally the equation for shear stress is mathematically given by

Where
r_i=internal Radius
Therefore


Generally



Generally the equation for outer diameter is mathematically given by


Therefore
Assuming that the thin cylinder is subjected to integral Pressure
Outer Diameter is

Answer:
Follows are the solution to this question:
Explanation:
Calculating the area under the curve:
A = as

Calculating the kinematics equation:


Calculating the value of acceleration:




If a controlled input can transfer (alter) the control system's initial states to some other desired states in a finite amount of time, the control system is said to be controllable.
Using Kalman's test, we can determine whether a control system is controllable. The evolution model for the state variables (time-varying unknowns) and the observation model, which connects the observations to the state variables, make up the state space representation of a dynamical system. The capacity to move a system about in its full configuration space using just specific permitted actions is generally referred to as controllability. The precise definition changes slightly depending on the model type or framework used.
Learn more about control here-
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