CPhill

tan (theta) =  (7 / -8)  

arctan (7/-8) = theta  = -41.1859°

The terminal point of this vector lies in the second quadramt....so the angle is

180 - 41.1859  ≈ 138.81407° ≈  138. 8141°

And this is the angle ( theta ) that the vector makes with the positive x axis

v =  < 1, - 1 >

w = < 1, 2  >

v1   = [ v (dot) w  ] / l w l^2  *  < w >

v(dot) w   =   1* 1 + 2* -1   =  1 - 2    =   -1

l w l  =  sqrt (1^2 + 5^2)   =  sqrt (5)           l w l ^2   = 5

So......

v1   =   -1 /  (5)  *  <1,  2 >     =   < -1/5, -2/ 5  >

v2  =  v - v1  =  < 1 - -1/5, -1 - - 2/5 >  =  < 1 + 1/5, -1 + 2/5 > =   < 6/5,-3/5 >

Check

Sum of v1 and v2    =  < -1/5 + 6/5, -2/5 + - 3/5 >   =  < 1  -1 >    = v

-4x(2x-3)+10x  =

-8x^2 + 12x + 10x =

-8x^2 + 22x

The on-site grapher is clunky.....I prefer Desmos, here : https://www.desmos.com/

Welcome, JW......!!!!!!

1in = 10 miles

(1 in)^2   = 1 in^2 =  (10 miles)^2   = 100mi^2

So

12.5  in^2  =   12.5 (100 mi ^2)   =  1250mi^2

So   1250mi^2  x 640 acres/mi^2   =  800,000 acres

If I multiply a number by 100 and the I devide it by -10, it is the same if I had multiplied by 10.

Not true.....

Multiplying by 100 and dividing by - 10   is the same as multiplying by  -10

220,000 =  2.2  x 10⁵

sin A  = 4/5

sin B   =   sqrt (r^2 - x^2) / r  =  sqrt (5 - 4) / sqrt (5)    =   1/sqrt (5)

tan A    =   [ 4/5[ / [3/5] =   4/3

tan B    =  [1/sqrt(5) / [ 2/sqrt (5)]  =  1/2

tan (A + B)   =   [ tanA + tanB] / [1 - tanA*tanB]  =   [ (4/3) + (1/2)] / [ 1 - (4/3)(1/2) ] =

[11/6] / [ 1 - 4/6]  =    [11/6] / [ 2/6]  =   11/2

70°..... sunny,......low humidity.....perfect camping weather.......!!!!