a .05 x = 1 x is the years to double
b (1.05)x =2 x is the years to double
c (1+ .05/2)2x = 2 x is the years to double
d (1 + .05/12)12x = 2 x is the years to double
common denominator is x (x+6) = x^2 +6x
[3 (x+6) - x(x) ] / x^2+6 = 18 / x^2 + 6 equate the numerators
3x+18 - x^2 = 18
3x = x^2
+-3 = x (throw out -3)
From first equation x = -3y/(1-k) sub this in to the second equation
3 (-3y)/(1-k) + y(1-k) = 0
-9y + y (1-k)^2 = 0
y ( k^2-2k-8) = 0 already stated y cannot be 0
(k+2)(k-4) = 0 k = -2, 4 (if I did the math correctly !)
Shape is a rectangle and triangle
Rectangle area = l x w = 9 x 20
triangle area = 1/2 b h = 1/2 9 x 5 Add them together
https://web2.0calc.com/questions/please-help_4628
rate x time = distance
rate1 = 40
rate 2 = 30 m/hr
t1 = t
t2 = t + 1/3 (1/3 = 20 minutes)
Equate the distances
40 t = 30 (t+1/3) solve for t then distance = 40 t
I believe the highest range would be -5 * -2 = 10
the lowest would be 3 * -2 = -6
[-6,10]
Let me know if this incorrect .... I am always learning too !
I will assume there cannot be a 0 in the first position
2 choices for first digit
3 choices for 2nd
3 choices for 3rd
3 choices for 4th
2 x 3 x 3 x 3 =....... choices
What do you know about cyclical quadrilaterals in a circle ? ( opposite angles sum to 180o )
What do you know about interna angles in a pentagon? (108o )
Now look at this diagram:
Tan 70 = opposite side /adjacent side
tan70 = height / 12 solve for height