CPhill

LOL, DS.....!!!

If we have

3z^2+14z-5  =    0        factor

(3z - 1) (z + 5)  = 0     set each factor to 0 and we have that

z = 1/3   or    z = -5

Plain = "Plane"

We can find the resultant by summing the vector components.....

For the vector pointing "south," the x component is 0 and the y component =     3sin(270)  = 3*(-1)  = -3

For the one with the magnitude of 7  at 150 degrees, we have

7cos150   =  7*-sqrt(3)/2     = - (7/2)sqrt (3)   as the x component   and

7sin150  = 7*(1/2)  =  7/2     as the y component

The sum of the x components   = -(7/2)sqrt(3)

And the sum of the y components  =  -3 + 7/2 =  1/2

The resulting magnitude is given by :

sqrt [ (-7sqrt(3)/2)^2  + (1/2)^2 )  = sqrt(37)  = about 6.083

And the direction is given by:

arctan  [ (1/2) / (-(7sqrt(3)/2)]  =  about -4.715° + 180  = about 175.28° ........this has to be so  because the sum of the x components are negative and the sum of the y components are positive.....thus....this must be a 2nd quadrant angle

So......the resultant vector  = 6.083<175.28°  = (C) seems to come closest to this

What Hayley said........!!!!!

N_{next year}  = N_{this year}  +   0.2(N_{this year})( 1 - N_{this year} / K)     .....filling in what we know

N_{next year}    = 3000 + 0.2(3000)(1 - 3000/4000)  = 3150

So.....we need to use this result for next year to find the result two years from now.....and we have

3150 + 0.2(3150)(1 - 3150/4000)   =  about 3284  [rounded] two years from now

This makes sense, since the number of plants increases each year  [ until the "carrying capacity"  of 4000 is reached ]

I think this is supposed to be:

tan^2 (B)  = 4    if so........take the square root of both sides

tan (B)  = [+/- ] 2

tan (B) = -2  at about  117°  and at about 297°

And

tan (B)  = 2 at about  63°    and at about  243°

First question......he hasn't  yet had his 13th birthday this year......

sqrt(3) + sqrt(3)   = 2*sqrt(3)

The race is won by the fastest.....!!!.....LOL!!!!