# Search results

1. ### Transistor circuit problem

To supplement O-Dan's circuit info, the following link is specific to Bipolar Junction Transistors (BJT), and in particular, covers their special switching applications (which is probably what you're looking for). Check the links below. (First link is main article, in which you'll need to...
2. ### RMS Current

SOLUTION HINTS: This problem is designed to distinguish between RMS and Peak values of Voltage, Current, and Power for a purely resistive load. We are given: {RMS Voltage} = (240 V) {RMS Power Rating for Resistive Load} = (1000 W) For standard AC systems, we know that: {RMS Power} = {RMS...
3. ### Solving with index notation

Good observation. "Sunshine" should make that correction for the final result (see Msg #2). ~~
4. ### Solving with index notation

SOLUTION HINTS: You did very well so far!! When indexing a vector result, remember to indicate the LEFT side component with the FREE index ("i" in this case). Thus, your result should have been (note the "i" subscript added on the LEFT side): (Note: To save time, the constant fraction...
5. ### Final exam questions: estimators.

For Problem #1, solve for "c" which makes the estimator unbiased, which (in this case) involves setting the Eq #2 integral equal to (1/θ). See Problem #1 statement for other info. An estimator \hat{\omega} of distribution parameter \omega is Consistent if 2 conditions are satisified: 4...
6. ### Final exam questions: estimators.

SOLUTION HINTS: For both cases, an Unbiased Estimator \hat{\omega} of distribution parameter \omega satisfies: 1: \ \ \ \ \ \ \mathbf{E}(\hat{\omega}) \, \ = \, \ \int \hat{\omega} \, f(y; \, \omega) \, dy \, \ = \, \ \omega \ \ \ \ \ \ \mbox{(Unbiased Estimator)} where f(y; ω) is...
7. ### Fluid Mechanics Help

Now solve the equation for spherical balloon radius "R": {Weight of Helium} + {Weight of Balloon + Load} = {Weight of Displaced Air} ::: <--- Buoyant Force ::: ⇒ {ρhelium*Vballoon*g} + {5905 N} = {ρair*Vballoon*g} ::: ⇒ {ρhelium*(4*π*R3/3)*g} + {5905 N} = {ρair*(4*π*R3/3)*g} ~~
8. ### How do you find to torque if force is applied over entire levl

HINT: Since fluid pressure ⊥ Hatch Surface: 1: \ \ \ \ \textsf{Torque} \ \, = \, \ \int_{Hatch} r \, P \ dA where "r" is the distance of Area Element "dA" from the Reference Point or Axis, and "P" is the fluid pressure on Area Element "dA". Both "r"and "P" will be functions of Area...
9. ### Fluid Mechanics Help

{Volume of Container} = V = (24.8 liter) {Moles of Water in Container} = n = (5.7 grams)/(18 grams/mole) = (0.3167 moles) {Temperature} = T = (115.8 degC) = (388.9 degK) {Ideal Gas Constant} = R = (0.08206 Liter*atm/(mol*degK)) Use the Ideal Gas Law to calculate Pressure "P" in units of...
10. ### Fluid Mechanics Help

When the valve is opened, the situation becomes {P2 = P1}. Recalculate your results using this fact together with the other given values. ~~
11. ### Transformations of Data

The graphs should be different. Unfortunately, without seeing what you've done or the results therefrom, it's difficult to help. Can you provide more details concerning your transformations and provide images of the graphs?? To provide images of your graphs, upload to the site shown below...
12. ### Linear Independent vector

O-Dan: You're certainly correct that there might be some confusion regarding notation in this thread. Nevertheless, the objective of Msg #9 (and subsequently of Msg #11) was to present this concept: 5: \color{red}\ \ \ \ \ \ \left | \begin{array}{ccc} a_{1} & a_{2} & a_{3} \\ b_{1} &...
13. ### How do u solve for n Permutations

SOLUTION HINTS: Factor 720 to help find the solution: 720 = (24)*(32)*(5) = n*(n - 1)*(n - 2) = (???)*(???)*(???) (Hint: Try 23) ~~
14. ### Linear Independent vector

. For Mathman23: *** POP QUIZ *** Given two (2) vectors {V1, V2 ∈ \mathbb{R}^{3}}, state a necessary and sufficient condition that these vectors are Linearly Independent. CLICK BETWEEN DASHED LINES BELOW To Reveal Answer In Pop-Up Window --------------------- \color{white}...
15. ### Linear Independent vector

Three (3) vectors in \displaystyle \mathbb{R}^2 are NEVER Linearly Independent. ~~
16. ### How to find r in the equation P(5,r)=20

SOLUTION HINTS: {# in C Block} = 3 {# in A Block} = 4 {# in M Block} = 2 a) There are (3!) arrangements of the 3 Block Units. For each Block Unit arrangement, there are (3!) sub-arrangements within the "C" Block, (4!) sub-arrangements within the "A" Block, and (2!) sub-arrangements...
17. ### Linear Independent vector

For the homogeneous case, if 1 non-trivial solution exists, then an infinite number exist (and of course the vectors are dependent). It should also be noted that Linear Independence for given vectors {V1, V2, V3 ∈ \mathbb{R}^{3}} is usually stated in terms of: 2: \ \ \ \, \ \ \ \ \ \...
18. ### Diffraction grating problem

The textbook's answer is CORRECT. Remember that the "2nd Order Minimum" occurs at m=(1.5). Using that value will result in the given answer. ~~

. Try the tutorial on Factoring available at the Web Site shown below: Navigate thru its 11 lessons by clicking the "NEXT" button when finished with each page. Have patience, start with the most basic lesson, and proceed carefully thru all the material. (Some pages take longer to load...
20. ### Linear Independent vector

The following summarizes and clarifies info already presented or referenced in this thread. Define three vectors {V1, V2, V3 ∈ \mathbb{R}^{3}} by the following: (Note: This definition differs from OP's.) 1: \ \ \ \ \vec{V}_{1} \ = \ \left [ \begin{array}{ccc} a_{1} \\ b_{1} \\...
21. ### I really need help and no one can seem to help

SOLUTION HINTS: {Density} = ρ ∝ P/(R*T) ::: ⇒ ρ1/ρ2 = T2/T1 {Density @ STP (0 degC)=(273.1 degK)} = ρ(273.1) = (1.29 kg/m^3) {Density @ SP & Temp=(T degK)} = ρ(T) = (1.29 kg/m^3)*(273.1 degK)/T {Bouyant Force} = {Volume Displaced}*(g)*{ρ(273.1) - ρ(T)} = = {Volume Displaced}*(g)*{(1.29...
22. ### I'm having loads of trouble

a) Square both sides. b) Sub {1 - cos2(θ)} for sin2(θ). c) Sub {x = cos(θ)}. d) Solve quadratic. e) Determine all candidate "θ" solutions. f) CHECK EACH candidate "θ" solution with ORIGINAL EQUATION. ~~
23. ### Home Lab Questions

The value of slope "m" corresponds to the value of "k". You are essentially fitting {F = k*x + b}, where "k" is the slope, "x" the displacement, and "b" the intercept ("b" should be close to 0). The value of {"Std Dev of Slope"} given by the regression corresponds to the "uncertainty Δk" in...
24. ### Primes of the form 4n+1

This is an indirect proof by contradiction. We first presume that only a finite number "R" of primes have form (4*nj + 1), where {nj, j=1,2,3,...,R, ∈ Integers}. We define integer "Q" with the following, where the product is over all "R" primes of form (4*nj + 1): 1: \ \ \ \ Q \ = \...
25. ### Home Lab Questions

If you have no regression software available, the Web Site below computes Linear Regression Slope and Intercept with corresponding error values for each. Scroll down page to use, input (x,y) data into individual boxes provided, type "0.95" for "confidence level", and click "calculate"...
26. ### Equation of a plane

Here's an alternate approach similar to those previously given except based on the ∇ operator: Given: Plane W ≡ {x + 3*y - z - 7 = 0} Required: Plane T ⊥ W containing Points P1=(2, 0, 5) and P2=(0, 2, -1) Step #1: Given Plane W ≡ {f(x,y,z) = 0}, then (∇f) ⊥ W and parallel to required...
27. ### IIT question help me

Torque vector \vec{\tau} is only defined when 3 items are specified: 1) Reference Point "P", 2) Application Point "Q", and 3) Force vector \vec{F}. Speaking generally about a "normal force" doesn't provide enough information to properly determine the torque vector. If you completely specify...
28. ### Water Pressure

SOLUTION HINTS: {River Elevation} = HA = (564 m) {Village Elevation} = HB = (2096 m) {Area of Pipe} = A =(π/4){Diameter}2 = (π/4){0.15 m}2 = (0.017671 m^2) {Flow Velocity} = v {Volume Flow Rate} = V = A*v = (4500 m^3/day) = (0.05208 m^3/sec) {Water Density} = ρ = (1 gram/cm^3) = (1000...
29. ### IIT question help me

Because torque "τ" is mathematically determined by TWO points: 1) Point "Q" where Force "F" is applied, and 2) Reference Point "P" about which "τ" is calculated. Force "F" might be normal to the Brick's surface, but it's not normal to the vector "R" pointing from Reference Point "P" to...
30. ### IIT question help me

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