Lab 1 - Monte Carlo Methods - Volume of the Library

WMLE=arg min log(1+e wx.) Discussion topic: • Explain why the loss is convex. (Take a look at the second derivative) • What function does the loss approximate as w x becomes large? Explain why the loss is convex. What happens when wax becomes larger. what happens when wTx becomes larger

Q3: Consider evaluation of different temperatures of solar photovoltaic/thermal system (PVT) as shown in Figure 1(a). The following set of differential equations represent energy balance equations to be solve using matrices and eigenvalues using MATLAB (or Octave): dTglass = -0.75Tolass + 0.75TpvtT dt (1) dTpyT = - dt 1.18Tglass – 22TPVT + 23Twax (2) dTwax = 127glass + 18Tpyt – 19 Twax dt (3) Where, Tatass, Tpyr, and Twax, are temperatures illustrated in Figure 1(b). At time t=0 the initial conditions are Tatass = 35 , TpyT = 33, and Twax = 31 °C. Call seppty Ia tree water Tank Glass PVT Expu Nane PCMPVT Callector Tub Tepe Sterg Tak e Ma Nanou Hest Eschanger Container Teket vae Pump for draie (a) (b) Figure 1. (a) Schematic diagram of the nano-PCM and nanofluid PVT system, (b) mathematical model in context of the PVT collector: glass, PV, wax layer and tube coil, respectively [1].

Generalizing the Product Rule The Derivative Product Rule gives the formula dv du dr dx (uv) = u- dx for the derivative of the product uv of two differentiable functions of x. a. What is the analogous formula for the derivative of the prod- uct uvw of three differentiable functions of x? b. What is the formula for the derivative of the product uj uz uz u4 of four differentiable functions of x? c. What is the formula for the derivative of a product uj Uz uz* Un of a finite number n of differentiable functions of x?

For each of the series below you find two answer fields. In the first answer field enter: (inputs are case sensitive) -inf if the series assumes the limit -∞ R if the series converges to a number R+ if the series converges absolutely to a number +inf if the series assumes the limit +∞ DNE if the series has no limit in real number line R In the second answer field select one of the following tests if it can be used to prove your claim in the first answer field: IT AST Geo RootT RatioT LASN LASE LC ∞ n=1 Check Integral Test for Alternating Series Test for comparison with a geometric series with r < 1. Root Test RatioTest The limit of absolute values of summands does not exist. The limit of absolute values of summands exists but is not 0. Limit comparison with the harmonic series Σ(-1)" tan(2/n) Σ(-1)" (1 – 7)" n=1 because because ∞ k=0 ?

What is the significance of the standard deviation value with to the mean?Explain.

Pls help ASAP. Pls show all work and explain thoroughly on what equation is being used and how you come up with the answer. Also, pls underline or square the final answers.

Please use the origin (0,0) as the starting point of the graph and 2pi on the x-axis as the point where th graph ends. Find a function of the form y = Asin(x) or y = Acos(x) whose graph matches the function below. 51 37/2 -2 -3 -4 -5+ Give an exact answer using fractions and/or multiples of pi as necessary. y = OType here to search

Please guide me in determining the dimensions of each of the constant parameters of the functions listed in the screenshot. Please refer to #12 and #14 as the correct answer is listed. Explain how to solve. Thank you.

If we have stabdard deviations for x and y data and we have mean values for x and y, how can we evaluate the standard deviation of (1-x/y).m ? (m is a constant value).

Friction Be able to calculate, for both kinetic and static friction: a. The frictional force, given the mass and coefficient of friction, including experimental uncertainty. b. The coefficient of friction, given the mass and frictional force, including experimental uncertainty. c. The mass or the normal force, given the friction coefficient and the applied frictional force, including experimental uncertainty. Be able to sketch a force diagram for a block either at rest or sliding, with friction. Example 1: A block of wood with a mass of 220 g (assumed exact) is sitting on a surface, where the coefficients of static and kinetic friction between the materials are μ = 0.31±0.01, Mk = 0.22 +0.01. What force is required to get the block moving? Quote your answer including an experimental uncertainty. (0.67N ± 0.02N) Once the block is moving, what horizontal force is required to keep the block sliding at constant speed? Quote your answer including an experimental uncertainty. (0.47N ± 0.02N)…

Write down Newton's 2nd Law for the forces acting on the cylinder. Solve your equation (algebraically) for the buoyant force. The force probe measures the tension in the string. The force probe measures 0.605 N for the Al cylinder and 1.166 N for the Pb cylinder. Use your algebraic expression to calculate the buoyant force. The uncertainty on the measured force is ?B = g?m + ?T, where g is 9.8 m/s2, ?m is the mass uncertainty (as given in the table above), and ?T = 0.001 N is the tension uncertainty from the force probe.FB on Al cylinder:  ____±_____  FB on Pb cylinder:  _____±____

Need a good explanation and step by step solution for this problem, not just copied out of the solutions manual.

P-4 Please help me with the below problem needed clearly with step by step explanation please. Hint: choose variables, and think about which are fixed, and which aren’t.

PLEASE CHECK THE ATTACHED ANSWER TO THE PROBLEM. Please make sure you're qualified to answer this question. THE DENOMINATOR SHOULD NOT BE CUBED THAT IS INCORRECT!! Whomever is doing that in their answer is wrong. PLease make sure you double check your work and answer my question. Is the attached answer CORRECT. IF IT IS NOT CORRECT. PLEASE MAKE SURE TO CALL OUT THE MISTAKE.  PLEASE DO NOT SKIP ANY STEPS. PLEASE ANSWER THIS QUESTION COMPLETELY. PLEASE MAKE NOTES WHERE APPROPRIATE. PLASE DOUBLE CHECK YOUR WORK. DO NOT CUBE THE DENOMINATOR THAT IS INCORRECT.

Part B: Error propagation Consider that you measured an angle 0 to be 40 degrees. The uncertainty of your measurement is + 1 degree. Using the rules for error propagations, determine the uncertainty of sin(0). Clearly show your work. Hint: The uncertainty of any function of a single variable, z = f(x), is the derivative of the function calculated at that point multiplied by the uncertainty of the variable. A(z) df Ax dx

Using any goodness of fit method, how would you determine which function is the best fit for the data? How would you use a spreadsheet to calculate the goodness of fit with using one of the inbuilt functions while providing a new column for each step?

Physics Solve the problem ALGEBRAICALLY. Read the problem carefully. Using pencil on paper, derive the solution(s) ALGEBRAICALLY from first principles. Show all mathematical steps. USE VARIABLES, NO NUMBERS, USE VARIABLES. For example, use: m, t, v, a, L, W, H, AW, and Ao for mass, time, velocity, acceleration, dimensions, atomic wt, density, Avogadro's, respectively. 0 0 0 0 0 0 pre 0 nn 0.2 S 0.4 time (s) 0.6 0.8 10P A small mass moves along a straight line such that its position as a function of time is: s=At^b -Ct^d where A = 5, b=4, C=7, d = 5 and where s is in meters and t is in seconds. Determine the acceleration in m/s/s at the instant the velocity is zero. Refer PPT Slide 2-8 Express algebraic solution in terms of A, b, c, d and t. A 5 b 4 с 7 d 5 acc PALA

Use the 6-Step problem technique. define, data, theory, estimate, solve, verify. Define all of these

Hi. Can you find part e of the question in terms of k, m, F, and delta t

A water droplet evaporates before they reach the ground. ond ord Figure 1: Water droplets [source] In this situation, a few assumptions are made: a) At initial point, a typical water droplet is in sphere shape with radius r and remain spherical while evaporating. b) The rate of evaporation (when it loses mass (m)) is proportional to the surface area, S. There is no air-resistance and downward direction is the positive direction. quat To describe this problem, given that p is the mass density of water, rois the radius of water before it drops, m is the water mass, V is the water volume andk is the constant of proportionality. QUESTION: (1) From assumption (b), show that the radius of the water droplet at time t is or r(t) = (=)t+ro- %3D (Hint: m = pV,V =tr³, S = 4nr²). 4 TTr 3

Please answer the following question. Please specify the correct equations that you use in your answer. Please put a box and LABEL each equation that you plan to use for each element of the problem. Please label every variable with an explanation. Please make sure to label and give a full explanation to every variable in the problem. Please make sure to double check your work. Please confirm the answer is correct before submitting your response. Please do not skip any steps.

Direction: Analyze the diagram below. Solve for the unknown value.  note: please explain your answer thoroughly and do not forget to include the solution. thank you!

Use the first equation attached below. To calculate the initial ball velocity vi with error found by propagating uncertainty in θ.  For error propgating use the following the equation to calculate the uncertainty in cos (θ), necessary for calculation using the derived expression. Note that the uncertainty comes from the 2/3 method.                                        δcos (θ) = | cos (θ + δθ) -2cos (θ - δθ) | Mass of ball 66.0 g 0.1 g Mass of pendulum 245.0 g 0.1 g         Theoretical velocity 4.19 +/- 0.02 m/s         Trial Final angle   1 28.00 degrees   2 28.00 degrees   3 28.10 degrees   4 28.00 degrees   5 28.10 degrees   6 27.90 degrees

TX Find the Normalize constant for function p(x) = Asin? L Answer Key. 8 A = 3L

Please fill out the template with the work for this problem. Note that you need to have a picture, list of knowns and unknowns, the general equation/s you will use, the math steps to solve for the unknown, only plug in the numbers after you have solved for the unknown, and the answer with units included.

Suppose that the length of an object is measured multiple times.  Assuming that random errors are the only source of error,  a. Does increasing the number of measurements change the standard deviation for the set?  Explain

Determine the absolute uncertainty for the calculated value in the following scenarios. Express as (computed result) ± (absolute uncertainty) (units).   You measure the volume of a stainless steel sphere by placing it into a100 mL graduated cylinder with an uncertainty of 1 mL, with 20 mL ofwater initially. After the sphere settles, the graduated cylinder now reads22 mL. What is the volume with uncertainty?   Please use the formula I posted ! Thank you!

can you please solve number 6 showing step by step on a picture. Show all your work and explain step by step on a PICTURE PLEASE.

Hello, I really need help with part A,Part B, and Part C because I don't know how to do this problem, is there any chance that you can help me with those problems and can you label them as well, thank you so much

Just before 1=1 k x=0 x=x; k v m x=0 x=x; |5|=0 m

Question 2 Pauli matrices are important in physics. They are: (: :). - 1 0 -i Ox = 1 0 Oy = i 0z = Now consider a vector where 0 is a number and în is a unit vector. Now consider the following matrix: P = ng0x + nyơy + nz0z. Prove that: I2 for k even, P for k odd. 1 Now consider the following matrix exponential: (i0P)™ m! m=0 Show that = I, cos 0 + iP sin 0 . Hint: You may find these two formulas useful: (-1)° 0²p Σ (2p)! (-1)º 0²p+1 sin 0 = Σ cos 0 = (2р + 1)! p=0 p=0