Kenzie

My professor did a problem on the board, but he is extremely bad at teaching. He does the problem, but doesn't tell you how or why he did certain steps.

Here is the problem: (pretend [x,y] means that x is on top and y is on bottom in a column.(idk how to represent column on here)

If T[1,1] = [2,3] and T [1,-1] = [5,-1] find T(x).

What he did:

e1 = [1,0] = 1/2([1,1] +[1,-1]) = T(e1) =[7/2.1]

e2 = [0,1] = 1/2([1,1] - [1,-1]) = T(e2) = [-3/2,2]

A = [ 7/2,1 : -3/2,2]

T(x) = Ax

I understand all the basic math, but I have no clue how he got e1 , e2??? Did he just choose random numbers? Are they always [1,0] and [0,1]? Please help. I am clueless where he came up with these matrices.

a = 3i + 4j - 4k

b = i - j

c = 2i + 3k

I thought the equation was |a dot (b X c)|.

My work:

<3,4,-4> dot (-3-0)i - (3-0)j + (0-2)k

<3,4,-4> dot -3i -3j -2k

-9 -12 +8

=13

However, I am getting the wrong answer. Can somebody please figure out what I am doing wrong? Thanks.

1. Use the binomial series to expand the function as a power series.

(1+x^2)^1/3

2. Use the binomial series to expand the function as a power series.

x^2/sqrt(2+x)

3.Use the binomial series to find the Maclaurin series of the following.

f(x)=1/(1+x^3)^1/2

Use this to evaluate f^(9) of (0)

1. What happens if a_n decreases to zero and you consider Sum (a_n)^n?

2. Does Sum of (-1)^[n*sin(1/n^p)] converge/diverge? Prove?

3. What Power Series Representation do you get when differentiating the Power Series Representation of 1/(1-x)?

1. Find the sum. From n= 1 to infinity, of (4^n + 3^n)/12^n

2. Find the values of x for which the series converges and find the sum of the series for those values of x. n=0...infinity . 2^n(x+1)^n

3. Find the interval of convergence for the series. n=1...infinity. [(-2)^n(x+3)^n]/sqrt(n)

Please help. I've tried but failed. I am almost clueless when it comes to this convergence stuff. Answers would be great but explanations would be even better.

Here is the sentence. For example, the US Space Shuttle had only two failures in 135 launches. These were national traumas in the US for the reason that they were unusual.

The only part I got from a site was "the Us Space Shuttle had only two failures in 135 launches. These were national traumas in the US"... its mostly word for word from the site.

So ... for my sentence I'm not sure how to cite it.

Which option is correct? (if any):

1. For example, “the US Space Shuttle had only two failures in 135 launches. These were national traumas in the US” for the reason that they were unusual (Martin).

2. For example, the US Space Shuttle had only two failures in 135 launches. These were national traumas in the US for the reason that they were unusual (Martin).

3. For example, “the US Space Shuttle had only two failures in 135 launches. These were national traumas in the US” (Martin) for the reason that they were unusual.

My teacher said you have to use quotations when it's word for word, but I don't understand where to put the citation at. It doesn't make sense.

What is the special significance of a reaction for which:

a) delta G = 0, b) delta G standard = 0

If you have an equation and you balance it by multiplying it by 2.. would the substrate be what the reactants were before the balancing or after?

1. What is the equation of a parabola with focus (6, -10) and directrix (x = -2)

2. The amount that a beam bends downward when its supported at each end and centrally loaded varies jointly as the mass of the load and the cube of the length, and varies inversely as the cube of the depth of the beam. A beam 4 meters long that has a depth of 15 cm. bends .7 cm. downward when loaded with a mass of 1000kg. To the nearest tenth, what is the maximum load that a beam 5 meters long and with a depth of 10cm. can carry at its center without bending more than 3.2 cm.?

Find 2 complex conjugate numbers that have a sum of 12 and product of 40. How did you find them?

Hero's formula for the area of a triangle is given by A = square root of [s(s-a)(s-b)(s-c), where a,b,and c are the lengths of the sides of the triangle and s= .5(a +b+c).

Find the lengths of the sides of the triangle given in this application of Hero's formula:

A = square root of (s^4 - 12s^3 + 47s^2 -60s)

I already made bleached shirts and melted crayons on a canvas. I'm looking for cool ideas like that. I don't want to make friendship bracelets, picture frames, purses, or anything lame like that. I want to make something cool. Could you please give me some ideas ? Thanks!

Researchers are very interested in studying identical twins seperated at birth and raised apart. So far, the data reveal that such twins frequently have similar personalities, mannerisms, habits, and interests. What general question do you think researchers hope to answer by studying such twins? Why do identical twins make good subjects for this research? What are the potential pitfalls of this research? What abuses might occur if the studies are not evaluated critically?

What properties are these problems?

1. [5 + (-2)] + (-4) = 5 + [-2 + (-4)]

2. (1 2/7) (7/9) = 1

Commutative..Associative...Identity....Inverse... or Distributive

What properties are these problems?

1. [5 + (-2)] + (-4) = 5 + [-2 + (-4)]

2. (1 2/7) (7/9) = 1

Find the measure of the angle whose supplement is 47degrees more than twice that of its complement.

Can you tell me how to do this or what the equation to find the measure would be? Thank you.