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...
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
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?
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 =...
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).
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Is the base \{u,v\} since w = u-2v? Is it really that...
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...
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)...
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}\}
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...
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...
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?
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.)]
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...
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...
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%...
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...