CPhill

Thanks, Melody, for that reference......

a.  u + v   =  < 2i + 10i, -5j - 25j >   =   < 12i - 30j >

b.  This doesn't make any sense to me......

c.  u (dot) v  = ([2)(10)  + (-5)(-25)]   =  20 + 125  = 175

d.  The unit vector  is given by :   < 2 / sqrt [ 2^2 + (-5)^2]i , -5 / [ 2^2 + (-5)^2] j >   =

< 2/sqrt(29) i  , -5/sqrt(29) j >

e.  For the vectors to be orthogonal, the dot product would have to = 0......it was shown in (c) that this is not the case

sin(62) / 10  = sinB / 7

sinB  = 10sin(62)  / 7

sin^-1 [7sin(62)  /10 ] =  B   = about 38.17°

To see if we have another possible triangle,  subtract 38.17 from 180   = about 141.83°

Note.......that when we add this to 62° we exceed 180°.....so.....only one triangle is possible

f(θ) = −1.75 cos(1/2(θ + 60°))   we can simplify this as

f(θ) = −1.75 cos([θ/2 + 30°]

The period is given by

θ/2   = 360°

θ = 720°

The amplitude is  =  abs [ -1.75]   = 1.75

Here's the graph :  https://www.desmos.com/calculator/7mhnsqww6c

We have this :

8^2 + L^2   = (L + 4)^2      simplify

64 + L^2   = L^2 + 8L + 16     subtract L^2 from both sides

64  = 8L + 16        subtract 16 from  both sides

48  = 8L      divide both sides by 8

6 ft = L    and this is the length of the other leg.......and the hypotenuse  is 4 feet more = 10 ft

I assume that we have this : -19/[17v]  

Since the denominator cannot = 0, the only thing that makes this undefined is when v = 0

Heck....you beat me to it, LambLamb.....!!!!!

All we need is one counter-example to show that this is not generally true......consider

a/b/c =  a*c/b   ???

24/3/2  =  24*2/3       ???

8/2 = 48/3  ???

4  = 16  ???   .......nope

Let L   be the original length

Then

L (1.18)   = 25       divide both sides by 1.18

L = about 21.18644 cm

Check that     [  25 - 21.18644] / 21.18644   =  about 18%

x(x^2-1)/ (1-x^2 )       factor  a negative out of  (x^2 - 1)   = - (1 - x^2)      ......and we have....

[x] [ - (1 - x^2)]  / (1 - x^2)  =

[-x (1 - x^2)] / (1 - x^2)  =

-x       [   this is a good "trick" to remember.....!!!!]