1) Find an estimate for the area under the graph of f(x)=x^2 from x=0 to x=8 using four rectangles and:

a) left end points

b) right end points

c) mid points

2) Find the volume of a solid obtained by rotating about the x-axis the region bounded by y=x^3 and y=2x.

Sketch the region, the solid, and a typical disk or washer.

Because I'm trying to learn how to solve this kind of problem in the future please show all intermediate steps so I can follow Suppose F= <xy+y, x-y^2> Let R be the triangular regiorn bounded by the curves y=x, y=4-x, and y=0, Let C be the boundary of this region, oriented counterclock wise.

a) Can you use Fundamental theorem for Line integrals to find ∮ F•dr? explain why or why not? What are the other two possible methods of finding this line integral ?

b) Find the easiest method to calculate ∮ F•dr and then evaluate the line integral using this method

Let S{a, b, c, d} be a set of four positive integers. If pairs of distinct elements of S are added, the following six sums are obtained:5,10, 11,13,14,19. Determine the values of a, b, c, and d. (There are two possibilities. )

solve the following differential question with method of undetermined coefficient and the method of variation of parameters

y''+4y=sin(x)-cos(2x)

????????? ?ℎ? ??? ?? ?ℎ? ?????? ?? ?ℎ??ℎ ???ℎ ????? ???????? ?? ??????????:

1) ?(?, ?) = ?−? 4−? 2− ?2

2) ?(?, ?, ?) = ln |? 2 + ? 2 − 6| ???? (? 2 − ? 2 + ? 2)

3) ℎ(?, ?, ?) = √? + 2? − ? ? 2 + ? 2

Find the third moment (find the 3rd derivative and then plug in zero) for the following:

a) ( 1 + p (e ^ t - 1) ) ^ n

b) ( p e ^ t) / ( 1 - (1 - p) e ^ t )

c) ( ( p e ^ t ) / ( 1 - (1 - p) e ^ t ) ) ^ r

d) e ^ ( k ( e ^ t -1) )

The command C = max(A,B) compares corresponding values in the A and B matrices assuming they are the same size. The problem is that MATLAB’s native version does not tell you from which matrix it found the largest value. Write a new function (in MATLAB) [C,from_which] = max_new(A,B) that also output a matrix, the same size as the inputs, with either 1’s or 2’s depending on from which matrix the larger value was found. Include a live script that tests your solution.

The R-rule for oysters is that you should only eat them in months that contain the letter R. Assuming that you like to get oysters on Saturday evenings with your friends write a program that uses the year as an input to determine how many times in that year you can get an oyster dinner and make a list of those dates for that year. Do this in a fully automated way and include a consideration of leap-years. In other words use logical statements to determine if the month has an R in it. Hint: my program is not that long, less than 20 lines, but it uses a separate function that I wrote called isleapyear, that is just a few lines. Also, I changed to format of datestr so that the month is fully spelled out. (Complete in MATLAB)

Finite Math

The Green Company manufactures an electric motorcycle, which it sells through two of its company-owned retail stores. Store A has requested between 40 and 50 motorcycles, inclusive, and Store B has requested between 30 and 40 motorcycles, inclusive. On the basis of previous sales, the Green Company has decided that the number of motorcycles shipped to Store B should equal or exceed 40% of the number shipped to Store A by 20 motorcycles. The shipping costs from the manufacturer to Store A and Store B respectively are $40 and $60 per motorcycle. How many motorcycles should the Green Company ship to each store in order to minimize its shipping costs? What is the minimum cost?

A population of 30 rabbits has been introduced into a new region. It is estimated that the maximum population the region can sustain is 400 rabbits. After 1 year, the population is estimated to be 90 rabbits. If the population follows a Gompertz growth model, how many rabbits will be present after 3 years?

Please show and EXPLAIN steps, thanks!

The population of the United States has grown at different rates over ten-year increments as shown by the following table.

If the maximum supportable population of the U.S. is 600 million people, use the logistic model to predict the population (in millions of people) of the U.S. in 2020 by using the following years as data points. (Round your answers to one decimal place.)

(a) using 1930 and 1940 as data points

(b) using 1950 and 1960 as data points

The growth rate from part (a) is ________ (smaller than, larger than, equal to) the growth rate from part (b).

solve the system X'={2 2, 3 1}X+{t 1}. (2 2 in column, 3 1 in column)

• Discuss the attributes or characteristics associated with common types of charts such as pie, line, bar, or time series charts.
• Discuss practical applications of such charts in business settings.
• Be certain to include in your discussion any special considerations for the chart types you discuss.
• Write a minimum of three well-formed scholarly paragraphs that include a topic sentence, several body sentences (aim for three to five), and a closing, summary, or transition sentence.

Emerson Corporation just completed its first year of operations. Planned and actual production equaled 17,000 units, and sales totaled 15,300 units at $107 per unit. Cost data for the year are as follows:

Required:

1. Compute the company’s total cost for the year assuming that variable manufacturing costs are driven by the number of units produced, and variable selling and administrative costs are driven by the number of units sold.
2. How much of this cost would be held in year-end inventory under (a) absorption costing and (b) variable costing?
3. How much of the company’s total cost for the year would be included as an expense on the period’s income statement under (a) absorption costing and (b) variable costing?

Consider the system x'= -y , y' = -x

Sketch the vector field using math-lab.

Please write the code with all the steps. I'm new on math-lab, and I tried to follow some online videos but it did not work right. I have the sketch, but I need the code and the steps to learn it.

Thank you,