EvaluateRC F·dr where F = hyzexz,exz,xyexzi and C : r = ht2 + 1,t2 −1,t2 −2ti, 0 ≤ t ≤ 2. Hint: Check whether F is conservative. If so, the Fundamental Theorem for Line Integrals might be useful

A piece of wire 28 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (Give your answers correct to two decimal places.)
(a) How much wire should be used for the square in order to maximize the total area?
(b) How much wire should be used for the square in order to minimize the total area?

Answer all the question below.

Table 2:

1.     Visualize data in table 2 in a 2-dimensional plot using Matlab.
2.     Interpolate data in table 2 to determine a value of temperature when t = 8 and t = 20.
3.     Formulate a mathematical function for data in table 2 using a curve fitting technique.
4.     Determine temperature value at t = 8 and t =20 and explain a different with a result from the interpolation technique.

Need to solve this all question. Please Provide the proper solution. Thank you

find the riemann sum f(x)=x^2 +3x over the interval [0,8] where x₀ =o, x₁=1 , x₂=6, x₄=8, and c₁=1, c₂=2, c₃=4, c₄=6

An economy is based on three sectors, agriculture, manufacturing, and energy. Production of adollar’s worth of agriculture requires inputs of $0.30 from agriculture, $ 0.30 frommanufacturing, and $0.30 from energy. Production of a dollar’s worth of manufacturing requires inputs of $0.30 from agriculture, $0.20 from manufacturing, and $0.20 from energy. Production of a dollar’s worth of energy requires inputs of $0.20 from agriculture, $0.30 frommanufacturing, and $0.30 from energy.

Find the output for each sector that is needed to satisfy a final demand of $67 billion foragriculture, $34 billion formanufacturing, and $14 billion for energy.

1) The output of the agricultural sector is ___ billion dollars

2) The output of the manufacturing sector is __ billion dollars

3) The output of the energy sector is __ billion dollars

Consider a region R bound by the coordinate axes and y = ( 9 + x 2 ) − 1 2 on 0 ≤ x ≤ 4.

a. Find the area of R.

b. Suppose R is revolved about the x-axis to form a solid. Find the volume of the solid.

c. Suppose R is revolved about the y-axis to form a solid. Find the volume of the solid.

Is this true or false? The foci for the hyperbola ((x-2)^(2))/(36)-((y+1)^(2))/(64)=1 are (2, -1 +4\sqrt(7) and (2, -1 - 4\sqrt(7)

The populations of termites and spiders in a certain house are growing exponentially. The house contains 110 termites the day you move in. After four days, the house contains 195 termites. Three days after moving in, there are two times as many termites as spiders. Eight days after moving in, there were four times as many termites as spiders.

How long (in days) does it take the population of spiders to triple? (Round your answer to one decimal place.)

Define

Instructions:

After reading Chapter 4 of the textbook, define the following terms:

-System of linear equations

-Solution to a system of equations

-Consistent system of equations

-Inconsistent system of equations

Write a good paragraph with at least 5 sentences using a minimum of 75 words.

Calculate an approximate value of the area of the place inside the curve. (So if you sketch it up (by using WolframAlpha or something else) then you will see that what is sought after is the calculated value of the area that is inside the curve

1 = (40+43)x^2y^2 + y^4 + (1+1)x^4

American General offers a 8 -year annuity with a guaranteed rate of 6.73% compounded annually. How much should you pay for one of these annuities if you want to receive payments of $600 annually over the 8 year period?

5 + (3 * 4)^2 - 2 = 147

            (5 + 3) * 4^2 - 2 = 126

            (5 + 3 )* (4^2 – 2) = 112

            5 + (3 * 4^2) - 2 = 51

1. Which is the correct answer to using the "order of precedence" and why?

the table gives a total U.S expenditure for health services and supplies selected years from 2000 and projected to 2018.

year $(billion)

2000 1264

2002 1498

2004 1733

2006 1976

2008 2227

2010 2458

2012 2746

2014 3107

2016 3556

2018 4086

a. find an exponential function model to these data, with x equal to the number of years after 2000. b) use the model to estimate the U.S expenditure for health services and supplies in 2020.

2.The percent of boys age x or younger who have been seually active are given below.

Age cumulative percent seuual active girls cumulative percent sexual active boys

15 5.4 16.6

16 12.6 28.7

17 27.1 47.9

18 44.0 64.0

19 62.9 77.6

20 73.6 83.0

a). Creat a logarithmic function that model the data using an input equal to the age of the boys.

b) use the model to estimate the percent of boys age 17 or younger who have been seually active

c. compare the percent that are sexually active for the two genders, what do you conclude.

3). if $12000 is invested in an account that pays 8% interest, compounded quaterly, find the future value of this investment

a) after 2 year. b) after 10 years.

4).if $9000 is invested in an account that pays 8% interest, compounded quaterly . find the future value of this investment

a) after 0.5 year b)after 15 years

5. Grandparents decide to put a lump sum of money into a trust fund on their gtanddaughters 10th birthday so that she will have $1000000 on her 60th birthday. if the fund pays 11% compounded monthly. how much money must they put in the account.

6.At the end of t years the future value of an investment of $25000 in an account that pays 12% compounded quaterly is

S=25000(1+0.12 /4t )^4t dollars.. a) How many years will the investment amount to $60000.

a) Calculate the maximum MaxDisk value of the function f (x,y) = 9 ln * (x^2+(1+1)y^2+(0.5+0.5)) on the circle disk with the center of origin and radius 4.

b) Also calculate the maximum the value MaxBorder that the function assumes on the border.