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1. ### MHB Natural and forced response of a differential equation

Greetings everyone, I am a bit new to differential equations and I am trying to solve for the natural and forced response of this equation: dx/dt+4x=2sin(3t) ; x(0)=0 Now I know that for the natural response I set the right side of the equation equal to 0, so I get dx/dt+4x=0, thus the...
2. ### Mass moment of inertia of a composite shape

I understand now, since I only know the mass moment of inertia about the base of the quartercircle, I first have to use this to find its mass moment of inertia about its centroid. Then I use this mass moment about the centroid to find the mass moment of inertia about the x-axis. I have to apply...
3. ### Mass moment of inertia of a composite shape

My thought process was to get the mass moment of inertia of the rectangle and then subtract the mass moment of inertia of the quartercircle from it. The MMoI of the rectangle is: (1/3)(0.005*7850*.6*.3)(.3^2)= 0.212 meters The MMoI of the quartercircle is: (1/4)(0.005*7850*¼π 0.3^2)(.3^2) + ? My...
4. ### MHB Maximum a posteriori

Here's the problem: Suppose that Carl wants to estimate the proportion of books that he likes, denoted by 𝜃. He modeled 𝜃 as a probability distribution given in the following table. In the year 2019, he likes 17 books out of a total of 20 books that he read. Using this information, determine...
5. ### MHB Merged Bernoulli process

for c and d, I'm visualizing it to be two sets of 10 spaces each. One has 5 items within it, and the other has 7. _ _ _ _ _ x x x x x x x x x x x x _ _ _ and x x x x x _ _ _ _ _ x x x x x x x _ _ _ It counts as a logic 1 or success if both corresponding spaces are filled. The minimum would...
6. ### MHB Merged Bernoulli process

Consider two Bernoulli processes X1 and X2 such that X1[k] is a Bernoulli random variable with P=0.5 and X2[k] is a Bernoulli random variable with P=0.7 for all k>=0 Let Y be a random process formed by merging X1 and X2, i.e. Y[k] =1 if and only if X1[k] = X2[k] = 1 and Y[k] = 0 otherwise. a.)...
7. ### MHB Solving 2 Problems with Exponential RVs: CLT & Probability

I have the following two problems that I need to solve: 1. Suppose that the service time for a student enlisting during enrollment is modeled as an exponential RV with a mean time of 1 minute. If the school expects 500 students during enrollment period, what is the probability that the...
8. ### Engineering Voltage drop across a diode

They are not ideal diodes, and saturation current was given, which I assumed was for calculating using the diode equation.
9. ### Engineering Voltage drop across a diode

So then my final answer would be V(D1) = 18mV, V(D2) = 4.974V and I = 0.998 nA. Would these be reasonable values for my final answer?
10. ### Engineering Voltage drop across a diode

My understanding of those data sheets is that voltage and current are dependent on each other. However, why was I taught in class to treat the voltage drop of a diode as a constant 0.7V (for silicon)?
11. ### Engineering Voltage drop across a diode

With this diode voltage, the current would then be 9.98 *10^-10 A However, does this mean that the voltage drop for the diodes is 18mV? I'm not sure I understand since in class, we use the constant voltage drop model of the diode where there is a drop of 0.7 volts for a diode in forward bias...
12. ### Engineering Voltage drop across a diode

I'm actually getting a relatively high number when I plug in the numbers. I = 10^-9 (e^(.7/.026)-1). The constants I used were I_s = 1 nA and kT = 0.026 V which were given by my professor. I'm getting around 493 A, which seems wrong.
13. ### Engineering Voltage drop across a diode

My understanding is that it should be a simple exercise to prove that we comprehend the idea of diodes. The final question posed in this two-part exercise was to actually find the current in the circuit if the diodes break down at 4.5V. Given that I had to find voltage in the first part, and all...
14. ### Engineering Voltage drop across a diode

In this case, I think I would get current using the Shockley diode equation I = I_s(e^(V_d/V_t)-1). I would then plug in the voltages 0.7 and 4.3 for the diode voltage. Although if I do this, each diode would have different currents, and I'm not sure if this is possible as I'm used to loops...
15. ### Engineering Voltage drop across a diode

In that case, the voltage across D1 is 0.7 and the voltage across D2 would then be 4.3 V?
16. ### Engineering Voltage drop across a diode

So I have this circuit up above and I need to find the voltages across each of the diodes. The only info given is that they are identical silicon diodes at T = 300K. My first thought was that since the diodes are opposite, D2 would be in reverse bias and would act as an open. However, I realized...
17. ### MHB Joint CDF of a word problem

So I have this word problem as seen below: Joy and Ethan have agreed to meet for dinner between 8:00 PM and 9:00 PM. Suppose that Ethan may arrive at any time between the set meeting. Joy on the other hand will arrive at the set meeting under the following conditions: • Joy will always arrive...
18. ### MHB Find the probability all 5 dice rolls are the same

For #2, I got 150 from the ff: number of choices for the number showing on the dice = 6 number of ways of choosing which 4 dice the four of a kind will appear on = 5C4 = 5!/(1!4!) = 5 number of choices for the last number on the last dice = 6-1 = 5 number of ways to choose the last dice = 1C1 =...
19. ### How would I draw this non-inverting amplifier?

Summary: So far, I have only dealt with ideal operational amplifiers, so I am kind of lost trying to visualize how a practical op amp should look like. A non-inverting amplifier with a gain of 10 uses 100K as its feedback resistor. It gets its input from a signal source whose source resistance...
20. ### MHB Find the probability all 5 dice rolls are the same

Given 5 dice rolls that are independent from each other, what is the probability for the following results? (order of roll does not matter) 1. all 5 dice rolls are the same 2. 4 dice rolls are the same 3. the dice rolls are in sequence (1-5 or 2-6) -order does not matter 4. two pairs of dice...
21. ### MHB Cdf, expectation, and variance of a random continuous variable

Given the probability density function f(x) = b[1-(4x/10-6/10)^2] for 1.5 < x <4. and f(x) = 0 elsewhere. 1. What is the value of b such that f(x) becomes a valid density function 2. What is the cumulative distribution function F(x) of f(x) 3. What is the Expectation of X, E[X] 4. What is...