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1. Asteroids momentum

An asteroid is spotted moving directly toward the center of Starbase Alpha. The frightened residents fire a missile at the asteriod, which breaks it into two chunks, one with 2.4 times the mass of the other. The chunks both pass the starbase at the same time. If the lighter chunk passes 1800 m...
2. Ideals in the ring Q[X]

Consider the ideal I of Q[x] generated by the two polynomials f = x^2+1 and g=x^6+x^3+x+1 a) find h in Q[x] such that I=<h> b) find two polynomials s, t in Q[x] such that h=sf+tg
3. Parabolic cylindrical coordinates

Can someone, please, show me an example of when you are better of with parabolic cylindrical coordinates than with cartesian coordinates when computing a triple integral over a solid?
4. Massless particle revolving in a circle

Given: A massless particle revolving in a circle with a rotational velocity = (2+sin(a)) To Find: Y-axis acceleration Method #1 (from rotational acceleration) Y-axis acceleration = (2+sin(a))(cos(a))^2 Method #2 (from Y-axis velocity) Y-axis acceleration =...
5. Partial integration help

How do I integrate: [tex]\frac{xarctan(x)}{(1+x^2)^2}[/itex]
6. Linear Algebra-question.

Linear Algebra-question. HELP!! Problem: Let L: R^3 \rightarrow R^4 be a linear transformation that satisfies: L(e_1) = (2,1,0,1)^T = u L(e_2) = (0,3,3,4)^T = v L(e_3) = (2,-5,-6,-7)^T = w. Determine a base for Range(L). ---- Is the base \{u,v\} since w = u-2v? Is it really that...
7. Continuous function.

Let f be that function defined by setting: f(x) = x if x is irrational = p sin(1/q) if x = p/q in lowest terms. At what point is f continuous? Continuous for irrational x, and for x = 0. Sketch: p*sin(1/q) - p / q = p(sin(1/q) -1/q) But sin x - x = o(x^2) when x -> 0 So, for large...
8. Probability HW (check my work & help)

Scenario: Mr. X is writing letters to five persons A1, A2, A3, A4, A5. After Mr. X has written them he has to leave the room where the letters and envelopes are. Mr X's son, who can't read, decides to help his dad and puts each letter in different envelopes. What is the probability that: a)...
9. Triple Integral-problem.

How do I solve this triple integral, \int\int\int_{\Omega}^{}zdxdydz, \hspace{8} \Omega = \{(x,y,z): x^2 + y^2 + z^2 \leq 1, \hspace{6} 0 \leq z \leq \sqrt{x^2+y^2}\}
10. L'Hospitals Rule

I have an examina soon and I need help with following proof. I don't know TEX that good so I'm attaching a screenshot from word instead.
11. Mean Value Teorem

How do I prove that (x-1)/x < lnx < (x–1), for x > 1 by using the mean value teorem?
12. Probability problem

I'm new to this, so can someone please explain how this problem is solved: What is the probability that your divisions manning will decrease given that corporation's retention rate? Corporation retention figures for first-term (0-4 years), second-term (4-8 years), and third-term contracts...
13. Sum of a series.

find the sum of the series 1 + 1/2 + 1/3 + 1/4 + 1/6 + 1/8 + 1/9 + 1/12 + ....., where the terms are the reciprocals of the positive integers whose only prime factors are 2's and 3's. Here's my work so far: 1 + 1/2 + 1/3 + 1/4 + 1/6 + 1/8 + 1/9 + 1/12 + ... = 1 + 1/2 + 1/4 + 1/8 + 1/16...
14. Sequences of positive numbers and limits

Let (x(n)) and (y(n)) be sequences of positive numbers such that lim(x(n)/y(n)) = 0. If lim(x(n)) = +∞, then lim(y(n)) = +∞ If (y(n)) is bounded, then lim(x(n)) = 0 To me this is self-evident. But HOW can it be proved?
15. Is this well-defined in the rational numbers

Need help with proving: Show that (a,b) + (c,d) = (a+c, b+d) is not well-defined in the rational numbers. [Note: (a,b) + (c,d) = (ad+bc, bd) is well-defined because (a,b) is related to (c,d) when ad = bc.)]
16. Geometry problem.

I need to find the mid point of the area of the shape described below. This would divide the area into 4 subparts of equal area.. The dimensions of the shape are: north side is 300 feet, east side is 5000 feet, south side is 1500 feet, west side is 5142 feet. The south side is perpendicular to...
17. Linear Programming

My assignment is to formulate a LP and find the optimal solution for the following problem: Acme estimates it costs \$1.50 per month for each unit of this appliance carried in inventory (estimated by averaging the beginning and ending inventory levels each month). Currently, Acme has 120 units...
18. Optimizing problem

I'm stuck on this optimizing problem: Tarmac Chemical Corporation produces a special chemical compound—called CHEMIX—that is used extensively in high school chemistry classes. This compound must contain at least 20% sulfur, at least 30% iron oxide, and at least 30% but no more than 45%...
19. Linear programming equation problem

I need someone to help me folumate a Linear Programming Problem based on the following story. The optimal solution should equal 26,740; however, I need to be able to outline the equation and graph it. The story is as follows: A farmer in Georgia has a 100-acre farm on which to plant...
20. Moment of inertia

Hello! I have a problem and I was kind of hoping that someone could help me out.