1.Calculate [ ( -2 ) ^ 0 y ^ -1 ( 2y ) ^ 3 / ( 2y ^ -2 ) ^ -1 y ^ -
4 ]
2. Use the absolute value notation " | | " to describe :
a. x is farther from 0 than it is from 5 .
b. x is more than b units from a but less than c units from a .
Brian's solution:
The first problem is not properly written and intended to give the
student grief.
Look at the part 0y^
Looking at it from this view, it is firmly agreed to mean …0*y^ …
Looking at the view (-2)^0y, it can be argued either way whether it
means 0*y or (0*y). However the second exponential sign means we
must accept the first interpretation.
However, from what I've seen, there are only certain times when
formulas can be written without using the multiplication sign.
In the formula (2x+1)(x+3)=2x^2+7x+3 there 4 multiplication signs
that are understood but not written. We can put bracketed terms or
exponentials together or other simple terms such as trig functions
together and it is understood that they are multiplied. We can put a
number in front of terms and it is understood that they are
multiplied. It is understood because it is done very commonly. It
is introduced to students without thinking and the students pick it
up automatically. If some stupid teacher tried to explain it, the
students would never grasp it.
However, if you have (-2)^0 times y^-1, then you cannot put them
together without a multiplication sign. This is never done. You
could if the 0 was written on a higher level as a superscript.
Mathematics doesn't have a lot of rules. Some you will not find this
written anywhere. It is like working for a company. There are too
many unwritten rules to write down, but if you violate any of them,
you will be on the way out and everyone else will know it.
When I see a term such as 0y or –1y or –1(2y), I think of the term as
being something that cannot be broken apart. That is why this
equation will throw people off.
However, it we have
0y^ always by convention means 0*y^
-1(2y)^ always by convention means –1*(2y)^
-1y^-4 always by convention means –1*y^-4
Your equation should never have been written in such a confusing and
incorrect manner, but after thinking about it for a couple days, the
only possible way to evaluate it is as:
[ ( -2 ) ^ 0 * y ^ -1 * ( 2y ) ^ 3 / ( 2y ^ -2 ) ^ -1* y ^ -4 ]
It then becomes trivial:
( -2 ) ^ 0 * y ^ -1 * ( 2y ) ^ 3 / ( 2y ^ -2 ) ^ -1* y ^ -4
= + + +1 * y ^ -1 * ( 2y ) ^ 3 / ( 2y ^ -2 ) ^ -1* y ^ -4
= + + + + y ^ -1 * ( 2y ) ^ 3 / ( 2y ^ -2 ) ^ -1* y ^ -4
= + + + + + + + + 8 * y ^ 2 / ( 2y ^ -2 ) ^ -1* y ^ -4
Here's another trap. Many students think the denominator after the
slash extends to the right forever, but it doesn't.
= + + + + + + + + 8 * y ^ 2 * ( 2y ^ -2 ) * y ^ -4
= + + + + + + + + 16* y ^ -4
= 16* y ^ -4 answer
I'm guessing your teacher wanted the answer to be 16. However when
we divide by (2^-2)^-1, this is like a triple negative. I stand by
my answer.
Question 2 is more fun. I agree with Rich's answer, but would carry
it further
2. Use the absolute value notation " | | " to describe :
a. x is farther from 0 than it is from 5 .
b. x is more than b units from a but less than c units from a .
Solution:
By farther, they mean absolute value of the difference between x and
0
which can be written
Ix-0I or I0-xI or IxI. You can use the greater than sign < or > to
indicate that the distance is greater.
Ix-0I>Ix-5I
Now this wasn't asked for, but we can square both sides. Since both
sides are positive, the direction of the greater than sign will not
change.
x^2 - 0x +0 > x^2 – 10x + 25
We can subtract x^2 from both sides.
0 >– 10x + 25
We can add 10x to both sides
10x > 25
We can divide both sides by 10
x>2.5
Regards,
Brian
--- In Math4u@yahoogroups.com, dghbosa alias <redgate3000@...> wrote:
>
> Hi everyone can you help me to solve these questions :
>
> 1.Calculate [ ( -2 ) ^ 0 y ^ -1 ( 2y ) ^ 3 / ( 2y ^ -2 ) ^ -1 y
^ -4 ]
>
> 2. Use the absolute value notation " | | " to discribe :
>
> a. x is farther from 0 than it is from 5 .
>
> b. x is more than b units from a but less than c units from a .
>
>
> ---------------------------------
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Try it now.
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