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• Yesterday, 10:12 PM
To multiply a radical expression like 9√3 by a number like 2, just notice that you are multiplying three numbers together: 2*9*√3. The associative...
3 replies | 49 view(s)
• Yesterday, 10:06 PM
You've made a great start; just continue! Write an equation stating that 16 = geometric mean of 4x and x. Solve that for x. Then let Pythagoras...
2 replies | 40 view(s)
• Yesterday, 10:01 PM
Actually, you don't end up needing Pythagoras. Try looking for similar triangles.
2 replies | 40 view(s)
• Yesterday, 07:45 PM
But ... those families with one child will constitute half of all families! And the families with more males than females constitute only a quarter....
11 replies | 103 view(s)
• Yesterday, 06:45 PM
The expected number of males before a female works out to 1; so the ratio will be 1:1. Also, as lev888 implied, each individual birth has an equal...
11 replies | 103 view(s)
• Yesterday, 03:49 PM
No, "implies" is not equivalent to "and"; if it were, we wouldn't need two different symbols, would we? Have you learned that p\rightarrow q...
1 replies | 55 view(s)
• Yesterday, 09:50 AM
Do you know what a median is? The solution starts with the definition. One good starting definition is that the median is a number such that no...
1 replies | 52 view(s)
• 05-21-2018, 04:00 PM
Can you show us the problem, and whatever you did write, and whatever thoughts you have about what you might use? The more you say, the better we...
4 replies | 134 view(s)
• 05-21-2018, 09:26 AM
What they are doing is to factor out √2 / 4 from each term. Note that the way to add or subtract radical expressions is to simplify each of them,...
3 replies | 82 view(s)
• 05-20-2018, 10:00 PM
There is an obvious solution; do you see it? But were you told the value of T, or what its possible values are? (If T were 1, everything would...
10 replies | 212 view(s)
• 05-20-2018, 09:47 PM
Before we can try to help, we need to be sure of the question. Do you mean, as what you wrote means, e^x - ln(x) <= e/x, that is, e^x - \ln(x) \le...
6 replies | 137 view(s)
• 05-20-2018, 08:27 PM
I was not familiar with the down-arrow in logic, but I see that it means "nor", so that p ↓ q ≡ ¬(p ˅ q) . If you don't know how to get started,...
2 replies | 122 view(s)
• 05-20-2018, 08:15 PM
Interesting proof; now at last I can see why you previously perceived circularity in the use of the fact it starts with. By the way, before...
2 replies | 136 view(s)
• 05-20-2018, 06:18 PM
Think of similar triangles. If you extend the legs of a trapezoid until they meet at the center, you will have two similar isosceles triangles....
2 replies | 138 view(s)
• 05-17-2018, 10:36 PM
There actually isn't enough information to calculate the actual areas; the sides could be at various angles that you don't know. (Nothing is...
2 replies | 108 view(s)
• 05-17-2018, 04:55 PM
It is very different to say that two quantities are "likely" to vary in the same direction, and to say that they are in fact directly proportional....
5 replies | 304 view(s)
• 05-17-2018, 04:33 PM
It is not necessary to put that vector on the x-axis; there are many ways you could assign a coordinate system to the problem. But where are you...
1 replies | 91 view(s)
• 05-17-2018, 03:32 PM
I like combinatorial proofs like this (counting the same thing in two ways), so I knew immediately what sort of thing I expected to do. But I didn't...
4 replies | 185 view(s)
• 05-17-2018, 02:14 PM
5 replies | 191 view(s)
• 05-17-2018, 11:06 AM
Your notation can't be correct, because delta is always written before something. Can you explain a little more? Does "tends to follow" mean "is...
5 replies | 304 view(s)
• 05-17-2018, 11:01 AM
The next thing to do is to show the steps of your work. Don't factorize until you have first written the result of the subtraction and addition you...
6 replies | 158 view(s)
• 05-17-2018, 09:07 AM
Note that I have inserted ^ in your expressions above to indicate exponents. Yes, the 6 comes from doing this: (3 + Δx)^2 = (3 + Δx)(3 + Δx) =...
4 replies | 152 view(s)
• 05-17-2018, 09:01 AM
Please show your actual calculations and results, so we can see if you did something wrong. My first concern is that the dimensions you gave are...
3 replies | 80 view(s)
• 05-16-2018, 10:29 PM
Interesting. Let's take an example. With n=5, r=3, you have 3*5C3 = 3*10 = 30, and 5*4C2 = 5*6 = 30. Looking for a way to see both sides as...
4 replies | 185 view(s)
• 05-16-2018, 10:19 PM
Presumably the literature you read says that these are the only possible rational zeros of the polynomial. That is a very different thing. You seem...
5 replies | 244 view(s)
• 05-16-2018, 12:23 PM
Maybe it would be good to start fresh, with your real question. Here is what I think you really wanted to ask: f(x)={1,when x is rational ...
11 replies | 333 view(s)
• 05-16-2018, 10:54 AM
Yes, that's the second key idea. Although ABC and ABD are not themselves similar, their altitudes are also the altitudes of other triangles that are...
5 replies | 202 view(s)
• 05-16-2018, 08:58 AM
It can be done much more simply than that. Once you have the lengths from part (a), you just need the fact that triangles on the same base have areas...
5 replies | 202 view(s)
• 05-15-2018, 09:25 PM
I'm having trouble finding a clear definition of the LRA system, but I think all you're asking for is the angle you marked, and that's pretty easy. ...
3 replies | 147 view(s)
• 05-15-2018, 04:39 PM
Okay; it would be helpful if you gave context in the first place. But how would you use the fact you have been asking about in a proof of the...
22 replies | 782 view(s)
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I was a software engineer for many years, and have been teaching at a community college since 2004. Since 1998, I was a part of Ask Doctor Math (http://mathforum.org/dr.math/ and now http://themathdoctors.org/).
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