3,1. Suppose that the price of an asset at close of trading yesterday was $350 and its volatility was estimated as 1.4Voper day. The price at the close of trading today is $347. Update the volatility estimate using
(a) The EWMA model with A = 0.95,
(b) The GARCFI(1,1) model with tir = 0.000003, o= 0.05, and B = Q.<15. (5)
3.2 The number of visitors to websites follows the power law in equation (10.1) with q = 2.
Suppose that 1 .5% of sites get 550 or more visitors per day. What percentage of sites get
(a) 1,500 more visitors per day
(b) 2,500 or more visitors per day

For example, a definite integral of a velocity function gives the accumulated distance over the period. You should also be growing more comfortable with how the units work – for example, integrating meters per second with respect to seconds gives meters.Your job is to find an article that refers to a definite integral. It is possible that you will be able to find an explicit mention of a definite integral. Much more likely, though, the definite integral will be implied – the article will actually be about accumulated change. You may look on the Internet, or in any newspaper, magazine, or trade journal. Your example must come from a setting outside of calculus. In particular, you may not use any example from our textbook, any other math textbook, or any other discussion of calculus you find online.

1. A copy of the article with complete source information. Highlight or write the part of the article that mentions the definite integral. 2. Write a few sentences telling what the integrand (the function inside the integral) represents, what the limits of integration are, and what the definite integral represents.3. Assign some letters to the variables here. Using the letters/variables you have chosen, write the definite integral that you have found. Show that the units work properly in your example. (I do not expect you to compute anything here.)

"Brief Discuss Homogeneous Differential Equations."
This is the presentation topic of my Subject Differential Equation

What are some valuable life skills that learning math sharpens or improves?

a. Prove that for any vector space, if an inverse exists, then it must be unique.

b. Prove that the additive inverse of the additive inverse will be the original vector.

c. Prove that the only way for the magnitude of a vector to be zero is if in fact the vector is the zero vector.

In each case below either show that the statement is True or give an example showing that it is False.

(V) If {x1, x2, . . . xk, xk+1, . . . xn} is a basis of R n and U = span{x1, . . . xk} and V = span{xk+1 . . . xn}, then U ∩ V = {0}.

1. Solve the following word problem. You should get infinite solutions. So find the pattern for them and give a range of t values that is possible based on the word problem. A trucking company plans on buying 4 kinds of trucks: a pick-up, a small flatbed, a large flatbed, and a dump truck. The pick-up needs one worker to operate, 4 hours of maintenance and 3 hours of cleaning. The small flatbed needs one worker to operate, 1 hour of maintenance and 1 hour of cleaning. The large flatbed needs one worker to operate, 3 hours of maintenance and 2 hours of cleaning. The dump truck needs 2 workers to operate, 3 hours of maintenance and 2 hours of cleaning. If the company has exactly 46 workers, exactly 140 hours for maintenance and exactly 112 hours for cleaning. How many of each kind of truck should they purchase?

Apply the Laplace Transform to solve the initial value problems

1. y' + 2y = 2cos(3t) , y(0) = 1

2. y'' - 3y' + 2y = 2 - 10e^-3t , y(0) = -1 , y'(0)= 1

• What is Clustering?
• What is the purpose of clustering?
• What assumptions are needed for clustering?
• Why do you need to transform qualitative variables to be presented by numbers in clustering?
• What is the purpose of normalizing quantitative variables?

Question H:

Let’s keep using the AM-radio style signal from Question G: f(x) = sin(12x) * sin(x) on [0,2*pi].

It’s okay to use Wolfram Alpha or Desmos to do the following integrals.

i)

ii) What do you get if you graph 0.5*cos(11x)+-0.5*cos(13x) ?

. During droughts, water for irrigation is pumped from the ground. When ground water is pumped excessively, the water table lowers. In California, lowering water tables have been linked to reduced water quality and sinkholes. A particular well in California’s Inland Empire has been monitored over many years. In 1994, the water level was 250 feet below the land surface. In 2000, the water level was 261 feet below the surface. In 2006, the water level was 268 feet below the surface. In 2009, the water level was 271 feet below the surface. In 2012, it was 274 feet below the surface. And in 2015, it was 276 feet below the surface. (a) Find a cubic (degree 3) polynomial model for this data on water level. First, define what x and y mean here, and write the data points you use. Then, find a cubic which is a best fit for this data, in the least squares sense. (b) Use your model to predict the water level of the well, in feet below the surface, in 2020. You may assume that the trends of 1994 to 2015 continue to 2020.