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2 months ago

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Define a function pyramid_volume with parameters base_length, base_width, and pyramid_height, that returns the volume of a pyram

id with a rectangular base. Sample output with inputs: 4.5 2.1 3.0 Volume for 4.5, 2.1, 3.0 is: 9.45 Relevant geometry equations: Volume

1 answer:

pantera1 [306]2 months ago

5 0

Hi, since you haven't mentioned the programming language needed for your code, I will illustrate how to accomplish it using Python, and you can then adapt the approach to any language you prefer.

Answer:

1. def pyramid_volume(base_length, base_width, pyramid_height):

2. volume = base_length * base_width * pyramid_height / 3

3. return volume

Step-by-step explanation:

The function pyramid_volume is defined in the first line with its parameters.
The subsequent line calculates the volume of a rectangular-based pyramid using the equation V = l * w * h / 3.
Finally, the calculated volume is returned.

The output displayed below demonstrates the function's result with inputs 4.5, 2.1, and 3.0.

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The top 3 most popular male names of 2017 are Oliver, Declan, and Henry according to babynames. Write a program that modifies th

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Answer:

The Python code is provided below with suitable comments

Explanation:

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# remove specified name from set

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2 months ago

A 50 Hz, four pole turbo-generator rated 100 MVA, 11 kV has an inertia constant of 8.0 MJ/MVA. (a) Find the stored energy in the

Mrrafil [318]

Given Information:

Frequency = f = 60 Hz

Complex rated power = G = 100 MVA

Inertia constant = H = 8 MJ/MVA

Mechanical power = Pmech = 80 MW

Electrical power = Pelec = 50 MW

Number of poles = P = 4

No. of cycles = 10

Required Information:

(a) stored energy =?

(b) rotor acceleration =?

(c) change in torque angle =?

(c) rotor speed =?

Answer:

(a) stored energy = 800 Mj

(b) rotor acceleration = 337.46 elec deg/s²

(c) change in torque angle (in elec deg) = 6.75 elec deg

(c) change in torque angle (in rmp/s) = 28.12 rpm/s

(c) rotor speed = 1505.62 rpm

Explanation:

(a) Calculate the rotor's stored energy at synchronous speed.

The stored energy is represented as

$E = G \times H$

Where G stands for complex rated power and H signifies the inertia constant of the turbo-generator.

$E = 100 \times 8 \\\\E = 800 \: MJ$

(b) If we suddenly increase the mechanical input to 80 MW against an electrical load of 50 MW, we shall find the rotor's acceleration while ignoring mechanical and electrical losses.

The formula for rotor acceleration is given by

$P_a = P_{mech} - P_{elec} = M \frac{d^2 \delta}{dt^2}$

Where M is defined as

$M = \frac{E}{180 \times f}$

$M = \frac{800}{180 \times 50}$

$M = 0.0889 \: MJ \cdot s/ elec \: \: deg$

$P_a = 80 - 50 = 0.0889 \frac{d^2 \delta}{dt^2}$

$30 = 0.0889 \frac{d^2 \delta}{dt^2}$

$\frac{d^2 \delta}{dt^2} = \frac{30}{0.0889}$

$\frac{d^2 \delta}{dt^2} = 337.46 \:\: elec \: deg/s^2$

(c) If the acceleration derived in part (b) persists over 10 cycles, we will calculate both the change in torque angle and the rotor speed in revolutions per minute at the end of this duration.

The change in torque angle is expressed as

$\Delta \delta = \frac{1}{2} \cdot \frac{d^2 \delta}{dt^2}\cdot (t)^2$

Where t is determined from

$1 \: cycle = 1/f = 1/50 \\\\10 \: cycles = 10/50 = 0.2 \\\\t = 0.2 \: sec$

Consequently,

$\Delta \delta = \frac{1}{2} \cdot 337.46 \cdot (0.2)^2$

$$ \Delta \delta = 6.75 \: elec \: deg$

The change in torque in rpm/s is provided by

$\Delta \delta = \frac{337.46 \cdot 60}{2 \cdot 360\circ }$

$\Delta \delta =28.12 \: \: rpm/s$

The rotor speed in rpm at the culmination of this 10-cycle period is calculated as

$Rotor \: speed = \frac{120 \cdot f}{P} + (\Delta \delta)\cdot t$

Where P indicates the number of poles on the turbo-generator.

$Rotor \: speed = \frac{120 \cdot 50}{4} + (28.12)\cdot 0.2$

$Rotor \: speed = 1500 + 5.62$

$$ Rotor \: speed = 1505.62 \:\: rpm$

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2 months ago

Given a 5x5 matrix for Playfair cipher a. How many possible keys does the Playfair cipher have? Ignore the fact that some keys m

alex41 [359]

Answer:

a. 25! = $2^{84}$ (Approximately)

b. 24!

Explanation:

a. In a Playfair cipher, there are 25 keys available because it is structured in a 5 * 4 grid. By using permutations to enumerate all potential configurations, we derive: 25! = 1.551121004×10²⁵ = $2^{84}$

Although there are 26 letters available, in the Playfair cipher, the letters 'i' and 'j' are treated as a single letter.

b. Considering any configuration of 5x5, each of the four row shifts yields equivalent configurations, amounting to five total equivalencies. Similarly, for each of these five setups, any of the four column shifts also results in equivalent arrangements. Therefore, each configuration corresponds to 25 equivalent arrangements. Consequently, the total count of distinct keys can be expressed as:

25!/25 = 24! = 6.204484017×10²³

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23 days ago

The critical resolved shear stress for iron is 27 MPa (4000 psi). Determine the maximum possible yield strength for a single cry

grin007 [323]

Answer:

The following represents the answer.

Explanation:

Calculation for the maximum yield strength of a single crystal of Fe subjected to tension can be found in the attached image.

The maximum yield strength value is 54 MPa.

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2 months ago

The manufacturer of a 1.5 V D flashlight battery says that the battery will deliver 9 mA for 40 continuous hours. During that ti

pantera1 [306]

Response:

a) 144.000 seconds

b) and c) Battery voltage and power graphs are in the attached image.

$V=-\frac{0.5}{144000} t + 1.5 V[tex] [tex]P(t)=-(31.25X10^{-9}) t+0.0135$ where D:{0<t h="" />

d) 1620 J

Description:

a) The initial response is derived via a rule of three

$s=\frac{3600s * 40h}{1h} = 144000s$

b) Using the line equation from the starting point (0 seconds, 1.5 V)

$m=\frac{1-1.5}{144000-0} = \frac{-0.5}{144000}$

where m denotes the slope.

$V-V_{1}=m(x-x_{1})$

where V represents voltage in volts and t signifies time in seconds

$V=m(t-t_{1}) + V_{1}$ along with P and m.

$V=-\frac{0.5}{144000} t + 1.5 V[tex] c) Using the equation VPOWER IS DEFINED AS:[tex] P(t) = v(t) * i(t) [tex]so.[tex] P(t) = 9mA * (-\frac{0.5}{144000} t + 1.5) [tex][tex]P(t) = - (31.25X10^{-9}) t + 0.0135$

d) By evaluating that count.

$E = \int\limits^{144000}_{0} {P(t)} \, dt = \int\limits^{144000}_{0} {v(t)*i(t)} \, dt$

$E = \int\limits^{144000}_{0} {-\frac{0.5}{144000} t + 1.5*0.009} \, dt = 1620 J$

4 0

1 month ago