In a survey of 300 individual investors regarding subscriptions to the New York Times (NYT), Wall Street Journal (WSJ), and USA Today (UST), the following data were obtained.

121 subscribe to the NYT.
147 subscribe to the WSJ.
66 subscribe to the UST.
40 subscribe to the NYT and WSJ.
25 subscribe to the WSJ and UST.
22 subscribe to the NYT and UST.
42 do not subscribe to any of these newspapers.

(a) How many of the individual investors surveyed subscribe to all three newspapers?
investors

(b) How many subscribe to only one of these newspapers?
investors

a. *If y=(x^3+7)/(x^2/3) , then find dy/dx . Make sure your answer is fully simplified.

b. *If y=(5x-8)/(4x+3)   , then find dy/dx .

c. *If x=(x2-5x+3)(2x2+4) , then find f ‘(x).

Please neatly show your work.

Matilda makes specialized chocolates. Her two best-selling chocolates, the chocolate heart and the chocolate flower, are made by pouring milk chocolate into a mold. A heart requires 3.5 ounces of milk chocolate and earns a profit of 20 cents, while a flower requires 1.5 ounces of milk chocolate and earns a profit of 30 cents. If she has 663 ounces of milk chocolate available and she wants to make at least twice as many hearts as flowers, what is the maximum profit she can make?

Maximum profit in dollars:

Find the maximum area of a rectangle inscribed in a triangle of area A.(NOTE: the triangle need not necessarily be a right angled triangle).

Explain and state the formula of (a) Trapezoidal rule, (b) the Midpoint Rule, and (c) Simpson’s Rule and the error formula of each

Find the charge on the capacitor in an LRC-series circuit at t = 0.05 s when L = 0.05 h, R = 3 Ω, C = 0.008 f, E(t) = 0 V, q(0) = 4 C, and i(0) = 0 A. (Round your answer to four decimal places.) C

Determine the first time at which the charge on the capacitor is equal to zero. (Round your answer to four decimal places.) s

DO NOT DO THE GRAPH OR THE DOMAIN OR RANGE PART. THOSE DO NOT COUNT. WE ARE NOT DOING THEM IN MATH 1003.Find the factors that are common in the numerator and the denominator. Then find the intercepts and asymptotes. (If an answer does not exist, enter DNE. Enter your asymptotes as a comma-separated list of equations if necessary.)

r(x) =

Given the following rational function:

            F(X) = (2X^2 - 20) / [( X - 5 )^2]

1. Find all horizontal and vertical asymptotes

2. Find the first derivative of F(X) and simplify

3. Find the critical values for X and determine if they are at a maximum or minimum, using the First Derivative Sign Test.

4. Find the Second Derivative and Use it to confirm your answers to part c. You may keep the 2nd derivative in “rough” form and simply substitute in the X value found in part c to see if you confirm a max or a min.

4x-2y-2z=2
-x-5y+2z=-8
4x-5y+z=11

Please make sure you show all steps numerically, becuse I want to be sure I know how to arrive at the same numbers.

A couple is deciding to invest in the laundromat business. There are two laundromat stores available for sale. They can only afford to buy one of them.

    The annual flow of income from each of the available laundromats is given below:

Laundromat 1: I’(t) = dI(t)/dt = 9000e^(.04t)

Laundromat 2: I’(t) = dI(t)/dt = 12500

The couple has decided to use the Present Value of each of the Laundromats after 8 years, at an annual interest rate of 10%, to compare the value of both investments.

They will buy the Laundromat with the highest Present Value.

1. Find the Present Value of each Laundromat

2. Which Laundromat should the couple buy? Explain.

         Hint: PV(t) = Definite ∫ I’(t)e^(-rt)dt, taken between ( a<t<b)

          Here a=0; b=8

                   r = 10%/100 = .10

I don't understand how to use beats using sum-to-product identity, or this assignment at all.

1. Dealing with vector fields is very common in engineering and science applications. Vector fields are often used to model a moving fluid throughout space, magnetic or gravitational force, and etc.

a. Provide two examples of vector field for engineering or science applications in two and three dimensions

b. Define a conservative vector field. Verify whether the given examples for vector fields in Part 1(a) are conservative? [15 marks]

c. Interpret the fundamental theorem of line integrals for conservative vector fields. Explain this with an example of a force field (i.e. vector field) and compute the work done by the force field in moving a particle from one point to another point along a curved path in three dimensional space. [20 marks

The function f(x, y) = 10−x 2−4y 2+2x has one critical point. Find that critical point and show that it is not a saddle point. Indicate whether this critical point is a maximum or a minimum, and find that maximum or minimum value.