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Normally I'd say yes but if you do the x cancel out and you're left with an inconsistency.
Just checking Wolfram Alpha
Back again. As suspected WA gives x=0 as the only real solution.
Bob
Now that we know that x = 0 is the only real solution, how do we find x?
When you encounter repeat indices like this the rule is work from the top down.
So 3^(3^27)=3^(3×3×3×....3)
That's one BIG number.
Bob
Thanks. Yes, it's a huge number that we can write using scientific notation.
Agree?
There are no patterns nor formulas for this, so I think you just have to list and count.
Keep the list: it'll be useful later.
Bob
I am not going to make such a list but thanks.
I am having a hard time with the following problem:
5 ÷ [cuberoot(2)]
What is the formula for determining the 7th number on the 20th row of the famous Pascal Triangle?
Which prime numbers under 100 are 8 less than a perfect square?
How is this done?
Solve for x.
3^(9x) = 9^(3x)
I am thinking about taking the log on both sides.
You say?
What is the best and fastest way to raise a number to itself several times?
Sample:
What is 3^(3)^(3)^(3)?
How many prime numbers are there between 1 and 100?
Is there a quick way to find these prime numbers?
That looks OK to me. If t=5.1 , abs(t) > 5 and its certainly more than 5 from the origin. If t = 4.9 it isn't.
Bob
Ok.
Of course. No other way. The positive value of a calculation is the same if its positive or zero and otherwise switch the sign.
Bob
Ok.
Here's a useful algebraic trick. It will help you to see if your working is right at each step. Choose values for a and b and work out what that makes R. Then use your values of R and b to see if the final value for a is the one you started with.
Normally I wouldn't choose the same for a as for b but your answer didn't look right. I needed a quick check.
I put a = b = 1/2 at the start and got R = 1.
R = 1 and b = 1/2 doesn't give a = 1/2.
I think it's the first R = where the trouble starts. That fraction is the wrong way up. But I think a new approach will get you to the answer more quickly. Make 1/a the subject and when you've simplified to one fraction invert it for a.
Bob
Ok.
a , b and c are correct.
d ) If you subtracted 5 from t the result would be positive.
Bob
A friend told me that the answer is | t | > 5.
How can this be?
Each one contains a calculation. If the result is positive or zero then the absolute sign is redundant; you can simply leave it out. If the result is negative then the result must be made positive (by multiplying by minus 1). In all of these you can decide whether the result is + or - .
Bob
Can the definition of absolute value be used to solve these?
Given R = 1/[(1/a) + (1/b)].
Let me see.
LCD for [(1/a) + (1/b)] is ab.
I get (b + a)/(ab).
R = (b + a)/(ab)
(ab)R = b + a
abR - a = b
a(bR - 1) = b
a = b/(bR - 1)
You say?
Rewrite each of the following statements using absolute value notation.
(a) The distance between 12 and 5 is 17.
| 12 - 5 | = 17
(b) The distance between xand 2 is 4.
| x - 2 | = 4
(c) The distance between x and 2 is less than 4.
| x - 2 | < 4
(d) The number t is more than five units from the origin.
| t | + 5
Is any of this right?
Rewrite each expression in a form that does not contain absolute values.
How is this done?
(a) | pi - 4 | + 1
(b) | x - 5 | given that x > or = 5
(c) | t - 5 | given that t < 5.
I have deleted the posts in this thread as you have broken our rules by making a personal attack on another member.
I have also removed your signature as I find it equally offensive Any further infringements and you will be banned. Bob
All correct.
Bob
Perfect.
Given R = (1/a) + (1/b) + (1/c), express R as a rational expression.
Let me see.
LCD on left side is abc.
So, abc ÷ a = bc.
Then, abc ÷ b = ac.
Finally, abc ÷ c = ab
On the right side, I get (bc + ac + ab)/(abc), which is a fraction in terms of a, b, and c.
I say R = (bc + ac + ab)/(abc) is the answer.
You say?
Yes. If you can get a few right it suggests you've mastered the why.
Bob
Ok.
Tanx
No problem. You're welcome.
Be guided by your success with practice questions. If you're getting on well then move on; if you're having difficulties , you need to do more.
Bob
Isn't it better to understand math than to solve hundreds of problems like a robot? In other words, knowing the WHY is more important than quantity.
You say?
How many math questions per chapter should a person answer when doing a self-study of mathematics? If I answer every question, I will never complete the textbook.
You say?
How can i get his website??? Or his YouTube channel? Thanks
I don't know his website. However, just type his name using YouTube search. It will take you to his channel.