Write an examples for each of the three special types of binomial (difference of squares, difference of cubes, and sum of cubes). Factor each of them and share your results.

Calculate the Y values corresponding to the X values given below.  Find the critical values for X for the given polynomial by finding the X values among those given where the first derivative, dy/dx = 0 and/or X values where the second derivative, d­²y/dx² = 0.    Be sure to find the sign (+ or -) of  dy/dx and of d²y/dx² at all X values. Reference Lesson 13 and the text Appendix A (pp 694 – 698), as needed.  Using the first and second derivative tests with the information you have calculated, determine which X value(s) represent maximums (MAX), which minimums (MIN) and which inflection points (INF).  Label the qualifying X value as such.  Attach work to convince me you carried out these calculations.  An Excel spreadsheet can make calculations easier.  If used, please attach the spreadsheet file and upload it with the rest of your work so that I can examine your formulas.  The beginning and ending X values below are not to be considered critical values.  In the space after the “Bonus Opportunity” write the first derivative (dy/dx) and the second derivative (d²y/dx²₎ you used or you will not receive credit for them.

                                                Y = 50 + 15X – 6.5X² – 2/3X³

Use the nine X values and their Y values you found above (which include the critical values) to help neatly sketch the graph of this polynomial function over the range of X values given. Your sketch must be consistent with the tabled values above (which means, if you claim a certain X value is a maximum, then the graph of it should show this same value as a maximum.  Similarly, if you claim an X value is an inflection point, then the graph of it should show it to be so.  A minimum should graph as a minimum, too.  The point is, if you figure out how the derivatives SIGNAL which X values are critical points, the graph of the values should show them as such.)

Let G be a group and H and K be normal subgroups of G. Prove that H ∩ K is a normal subgroup of G.

Find the matrix A' for T relative to the basis B'.

T: R³ → R³, T(x, y, z) = (y − z, x − z, x − y), B' = {(5, 0, −1), (−3, 2, −1), (4, −6, 5)}

Maximize p = 2x + 7y + 5z subject to

P= ? (x, y, z)= ?

Three digits are randomly chosen from {1,2,3,4,5,6,7} without replacement.

a) What is the probability the number formed is 123 or 567?

b) What is the probability the number formed has first digit 1?

c) What is the probability the number formed by the three digits is greater than 520?

0.25y''+1y=15cos(0.5t)-7sin(1.5t) Dole by method of undetermined Coefficient

Write a program to compute the root of the function f(x) = x³ + 2 x² + 10 x - 20 by Newton method ( x₀ =2 _{). Stop computation when the successive values differ by not more than 0.5 * 10^-5 . Evaluate f(x) and f '(x) using nested multiplication. The output should contain:}

_{(1) A table showing at each step the value of the root , the value of the function,and the error based upon successive} approximation values and percentage error for each method.

(2) A plot showing the variation of percentage error with iteration number for each method on the same graph so as to compare the method.

what role does budgeting play personal finance ?and how you can improve it.

TV Circuit has 30 large-screen televisions in a warehouse in Erie and 60 large-screen televisions in a warehouse in Pittsburgh. Thirty-five are needed in a store in Blairsville, and 40 are needed in a store in Youngstown. It costs $17 to ship from Pittsburgh to Blairsville and $24 to ship from Pittsburgh to Youngstown, whereas it costs $18 to ship from Erie to Blairsville and $27 to ship from Erie to Youngstown. How many televisions should be shipped from each warehouse to each store to minimize the shipping cost? Hint: If the number shipped from Pittsburgh to Blairsville is represented by x, then the number shipped from Erie to Blairsville is represented by 35 − x.

from Pittsburgh to Blairsville televisions?

from Pittsburgh to Youngstown televisions ?

from Erie to Blairsville televisions ?

from Erie to Youngstown televisions?

Express the inverse transform as an integral s(s+3)/[(s^2+4)(s^2+6s+10)]

For m, n in Z, define m ~ n if m (mod 7) = n (mod 7).

a. Show that -341 ~ 3194; that is to say 341 is related to 3194 under (mod 7) operation.

b. How many equivalence classes of Z are there under the relation ~?

c. Pick any class of part (b) and list its first 4 elements.

d. What is the pairwise intersection of the classes of part (b)?

e. What is the union of the classes of part (b)?

Use the Laplace transform to solve the following initial value problem: y′′−3y′−28y=δ(t−7) y(0)=0, y′(0)=0

y(t)=

Let G and H be groups. Define the direct product

G X H = {(x,y) | x ∈ G and y ∈H }

Prove that G X H itself is a group.

find the stedy-periodic solution cap of the initial value problem
x"+2x'+50x=6cos(4t),x(0)=0,x'(0)=0