Question

HELP!? WILL MEDAL!

Answer 1

I will do the first one for you and you will do the rest
1056-355 < Chicago to Houston < 1056+355
701 < Chicago to Houston < 1411

Answer 2

The other ones are similar

Answer 3

Are you with me?

Answer 4

@eliesaab, Not really but aren't inequality is like a+b >c ?

Answer 5

1584 - 355 > San Francisco and Chicago > 1584 + 355
1229 > San Francisco and Chicago > 1939
@eliesaab

Answer 6

If you put D=distance from Chicago to Houston, then
701<D< 1411
That distance is bigger than 701 and less than 1411

Answer 7

The other way around. The way you wrote it implies that 1229 > 1939 which is not true

Answer 8

1229 < SF and Chigago<1939

Answer 9

How do I know which way?

Answer 10

Or if you prefer you can write it as
1939> SF and Chicago>1229

Answer 11

Which means that distance is between 1229 and 1939

Answer 12

Did you get it?

Answer 13

@Awolflover1 @DanJS @harman.singh @mww @shaylynn16 @sweetburger @tHe_FiZiCx99 @zepdrix

Answer 14

B. 1584 + 355 > San Francisco and Chicago > 1584 - 355
1939> SF and Chicago>1229
C. 1018-1584 <NY and SF < 1018+1584
566 < NY and SF < 2602
D. 1056 - 1018 < Houston and NY < 1056 + 1018
38 < Houson and NY < 2074

Answer 15

Is that it?

Answer 16

@eliesaab

Answer 17

The triangular inequality in full is
\[||a|-|b|| < |a+b| < |a| +|b|\]
The latter is more familiar to you as the sum of two sides if greater than the third.
If you sub in your two pts for each city into this you should find your range of possible values for distance (which is the |a+b| bit)

Answer 18

But am I doing it correctly?

Answer 19

yes that looks right. All this is saying is if you disregard the angle between the points, and you just look at the distances from two pts to a third pt, you can automatically tell the range of distances between the points.

Answer 20

What do you mean ? o-o

Answer 21

If you have done vectors before, it should be familiar.
If you line up the distances of two vectors the longest distance is achieved when they are facing the same way and the shortest when they are facing 180 opposite ways.

Answer 22

Oh but the answers are correct?

Answer 23

yes.

A - B < distance vector AB < A+B
for A > B

Answer 24

So all of them are correct?
A. 1056-355 < Chicago to Houston < 1056+355
701 < Chicago to Houston < 1411
B. 1584 + 355 > San Francisco and Chicago > 1584 - 355
1939> SF and Chicago>1229
C. 1018-1584 <NY and SF < 1018+1584
566 < NY and SF < 2602
D. 1056 - 1018 < Houston and NY < 1056 + 1018
38 < Houston and NY < 2074

Answer 25

@mww