Outline an algorithm in **pseudo code** for checking whether an array H[1..n] is a heap and determine its time efficiency.
1 answer:
Answer:
Condition to break:
Efficiency: O(n).
Explanation:
Previous concepts
Heap algorithm is used to create all the possible permutations with K possible objects. Was created by B. R Heap in 1963.
Parental dominance condition represent a condition that is satisfied when the parent element is greater than his children.
Solution to the problem
We assume that we have an array H of size n for the algorithm.
It's important on this case analyze the parental dominance condition in order to the algorithm can work and construc a heap.
For this case we can set a counter j =1,2,... [n/2] (We just check until n/2 since in order to create a heap we need to satisfy minimum n/2 possible comparisions
And we just need to check on the array the last condition and if is not satisfied for any value of the counter j we need to stop the algorithm and the array would not a heap. Otherwise if we satisfy the condition for each then we will have a heap.
On this case this algorithm needs to compare 2*(n/2) times the values and the efficiency is given by O(n).
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Answer:
a) Mechanical efficiency ()=63.15% b) Temperature rise= 0.028ºC
Explanation:
For the item a) you have to define the mechanical power introduced (Wmec) to the system and the power transferred to the water (Pw).
The power input (electric motor) is equal to the motor power multiplied by the efficiency. Thus, .
Then, the power transferred (Pw) to the fluid is equal to the flow rate (Q) multiplied by the pressure jump . So
.
The efficiency is defined as the ratio between the output energy and the input energy. Then, the mechanical efficiency is
For the b) item you have to consider that the inefficiency goes to the fluid as heat. So it is necessary to use the equation of the heat capacity but in a "flux" way. Calling <em>H</em> to the heat transfered to the fluid, the specif heat of the water and the density of the water:
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Finally, the temperature rise is:
Answer:
a.) -147V
b.) -120V
c.) 51V
Explanation:
a.) Equation for potential difference is the integral of the electrical field from a to b for the voltage V_ba = V(b)-V(a).
b.) The problem becomes easier to solve if you draw out the circuit. Since potential at Q is 0, then Q is at ground. So voltage across V_MQ is the same as potential at V_M.
c.) Same process as part b. Draw out the circuit and you'll see that the potential a point V_N is the same as the voltage across V_NP added with the 2V from the other box.
Honestly, these things take practice to get used to. It's really hard to explain this.
Answer:
Magnitude of force P = 25715.1517 N
Explanation:
Given - The wires each have a diameter of 12 mm, length of 0.6 m, and are made from 304 stainless steel.
To find - Determine the magnitude of force P so that the rigid beam tilts 0.015∘.
Proof -
Given that,
Diameter = 12 mm = 0.012 m
Length = 0.6 m
= 0.015°
Youngs modulus of elasticity of 34 stainless steel is 193 GPa
Now,
By applying the conditions of equilibrium, we have
∑fₓ = 0, ∑ = 0, ∑M = 0
If ∑ = 0
⇒×0.9 - P × 0.6 = 0
⇒×3 - P × 2 = 0
⇒ =
If ∑ = 0
⇒×0.9 = P × 0.3
⇒ ×3 = P
⇒ =
Now,
Area, A = = 1.3097 × 10⁻⁴ m²
We know that,
Change in Length , =
Now,
= 9.1626 × 10⁻⁹ P
= 1.83253 × 10⁻⁸ P
Given that,
= 0.015°
⇒ = 2.618 × 10⁻⁴ rad
So,
⇒2.618 × 10⁻⁴ = ( 1.83253 × 10⁻⁸ P - 9.1626 × 10⁻⁹ P) / 0.9
⇒P = 25715.1517 N
∴ we get
Magnitude of force P = 25715.1517 N