Hi, I was wondering if i can get some help for a few math B regents help. one problem that i dont get is from the june 2005 regents number 3
question:http://www.nysedregents.org/testing/mathre/b605.pdf
answer: http://www.nysedregents.org/testing/mathre/b-key605.pdf
Logs are exponents. there's nothing to be freaked out about.
There are four laws you NEED to know in order to do pretty much any log problem. There are about 10 laws you need to know to do any log problem comfortably, that is, the other laws are derived from the first four, so knowing them gives you a shortcut.
Here are the four laws you MUST know. the first law is the definition of a logarithm.
LAW 1: The logarithm of a number, to a given base, is the power to which the base must be raised to give the number.
That is, if
then
LAW 2: .....that is, we can make the power of something being logged into a multiplyer
LAW 3:
LAW 4:
Now on to your question.
We have
......LAW 3
.......rewrite the second log
.............apply LAW 2 to second log
..............inserted the values given
this is choice 4
ooh i got stuck with the square root i didnt know you had to make it into an exponent
for the same regents i also have questions with 16, 17, and 18 if you dont mind helping.
i did the first part of the regents and these are pretty much the questions i didnt understand. my teacher doesnt really help out too much
(16)
recall that when we raise a number with a power to another power, we multiply the powers to get the new power of the base.
also recall that 1 over something to a power, means the something to the negative of that power. negative powers means inverse. you should look up all the log and power rules. earboth posted them in a PDF here
Now equate the powers since the bases are the same
(17)
By the Binomial theorem, or Pascal's triangle (you should look these up, either here or at wikipedia)
The third term of is
(18)
By inspection we see that choice 3 is what we should choose. why?
This number is never zero, so the roots are imaginary.
Why did i decide to choose this choice? if you see something squared equals a negative number, chances are that the guy you want.
thanks for the answers, they are very helpful
i have a quick question for number 7, when you put the values on the calculator then you press stat, which button should you press to get the mean?
on number 27 i have a faint idea of what to do but im not too sure. would you make the exponents equal by getting the same base?
number 24: i dont knkow how i should add the fractions to simplest form
so far thats as far as i got if you can help with those thanks alot
for number 7, i'm not familiar with that feature on the calculator. here' how to do the problem other wise.
the sum of all the frequencies is the total amount of numbers used. now, for each , the corersponding tells you how many times it shows up, since it gives the frequency. so for we have , that means 25 shows up 3 times.
to find the mean, it is the sum of all the numbers divided by the amount of numbers you have. remember when summing the numbers, you need to take their frequency into account. we do this by multiplying each number by its corresponding frequency.
So, mean
18. Which of the following has imaginary roots?
I'm going to post this one anyway, even though Jhevon has given you a good answer.
The roots of a quadratic equation have an imaginary component if the discriminant is negative.
So let's put all of these into standard form and see which ones have negative discriminants:
==> ==>
==> ==>
==> x^2 + 6x + 10 = 0[/tex] ==>
==> 2x^2 - 5x - 7 = 0[/tex] ==>
So we see that #3 has a negative discriminant and thus has an imaginary component. (As Jhevon already told you.)
-Dan