Answer:
Explanation:
Considering the flow of mercury in a tube:
When it comes to laminar flow of mercury, the thermal entry length is quite smaller than the hydrodynamic entry length.
Also, the hydrodynamic and thermal entry lengths which is given as DLhRe05.0= for the case of laminar flow. It should be noted however, that Pr << 1 for liquid metals, and thus making the thermal entry length is smaller than the hydrodynamic entry length in laminar flow, like I'd stated in the previous paragraph
Answer:
The sentence that uses the word malleable correctly is;
The gold wedding band was malleable as it was shaped into a beautiful ring
Explanation:
Malleability is the property of metal to have their shape changed by means of hammering, pressing or rolling so as to form sheets without them breaking such that the metals assume a new shape by compression
An example of a malleable metal is gold, which can be hammered into a gold leaf
Malleability in metals is due to their ability to have their nuclear shifted while maintaining their bonds due to the ability for electrons to move freely such that they are replaced with ease
Therefore, the sentence that uses the word malleable correctly is the gold wedding band was malleable such that it was able to be shaped into a beautiful ring.
Answer:
- |z*| = r , ∠(z*) = -∅
- |z²| = r² , ∠(z²) = 2∅
- |jz| = r , ∠(jz) = ∅
- |zz*| = r² , ∠(zz*) = 0
- |z/z*| = 1 , ∠(z/z*) = 2∅
- |1/z| = r ⁻¹ , ∠(1/z) = -∅
Explanation:
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1.) The * mean you take the conjugate of the value. This means you change the sign of the imaginary part, so if it's positive, turn it negative and vice versa.
2.) The magnitude with an exponent can have the exponent moved outside the magnitude. |zⁿ| = |z|ⁿ
The angle multiplies with its exponent instead. ∠zⁿ = n∠z
3.) This part is just testing if you can convert the number using the eulers formula and convert back.
The magnitude could be found using the distance formula. √(R² + I²)
The angle could be found using tan⁻¹(Imaginary/Real).
4.) Magnitude of a product could be split up. |zv| = |z|·|v|
Angle of a product could be splitted up and added. ∠(zv) = ∠z + ∠v
5.) Simplify it first using some algebra and use the euler's identity to identify the magnitude and angle. It takes in a form like this:
A is your magnitude, ∅ is your angle.
6.) Same rule as part 2
Answer:
-2/√3 atan ((2t + 1)/√3) + C
Explanation:
∫ (t − 1) / (1 − t³) dt
Factor the difference of cubes:
∫ (t − 1) / ((1 − t)(1 + t + t²)) dt
Divide:
∫ -1 / (1 + t + t²) dt
-∫ 1 / (t² + t + 1) dt
Complete the square:
-∫ 1 / (t² + t + ¼ + ¾) dt
-∫ 4 / (4t² + 4t + 1 + 3) dt
-∫ 4 / ((2t + 1)² + 3) dt
If u = 2t + 1, du = 2 dt:
-∫ 2 / (u² + 3) du
Use an integral table, or use trigonometric substitution:
-2 (1/√3) atan (u/√3) + C
-2/√3 atan (u/√3) + C
Substitute back:
-2/√3 atan ((2t + 1)/√3) + C