9 times
A line passing through the origin and perpendicular to the line 4x + y = k will have a slope of (1/4) and the equation of this line will be y = (1/4)x
And at (t, t +1 ) we have that
t + 1 = (1/4)t
(3/4) t = -1
t = -4/3 then t + 1 will = -1/3
And we can find k as
4t +[ t + 1 ] = k
-16/3 - 1/3 = k = -17/3
Here's a graph of both lines and the intersection point :.......https://www.desmos.com/calculator/c5qsf7jlo2
0.785*x^2=78.5 divide both sides by 0.785
x^2 = 100 take the pos/neg square roots of each side
x = pos/neg sqrt(100) = pos/neg (10)
Don't we at least get a donut, DS?????
sin2x - cosx = 0
2sinx cos x - cosx = 0 factor out cosx
cosx [ 2sinx - 1] = 0 set each factor to 0
cosx = 0 and this happens at 180°
2sinx - 1 = 0 add 1 to both sides
2sinx = 1 divide by 2
sinx = 1/2 and this happens at 30° and at 150°
The married ones survived.......??????
x=y-3
x+3y=13 substituting the first equation for x into the second, we have
[ y - 3] + 3y = 13 simplify
4y - 3 = 13 add 3 to both sides
4y = 16 divide both sides by 4
y = 4
And using the first equation, x = 4 - 3 = 1
Let the number of plants in each row = x.........then, the number of rows was 9 more = x + 9
And the number of plants in each row times the number of rows = 52
x(x + 9) = 52
x^2 + 9x = 52 subtract 52 from each side
x^2 + 9x - 52 = 0 factor
(x + 13) ( x - 4) = 0
Only the second factor produces a positive result when set to 0.....so .....x = 4 .....and this is the number of plants in each row
3.516 x 107
You're welcome, GL......don't be a stranger.....!!!!
See ya' next time.....
