Question

http://moodle.chca-oh.org/pluginfile.p

In the book we have, all the numbers were squared first.

http://prntscr.com/aris5u

We added the two numbers on the right first before subtracting them from the left side.
So, what the individual in the original post is doing is confusing me.

Why did he take away 6.7 and 7.1 before they were squared? Also, wouldn't that yield a positive number when combined with 4.4 squared?

Next, we are we dividing -2(6.7)(7.1)?

Why not multiply everything and then add what we multiplied to the left side when we were done to get Cos V?

Answer 1

@jim_thompson5910

I would like to understand some of his steps.

Answer 2

The first link doesn't work for me

Answer 3

I'm guessing the second link is a screenshot of the first?

Answer 4

Nope. Let me try again. It wasn't working for me either.

Answer 5

http://prntscr.com/arjzmi

How's this?

Answer 6

that's the same as the second link

Answer 7

Attached the wrong one haha.

http://prntscr.com/ark01b

Answer 8

`Why did he take away 6.7 and 7.1 before they were squared?`
you can decide to square the values 6.7 and 7.1 to get 50.41 and 44.89
then you can combine them and subtract the result from both sides

OR

you can just treat 6.7^2 as x^2 and move it to the left side by subtracting the expression from both sides. The same applies to 7.1^2

It really doesn't matter which method you choose. Often with math, there are multiple paths to the same answer

Answer 9

Ah, so he just combined the like terms basically and then squared?

Answer 10

More like he just kept it as 6.7^2 and 7.1^2 and moved them to the left side (by subtracting them from both sides). Then afterward the person used a calculator to compute 4.4^2-6.7^2-7.1^2 to get -75.94

Answer 11

If you squared the values 6.7 and 7.1 on the right side, you'd get 50.41 and 44.89 which combine to

50.41 + 44.89 = 95.3

then if you subtract 95.3 from both sides, you'd get

4.4^2 - 95.3 = -75.94

Answer 12

So that's another route to take

Answer 13

Oh, if that's so, wouldn't it turn -6.7^2 and -7.1^2 into positive numbers? So, when they're combined with the square of 4.4^2, wouldn't it produce a positive number? Where did the negative number come from?

Answer 14

you're mixing up `-6.7^2 ` with `(-6.7)^2`

Answer 15

-6.7^2 = -1*6.7^2 = -1*6.7*6.7 = -44.89

Answer 16

(-6.7)^2 = (-6.7)*(-6.7) = 44.89

Answer 17

Ah, that makes sense. Is there a reason that's why the way it is?

Perhaps a basic algebra rule I missed when I was learning algebra?

I assume this is an exponent or parentheses rule.

Answer 18

well PEMDAS says that parenthesis comes first, then exponents, then multiplication next

so if you had -6.7^2, which is really -1*6.7^2 you compute the `6.7^2` part first because exponents come first before multiplication. Then you'll have -1*44.89 which turns into -44.89

Answer 19

(-6.7)^2 means you square all of -6.7 including the negative portion

(-6.7)^2 is the same as (-6.7)*(-6.7). Ie two copies of -6.7 multiplied together

notice how the two negatives multiply to a positive

Answer 20

Most of that makes sense. I understood the PEMDAS reasoning and the multiplication reasoning.

Just having a bit of trouble understanding the
-6.7^2 = -1*6.7^2 = -1*6.7*6.7 = -44.89 part.

Answer 21

do you agree that if I had a number like -5, it's really the same as -1*5 ?

Answer 22

Yes! Oh, I see what you did there.

Alright, so, why is it -1*6.7*6.7 ?

I get that -6.7=-1x-6.7, but where does the -1x6.7x6.7 come from?

Answer 23

because

-6.7 = -1*6.7

and when you square something without parenthesis, you're only squaring that number

example

5*7^2 means we only square the 7 and not the 5 in front

Answer 24

Wouldn't that be 7x7?

Answer 25

5*7^2 turns into 5*7*7

Answer 26

5*7^2 does NOT turn into 5*5*7*7

if you want to square the 5, then you'll have to use parenthesis

(5*7)^2 = (5*7)*(5*7) = 5*5*7*7

is the correct way to do it

Answer 27

Alright, so why doesn't -6.7^2=-6.7x7?

Answer 28

because the 6.7 doesn't mean 6 times 7

it means 6 and 7 tenths

Answer 29

let's say we have this equation

10 = 5+x^2

we can get the x^2 to the other side by subtracting it from both sides to get

10-x^2 = 5

agreed?

Answer 30

Yes

Answer 31

ok let's say x is equal to 3

x = 3

that means

10-x^2 = 10-3^2 = 10-9 = 1

notice how I did the exponent first before subtraction

Answer 32

Yes I did!

Answer 33

so saying something like 10-6.7^2 means you subtract 10 minus whatever the result of 6.7^2 is

ie

10 minus (6.7^2) = 10 minus 44.89 = -34.89

Answer 34

the parenthesis I added in isn't necessary but it might be handy to put it in to see that you do the exponent first then subtract

Answer 35

I understand so far.

Answer 36

so you're able to see how that person got
-75.94 = -2(6.7)(7.1)cos(V)
??

Answer 37

Yes!

Answer 38

ok great

Answer 39

So, now, why do we divide? Why not just do 2(6.7)(7.1) and then add it to the other side?

Shouldn't we add it to both sides since we have to do the opposite?

Why are we subtracting and why are we dividing?

Answer 40

-2(6.7)(7.1) is being multiplied with the cosine

to undo this, we can divide both sides by the whole block -2(6.7)(7.1) which isolates the cos(V)

OR

we can multiply out -2(6.7)(7.1) to get -95.14 and then divide both sides by -95.14 to isolate the cos(V)

Answer 41

the person doing the work decided to divide both sides by the block -2(6.7)(7.1) and then used a calculator to compute the stuff on the left side to be approx 0.79819...

Answer 42

Ah, so if we multiply by both sides we don't change it into a positive?

Answer 43

Divide or multiply I mean.

Answer 44

you bring the negative over when dividing

eg:

-2x = 10

divide both sides by -2 to isolate x

-2x/(-2) = 10/(-2)

1x/1 = -5

1x = -5

x = -5

Answer 45

That makes sense.

Alright! Answered all my questions! Thanks again!

Mind if I ask two more and tag you?

They're shorter than the two I had here. : )

Answer 46

`Mind if I ask two more and tag you?` sure go ahead