course Mth 158
I have a few questions for you... 1. R.1.14 (was R.1.6) Of the numbers in the set {-sqrt(2), pi + sqrt(2), 1 / 2 + 10.3} which are counting numbers, which are rational numbers, which are irrational numbers and which are real numbers?
I do not know how to read this... I see the one half and the 10.3 but I don't know what other numbers you are talking about...
This corresponds to problem 14 in section 1 of Chapter R. In general it is expected that you are reading problems from the text, not from the abbreviated statement in the Query. Because it is an abbreviated statement, it might well be more difficult to interpret, and it is there as a guideline rather than a statement to be understood on its own.
However in this case the statement does stand on its own. Comparison with the problem in the text will show you what the notations mean. Provided, of course, that the numbering of the problem in the text agrees with the numbering in the Query (there might be some discrepancies but there should not be many).
Let me know if the following explanation doesn't help:
In set notation the elements of the set are separated by commas. So there are three elements in the set:
-sqrt(2)
pi + sqrt(2) and
1/2 + 10.3
You probably know this much already. The thing you probably really need to know is what sqrt means and what pi means.
-sqrt(2) means the negative of the square root of 2. You should have encountered this notation also in the Describing Graphs exercise of the Orientation.
pi means the number pi, the ratio of the circumference of a circle to its radius. pi can be expressed as a nonrepeating nonterminating decimal number. Its first three digits are 3.14, but it goes on forever. You would also have encountered the notation for pi in the q_a_areas_volumes ... assignments of the Orientation.
I believe you understand 1/2 + 10.3.
2. Assignment #2... # 93 I don't remember what to do with a negative exponent. The problem is (3x^-1/4y^-1)^-2 I don't know how to figure that one out.
Thanks for your time!
That expressio probably requires a little additional grouping:
It might be (3x^(-1/4) y^-1)^-2.
In any case the behavior of negative exponents is given by the definition
a^(-b) = 1 / (a^b).
So for example:
2^(-3) = 1 / 2^3 = 1 / 8
(1/2)^(-5) = 1 / ((1/2)^5) = 1 / (1/32) = 1 * 32/1 = 32.
(4 x^-2)^(-3) = 4^(-3) * (x^(-2))^(-3) = (1 / 4^3) * (1 / x^2)^-3 = 1 / 64 * 1 / (1 / (x^2))^3 = 1/64 * 1 * (x^2)^3 = 1/64 * x^6, or (x^6) / 64.
Your text will have additional examples.
If you want to try a few examples for feedback copy these and insert your solutions and/or questions:
3^(-2)
(-2)^(-3)
(2 x)^(-3)
(3 x^2)^(-4)
(2 x^(-2) ) ^(-5).