Question

The vector u = (3900, 5300) gives the number of units of two models of laptops produced by a company. The vector v = (2000, 1100) gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector operation used to increase revenue by 5%.

Answer 1

It's a scalar pruduct and a dot-product, right fewscrew?

Answer 2

*product

Answer 3

yes.

Answer 4

Yes.

Answer 5

so it looks to me like\[1.05\overrightarrow{u}*\overrightarrow{v}\]where that is a dot product above

Answer 6

the 1.05 should be tacked on to the v I guess, but it doesn't really matter as long as you don't distribute.

Answer 7

So identifying the operation to increase revenue, it is a scalar multiplication by 1.05. The other operation is just to find the revenue in the first place.
Seems to be what they want...

Answer 8

so would it be u*(1.05)\[\left| v \right|\]

Answer 9

or just (1.05)u*v

Answer 10

wait i meant 1.05(u*v)

Answer 11

if * represents the dot product, then they're all the same thing

Answer 12

well it would be just the \[1.05\overrightarrow{v}\]to increase the price, and\[1.05\overrightarrow{v}*\overrightarrow{u}\]which is the same as you have. Just don't distribute the scalar to BOTHand it should be the same.
^Yeah you got it...

Answer 13

@turingtest: that can't be distributed anyway\[c(\vec{u}\cdot\vec{v})\neq c\vec{u}\cdot c\vec{v}\]

Answer 14

well the options are put in different ways :
u*(1.05)\[\left| v \right|\]
1.05(u*v)
1.05\[\left| u*v \right|\]
1.05\[\left| u \right|\]*v

Answer 15

That's what I am saying, note that there are no parentheses is my point.

Answer 16

I'm trying to decipher what you wrote there ahaikal

Answer 17

didnt you say the 1.05 had to be attached to the v
as in U*(1.05)\[\left| v \right|\]

Answer 18

yeah i know it got all broken up idk why

Answer 19

its because i put that absolute value things

Answer 20

it doesn't matter in the end because you can't distribute the 1.05 as pre-algebra pointed out.
I am wondering if your bars are absolute value or magnitude, because you can't have the magnitude of a dot-product since it is already a number, and similarly you can't get the absolute value of a vector. So why are the symbols on both?

Answer 21

typically, with |x|, if x is a scalar, then that's just the absolute value, and if x is a vector, then that's the length/magnitude of the vector.

Answer 22

so if you take it that way^
then your formula is the same as mine

Answer 23

absolute value isn't mentioned in mine because all values are positive.

Answer 24

yes, but it must matter whether to put the parenthesis or not, or where to put the 1.05, because only one of the choices is correct. i think it is u*(1.05)v. (i just left our the absolute value sign or magnitude sign whichever)

Answer 25

ahaikal10, like turingtest said, the only answer that makes sense here is 1.05(u*v)=1.05*u*v=u*1.05*v=u*v*1.05=etc.

Answer 26

the parenthesis doesn't matter...

Answer 27

so do you have a multiple choice and the things pre-algebra had are given as different choices?

Answer 28

oh okay. yes i have multiple choice. so it would be 1.05(u*v)

Answer 29

looks like it :)

Answer 30

thank you very much guys :)