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3 years ago

Seperate real and imaginary parts tan(2x+i3y)

Engineering

1 answer:

ahrayia [7]3 years ago

3 0

Answer:

First you have to separate real and imaginary parts of Tan(x+iy)=Tan(z)=sin(z)/cos(z)

sinz=sin(x+iy)=sinxcos(iy)+cosxsin(iy)=sinxcoshy-icosx sinhy

cosz=cos(x+iy)=cosxcos(iy)-sinxsin(iy)=cosxcoshy−isinxsinhy

Now if you plug in Tan(z) and simplify (it is easy!) you get

Tan(z)=(sin(2x)+isinh(2y))/(cos(2x)+cosh(2y))= A+iB.

This means that

A=sin(2x)/(cos(2x)+cosh(2y)) and B= sinh(2y)/(cos(2x)+cosh(2y))

Now,

A/B=sin(2x)/sinh(2y)

If any questions, let me know.

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determine the position d of the 6- kn load so that the average normal stress in each rod is the same.

Zinaida [17]

The load is placed at distance 0.4 L from the end of $$12 \mathrm{~mm}^{2}$ area.

<h3>What is meant by torque?</h3>

The force that can cause an object to rotate along an axis is measured as torque. Similar to how force accelerates an item in linear kinematics, torque accelerates an object in an angular direction. A vector quantity is torque.

Let the beam is of length L

Now the stress on both the end is the same now we can say that torque on the beam due to two forces must be zero

$N_1 * x=N_2 *(L-x)$

also, we know that stress at both ends are same

$\frac{N_1}{12}=\frac{N_2}{8}$

$2 * N_1=3 * N_2$

Now from two equations we have

$$\frac{3}{2} N_2 * x=N_2 *(L-x)$

solving the above equation we have

$$x=\frac{2}{5} L$

so the load is placed at distance 0.4 L from the end of $$12 \mathrm{~mm}^{2}$ area.

The complete question is:

47. the beam is supported by two rods ab and cd that have cross-sectional areas of $$$12mm^2$ and $$$8mm^2$ , respectively. determine the position d of the 6-kn load so that the average normal stress in each rod is the same.

To learn more about torque refer to:

brainly.com/question/20691242

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2 years ago

Your driver license will be _____ if you race another driver on a public road, commit a felony using a motor vehicle, or are fou

Georgia [21]

Hello there,

In the problems given in the question, the driver's license is confiscated and suspended.

So our answer is: A)

Achievements.

6 0

4 years ago

Read 2 more answers

What do you think of this schematic diagram?

Sholpan [36]

Explanation:

A schematic diagram is a picture that represents the components of a process, device, or other object using abstract, often standardized symbols and lines. ... Schematic diagrams do not include details that are not necessary for comprehending the information that the diagram was intended to convey.

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3 years ago

What are the conditions for sheet generator to build up its voltage?

MA_775_DIABLO [31]

Answer:

There are six conditions

1. Poles should contain some residual flux.

2. Field and armature winding must be correctly connected so that initial mmm adds residual flux.

3. Resistance of field winding must be less than critical resistance.

4. Speed of prime mover of generator must be above critical speed.

5. Generator must be on load.

6. Brushes must have proper contact with commutators.

Explanation:

3 0

3 years ago

Annealing is a process by which steel is reheated and then cooled to make it less brittle. Consider the reheat stage for a 100-m

kodGreya [7K]

Complete question is;

Annealing is a process by which steel is reheated and then cooled to make it less brittle. Consider the reheat stage for a 100 mm thick plate (ρ = 7830 kg/m3, Cp = 550 J/kg K, k = 48 W/m K). The plate initially is at 200 °C and is to be heated to a minimum temperature of 550 °C. Heating is effected in a gas-fired furnace where the products of combustion at T∞ = 800 °C maintain a convection heat transfer coefficient of h = 250 W/m.K on both surfaces of the plate. How long should the plate be left in the furnace?

Answer:

860 seconds

Explanation:

We are given;

Initial Temperature; Ti = 200 °C

Minimum Temperature; T_i = 550 °C

T∞ = 800 °C

convection coefficient; h = 250 W/m².K

ρ = 7830 kg/m³

Cp = 550 J/kg K

k = 48 W/m K

Plate thickness = 100mm

Thus,L = 100/2 = 50mm = 0.05 m

Let's find the biot number from the formula;

Bi = hL/K

Bi = (250 × 0.05)/48

Bi = 0.2604

Now, lowest temperature in the slab is given as;

θ_o = (T_o - T∞)/(T_i - T∞)

θ_o = (550 - 800)/(200 - 800)

θ_o = 0.4167

Now, from online tables calculation, we can find the root of the biot number.

Thus, root of the biot number Bi = 0.2604 is;

ζ1 = 0.488 rad

Also, C1 is gotten as 1.0396

Now,formula for thermal diffusivity is;

α = k/ρc

α = 48/(7830 × 550)

α = 1.115 × 10^(-5) m²/s

Also, from online tables, f(ζ1) = 0.401

Thus, we can find the time the plate should the plate be left in the furnace from;

-(ζ1)²(αt/L²) = In 0.401

-(ζ1)²(αt/L²) = -0.9138

t = (-0.9138 × 0.05²)/-(0.488² × 1.115 × 10^(-5))

t ≈ 860 s

8 0

3 years ago