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Wed Feb 18, 2009 5:59 pm
Forum: Discrete Math
Topic: word problem: number of ways to order n things in r groups
Replies: 2
Views: 4265

### Re: word problem: number of ways to order n things in r groups

The title seems to suggest that it is not just asking how many ways can you choose r students from a class of n students. Instead it suggests that it is asking, "How many ways can I group n students into r disjoint committees?" There are two possible problems this could be asking for. The easy one i...
Fri Feb 13, 2009 5:30 pm
Forum: Calculus
Topic: Differential Equations: x(dy/dx) = 6y + (12x^4)[y^(2/3)]
Replies: 5
Views: 8496

### Re: Differential Equations: x(dy/dx) = 6y + (12x^4)[y^(2/3)]

Excellent work. The more general lesson here is that any time you have an equation in the form of: p(x)\frac{dy}{dx} = q(x)y + r(x)y^s the way to attack it is to substitute u^{\left(\frac{1}{1-s}\right)} = y so that \left(\frac{1}{1-s}\right)u^{\left(\frac{s}{1-s}\right)}\left(\frac{du}{dx}\right) =...
Thu Feb 12, 2009 5:39 pm
Forum: Beginning Algebra
Topic: What does "linear" mean?
Replies: 1
Views: 11886

### Re: Linear .....

The equation of a straight line is the best example from basic algebra of something that is linear. And indeed the word "linear" and the word "line" are from the same root. In a more general sense, though, something is linear if what comes out is in direct proportion to what goes in. For example, in...
Thu Feb 12, 2009 3:57 pm
Forum: Calculus
Topic: Differential Equations: x(dy/dx) = 6y + (12x^4)[y^(2/3)]
Replies: 5
Views: 8496

### Re: Differential Equations: x(dy/dx) = 6y + (12x^4)[y^(2/3)]

Yes I am the same Karl as on KCT. In my previous post on this thread I got as far as 3xu^2 (du/dx) = 6u^3 + 12x^4u^2 where u^3 = y Dividing out 3u^2: x (du/dx) = 2u + 4x^4 You seem to have miscopied the last exponent in your solution. This equation is linear. To put it into standard form, divide by ...
Wed Feb 11, 2009 10:33 pm
Forum: Calculus
Topic: Differential Equations: x(dy/dx) = 6y + (12x^4)[y^(2/3)]
Replies: 5
Views: 8496

### Re: Differential Equations: x(dy/dx) = 6y + (12x^4)[y^(2/3)]

Substitute u^3 = y. Hence 3u^2 (du/dx) = dy/dx. Equation becomes

3xu^2 (du/dx) = 6u^3 + 12x^4u^2

Divide out 3u^2 and the equation is linear and can be solved for u in the usual way for linear first order equations. Then backsubstitute u to get y.
Fri Jan 30, 2009 11:15 pm
Forum: Intermediate Algebra
Topic: A motor boat can travel 45 km downstream in 2 hr 30 mins
Replies: 3
Views: 5427

### Re: A motor boat can travel 45 km downstream in 2 hr 30 mins

Let me add a little more to Ms. Stapel's response, hopefully without giving too much away. The problem asks for two things -- that is there are two questions at the end of it. Both are velocities; that is the velocity of the boat in still water, v, and the velocity of the current, w. Upstream the bo...
Sat Jan 24, 2009 5:59 pm
Forum: Discrete Math
Topic: Fibbo-something sequences
Replies: 3
Views: 4527

### Re: Fibbo-something sequences

The problem appears to be asking for the sequence of the number of dandelions each Saturday. The problem gives that on the first Saturday, the number of dandelions is 225. So n[0] = 225 To get from any Saturday's number to the next Saturdays number, you subtract 100 and double the result. The equati...

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