algebra

- anonymous

algebra

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- chestercat

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- abb0t

This is \(\sf \color{red}{not}\) linear algebra.

- anonymous

i thought it is algebra

- abb0t

To find the magnitude, speed, \(|\sqrt{a^2+b^2}|\), where a = 3, b = 4. Now, to finf direction,
tan(\(\theta\)) = \(\frac{b}{a}\)

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## More answers

- anonymous

You don't need those \(|\) dude. \(\sqrt{\ldots }\iff |\sqrt{\ldots}|\)

- anonymous

magnitude = 5 m/s and direction theta = 53 degree

- abb0t

Hmm...that's how I remember it. But I guess I should check b4 hand next tym. Thanks @wio

- anonymous

and 53 degree would be northeast right????

- anonymous

Remember that \(|x|
\iff \sqrt{x^2}\) and \(\sqrt{x} \iff |\pm \sqrt{x}|\)

- anonymous

Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis.
For historical reasons, the word "algebra" has several related meanings in mathematics, as a single word or with qualifiers.

- anonymous

Algebra can essentially be considered as doing computations similar to that of arithmetic with non-numerical mathematical objects.[1] Initially, these objects represented either numbers that were not yet known (unknowns) or unspecified numbers (indeterminate or parameter), allowing one to state and prove properties that are true no matter which numbers are involved. For example, in the quadratic equation
ax^2+bx+c=0,

- anonymous

IN this case \(x=-3\), \(y=-4\)\[
\tan \theta = \frac y x \implies \theta = \tan ^{-1} \left(\frac {4}{3}\right)
\]

- abb0t

\(\huge o.O\)

- anonymous

Does algebra have a wee wee or a coochie?

- anonymous

We can start with a graph for this one, with arrows representing the two velocities...
3m/s west and 4m/s south|dw:1378455204639:dw|

- anonymous

Then we can draw an arrow for the change in velocity, which will go from the tip of the original (3m/s line) arrow to the tip of the final (4m/2) arrow

- anonymous

@Archie thats what i started with but i didnt write the axises

- anonymous

Do you have any ideas about how to find its magnitude?

- anonymous

ya x^2 + y^2 = 5

- anonymous

ohh|dw:1378455437063:dw|

- anonymous

Good idea! It looks like you're using the Pythagorean theorem. What does that give us for the length of the black arrow?

- anonymous

so you agree with abbots process right archie

- anonymous

its 5

- anonymous

right, would you like to go through how to get that answer together?

- anonymous

or are you fine?

- anonymous

sure go ahead

- anonymous

|dw:1378455660607:dw|

- anonymous

shoudnt 3 and 4 be negative bcz they are in opposite to x and y direction

- anonymous

|dw:1378455719936:dw|

- anonymous

Basically we can plug in the two shorter sides of the triangle for a and b in the Pythagorean theorem, then solve for the hypotenuse, c like it is written on the board. Also Good question, generally we just use the positive lengths of the sides... in the Pythagorean theorem even if they're going in the negative direction.

- anonymous

so magnitude of object's velocity is 5 m/s right?

- anonymous

But since, a,b and c are each squared, a^2, b^2 and c^2 will turn out to be positive either way.

- anonymous

right!

- anonymous

So, do you have any questions on that part or does it make sense?

- anonymous

arc tan -4/-3 = 53 degree that means it is in northeast direction

- anonymous

then we also need to state the direction of this change in velocity, so say which direction the black arrow is pointing. Which direction does that look like?

- anonymous

northheast

- anonymous

Good idea about using arctan... that gives the value of this angle here:
But not the direction of the black arrow, since there are other triangles that could have the same arctan to see the direction of the black arrow, we need to look at the graph. And state the direction we have to go to get from the end of the 3/ms arrow to the end of the 4m/s one.

- anonymous

Does it make sense why that is, or would you like me to explain it differently? xD

- anonymous

yep thx hey u know how to do transfer momentum

- anonymous

Yes! :)

- anonymous

Do you have a specific question on that?

- anonymous

ya just a sec lemme post it

- anonymous

already did ;)

- anonymous

ok, lol.

- anonymous

hey sry again but the direction is southwest or northeast

- anonymous

Southeast, because the red arrow points toward the southeast.

- anonymous

|dw:1378457820720:dw| there is no arrow pointing se...sorry lol confused again

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