Question

Find the angle between the given vectors to the nearest tenth of a degree. u = <8, 4>, v = <9, -9> help please!!

Answer 1

use the formula

\[\Large \theta = arcos\left( \frac{u \cdot v}{|u||v|}\right )\]

Answer 2

where

|u| = length of vector u

|v| = length of vector v

Answer 3

I got 71.6degrees is that correct?

Answer 4

close enough, I'm getting 71.56505117707799

which rounds to 71.6

Answer 5

okay thank you!

Answer 6

yw

Answer 7

could you help me with this one too? Given that P = (-7, 16) and Q = (-8, 7), find the component form and magnitude of QP

Answer 8

if you want QP, then you subtract the corresponding coordinates

x: -7 - (-8) = -7 + 8 = 1

y: 16 - 7 = 9

So the vector QP is <1,9>

If you wanted vector PQ, you would flip the signs to get <-1,-9> since it's just going in the complete opposite direction

Answer 9

The magnitude of QP is equal to sqrt(x^2+y^2) where x and y are the components of the vector

Answer 10

okay I got.... (1, 9), 82

Answer 11

should be \[\Large \sqrt{82}\]

Answer 12

okay, thank you! on this question I keep getting 28, -6....but i know thats wrong.....Let u = <-6, 3>, v = <-1, -6>. Find 4u + 2v.

Answer 13

that's not correct

Answer 14

4u means you multiply each component of vector u by 4

Answer 15

u = <-6, 3>

4u = 4*<-6, 3>

4u = <4*(-6), 4*3>

4u = <-24, 12>

Answer 16

Do the same for 2v

Answer 17

Then add the resulting vectors

Answer 18

-26,0 got it...still up for more help :) lol

Answer 19

<-26, 0> is correct

Answer 20

and I can do one more

Answer 21

Determine whether a triangle can be formed with the given side lengths. If so, use Heron’s formula to find the area of the triangle.

a = 240
b = 121
c = 302

Answer 22

if a triangle with side lengths a, b,c could be formed, then ALL of the following must be true

a+b > c

a+c > b

b+c > a

Answer 23

basically, the sum of any two sides must be larger than the third side

Answer 24

so no triangle can be form?

Answer 25

nevermind..

Answer 26

so what's next

Answer 27

let's see

a+b > c

240+121 > 302

361 > 302

So that's true

Answer 28

a+c > b

240+302 > 121

542 > 121

that's true as well

Answer 29

b+c > a

121+302 > 240

423 > 240

and that's true

Answer 30

So all 3 are true, meaning that a triangle could be formed

Answer 31

now how do I got about finding the area..

Answer 32

Now you must find the semi-perimeter S

S = (a+b+c)/2

Answer 33

332.5

Answer 34

now use that, along with a,b,c in the formula below

A = sqrt( S*(S-a)*(S-b)*(S-c) )

this is heron's formula

Answer 35

and it's used to find the area of any triangle if you know all 3 sides (it doesn't have to be a right triangle and you don't have to find the height)

Answer 36

24,172.48 correct?

Answer 37

let me check

oh and btw, you can read more about heron's formula here

http://en.wikipedia.org/wiki/Heron%27s_formula

Answer 38

no that's way too high

Answer 39

ahhh I see what I did... 13,724.27?

Answer 40

much better

Answer 41

thank you sooooo much for all the help! I can't thank you enough!!

Answer 42

yw