geno3141

It is just 21r^3.

You can set up a proportion:     time / distance  =  time / distance

      28 min / 8 mi    =    x / 15 mi

Cross multiply:

     8 · x  =  28 · 15     --->     8x  =  420     --->     x  =  

To estimate the correctness of your answer since 15 min is a little less than twice 8 min, your answer should be a little less than twice 2 min.

A positive times a negative is negative.

The rules of operation tells us to do multiplications before addition.

0,5 * -3  =  -1,5

-3 * 3  =  -9

-1,5 - 9 + 3  =  -7,5  

This question can lead to some serious stuff  --

For instance if nothing is something, then it can't be nothing anymore ...

But, if nothing is nothing, by the fact that it "is", it must exist, therefore it is something and one's brain begins to explode ...

But, Western thought (possibly horrendously) is continually brought back to the work of Plato and Aristotle and their ideas. Aristotle's work on Logic, provided only two possibilities, true or false, and this influence exists to this day, even though mathematical logic provides with greater possibilities.

There was no symbol for zero in Western mathematics until past the Middle Ages, partially due to the philosophy (which was backed by religion) that if you gave "nothing" a symbol, it became something and then you are messing with God's creation and then you are in deep trouble.

Possibly, the question "Is nothing something?" is confusing only because our brains haven't been sufficiently developed to answer this question, or that the creation of our language made this a confusing question.

Actually, if you read a little about modern physics with its quantum mechanics, you read about items that are both here and there and wherever, all at the same time.

So, keep asking strange questions because then you are invited into strange, and marvelous places.

2 ^ -4     =    1 / 2^4    =    1 / 16    =    0.0625

If you have a number to a negative exponent, rewrite that number in the denumerator with a positive exponent.

Place them in the same order as they are written in the triangle similarity:

     CG / MK     =     GJ / KP     =     JC / PM

First, factor out the x² term:     x²(121x² - 36)  =  0

Now, factor the remaining term as the difference of two squares:

                                              x²(11x - 6)(11x + 6)  =  0

Set each of the factors equal to 0:          x² = 0         11x - 6  =  0          11x + 6  =  0

Finally, solve each of these reduced equations.

First, factor out an x:     x(100x² - 121) = 0

Now, use he idea of the difference of two squares:  x(10x-11)(10x+11) = 0

To solve this equation, set each factor to zero:  x = 0     10x - 11  =  0        10x + 11 = 0

Now, solve each of the three little equations.

Since  x / x = 1, if you have a string of multiplications in the numerator and a string of multiplications in the denominator, you can cancel one factor in the numerator with an equal factor in the denominator.

(3x^5) / (5x^7)     =     (3·x·x·x·x·x) / (5·x·x·x·x·x·x·x)

The five x-factors in the numerator will cancel five x-factors in the denominator; so the answer reduces to:

     =  (3) / (5·x·x)     =     3 / (5x²)

(This can be done, in division, more simply by subtacting the exponents (7 minus 5) and since the greater number of x's is in the denominator, the value of x² is in the denominator. 

If the scale is 18" x 36" with the width represented by the 18" and the length represented by the 36",

these value can be changed into feet by dividing by 12:  18" = 1.5' and 36" = 3'. 

If the real length is to be 9' while the scale is 3', the multiplying factor (the expansion factor) is 3.

(Because 9' ÷ 3'  =  3.)