9. If Ā=B+C and the magnitudes of A, B and T are 5,4 and 3 units respectively, the angle Between
Aand B is
Answers
Answer:
the angle between A and B is approximately 82.5 degrees.
Explanation:
Carnot engine efficiency calculation
Manan Jinjuwadia
The temperature of the source and sink of a carnot engine is respectively 227°C and 77°C The efficiency of the machine is a) 40% b) 35% c) 30 % d) 32% Give answer with explanation
The efficiency of a Carnot engine is given by the formula:
efficiency = 1 - (Tc/Th)
where Tc is the temperature of the cold reservoir (sink) and Th is the temperature of the hot reservoir (source).
Given: Tc = 77°C and Th = 227°C
Plugging in the values, we get:
efficiency = 1 - (77/227) = 0.6611
The efficiency of the Carnot engine is 66.11%, which is not one of the given answer choices.
To select the closest answer choice, we can round the efficiency to the nearest percentage.
Rounding to the nearest percentage, we get:
efficiency = 66%
Therefore, the closest answer choice to the efficiency of the Carnot engine is (c) 30%. However, it is important to note that the actual efficiency is closer to 66% than 30%.
Manan Jinjuwadia
If Ā=B+C and the magnitudes of A, B and T are 5,4 and 3 units respectively, the angle Between
Aand B is give answer with explanation
We can use the cosine law to find the angle between A and B. The cosine law states that in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of the lengths of those sides and the cosine of the included angle.
In this case, A, B, and C form a triangle. Let's denote the angle between A and B as θ. Then we can write the cosine law as:
|A|^2 = |B|^2 + |C|^2 - 2|B||C|cos(θ)
Substituting the given values, we get:
5^2 = 4^2 + 3^2 - 2(4)(3)cos(θ)
Simplifying, we get:
25 = 16 + 9 - 24cos(θ)
Combining like terms, we get:
cos(θ) = 1/8
To find θ, we can take the inverse cosine of both sides:
θ = cos^(-1)(1/8)
Using a calculator, we get:
θ ≈ 82.5 degrees
Therefore, the angle between A and B is approximately 82.5 degrees.