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Answers by Robert B.

Solve the initial value problem? (answer)

Begin by dividing both sides of the equation by sqrt(y). This gives, ( dy /dx ) / sqrt(y) = sqrt(x), and after multiplying by dx, dy / sqrt(y) = sqrt(x) dx. Now integrate both sides and get S dy/sqrt(y) = S sqrt(x) dx ... 2*sqrt(y) = (2/3)*x*sqrt(x) + C. The initial...

Factor the following sum of two cubes. (answer)

z3 + 125 = z3 + 53 = (z + 5)(z2 - 5z + 25). This follows from the "sum of cubes" formula, below. a3+ b3 = (a + b)(a2 - ab + b2). Hope this helps. If there's any more I can do to help please ask. I or another tutor...

(2x+5)/5 = (x-2)/3 (answer)

I'm reading your equation as ( 2x + 5 )/5 = ( x - 2 )/3. "Cross-multiplying" refers to rewriting 'A/B = C/D' as 'AD = BC.' Try this first.  

Pre calculus (answer)

Problem:  To maximize  8R + 10F [profit] subject to the two constraints 8R + 7F <= 208 [fab dept], R + 3F <= 60 [fin dept]. Work with this and if you would like more help, I or another tutor will be happy to assist you.     &...

Summation Convergency tests by 3-condition test (answer)

The Alternating Series Test ∑(-1)nBn converges when the following two conditions are met: (i) lim Bn = 0 and (ii) {Bn} is (eventually) decreasing. Note: AST doesn't apply when either of the conditions is not met, and so never is a test for divergence.  If the first condition isn't...

how do you simplify this expression: 12x(9xy^12)(-5x^-8y^7)? (answer)

Remember the following rules when dealing with exponents. am*an = am+n. am/an = am-n. a-n = 1/an. Also remember that a0 = 1. Also it may help to remember that you can regroup the terms according to bases. To illustrate I'll use another example, and leave yours for...

latest mathematician? (answer)

Sadly, I'd say there are no famous mathematicians today, in the same sense that celebrity athletes, actors, politicians, and the like are famous. But that doesn't stop people from going into the field and continuing the work of mathematicians past.  They just don't do it for the fame...

Havin a problem with this slope equation. Can you help?(9,-5); 3x-5y=6 (answer)

Read the instructions for this problem carefully, and make sure you have included them in this post. As you've written it here so far, I can't figure what the problem is asking you to do. I certainy could guess, but that wouldn't be too instructive, and I would really like to help.

How do I find the (LCM) or the (LCD) of fraction? (answer)

Yes they are the same number, but LCM, for Least Common Multiple is a more descriptive term, as it hints at a way to find it. To find these, one could list the multiples of each number (or denominator). For example, say one needs the LCM of 6 and 15. 6:  6, 12, 18, 24, 30, 36,...

y=-x^2+4x+3 (answer)

I think a technique called "completing the square" is needed here.  It rewrites y = Ax2 + Bx + C in the form y = A(x + P)2 + Q. It is accomplished in several steps.  To demonstrate, I'll use an example like your own, leaving it for you to try yourself...

What are 3 common multiples of 7 and 21? (answer)

The "multiples" of a number, N, are the numbers N, 2*N, 3*N, ..., etc.  For example, the multiples of 4 are listed below in the usual order. 4, 8, 12, 16, 20, ..., and so on. So by "common multiple" one means a number that is a multiple of 2 or more numbers. Try...

how to simplify (2x-3)^2 (answer)

(a + b)2 = (a + b)(a + b) = a2 + ab + ba + b2 = a2 + 2ab + b2. Above I've given a short derivation of a very useful formula which demonstrates how to "square a binomial," which is just a fancy way of saying "raise the sum to the 2nd power." In...

how to do (6-c)+3(2c-7)=1 (answer)

Let's work an example like yours that will require similar steps to complete. Say we need to solve the following equation for 'b': (5-b) + 4(3b - 1) = 23. The first step would be to expand the LHS by distributing the 4. 5 - b + 12b - 4 = 23. Now simplify this as follows,...