Answer:
C.
Step-by-step explanation:
The line that is a perpendicular bisector of the segment connecting the two points.
Answer:
Step-by-step explanation:
Given the equation
Sin(5x) = ½
5x = arcSin(½)
5x = 30°
Then,
The general formula for sin is
5θ = n180 + (-1)ⁿθ
Divide through by 5
θ = n•36 + (-1)ⁿ30/5
θ = 36n + (-1)ⁿ6
The range of the solution is
0<θ<2π I.e 0<θ<360
First solution
When n = 0
θ = 36n + (-1)ⁿθ
θ = 0×36 + (-1)^0×6
θ = 6°
When n = 1
θ = 36n + (-1)ⁿ6
θ = 36-6
θ = 30°
When n = 2
θ = 36n + (-1)ⁿ6
θ = 36×2 + 6
θ = 78°
When n =3
θ = 36n + (-1)ⁿ6
θ = 36×3 - 6
θ = 102°
When n=4
θ = 36n + (-1)ⁿ6
θ = 36×4 + 6
θ = 150
When n =5
θ = 36n + (-1)ⁿ6
θ = 36×5 - 6
θ = 174°
When n = 6
θ = 36n+ (-1)ⁿ6
θ = 36×6 + 6
θ = 222°
When n = 7
θ = 36n + (-1)ⁿ6
θ = 36×7 - 6
θ = 246°
When n =8
θ = 36n + (-1)ⁿ6
θ = 36×8 + 6
θ = 294°
When n =9
θ = 36n + (-1)ⁿ6
θ = 36×9 - 6
θ = 318°
When n =10
θ = 36n + (-1)ⁿ6
θ = 36×10 + 6
θ = 366°
When n = 10 is out of range of θ
Then, the solution is from n =0 to n=9
So the equation have 10 solutions in the range 0<θ<2π
Answer:
Step-by-step explanation:
Recursive formula
tn = t_n-1 / 4
t2 = t1 / 4
t2 = 10240
t1 = 10240 / 4 = 2560
Explicit formula
tn = 10240 / 4^(n-1)
t4 = 10240 / 4^(4 - 1)
t4 = 10240 / 4^3
t4 = 10240 / 64
t4 = 160
t8 = 10240 / 4^7
t8 = 0,625
Answer:
Condition 1: y>0
Condition 2: x+y>-2
Step-by-step explanation:
We are told that we have a set of points in the Cartesian system (i.e. x-y coordinate), so we can define our point as:
We are given two conditions and we want to create a system of inequalities. Now, generally speaking, inequalities are expressions relating mathematical expressions through 'comparison' (i.e. less than, greater than, or less/greater and equal to) usually recognized by 
, 
, 
and 
, respectively.
So in our case let set up our inequalities.
Condition 1: the y-coordinate is positive
This can be mathematically translated as
(i.e. 
is greater than 0, therefore positive)
Condition 2: the sum of the coordinates is more than -2
This can be mathematically translated as
(i.e. the summation of the two coordinates is greater than -2 but not equal to).
The system of inequalities described by the two conditions is:
I'll use subscript notation for brevity, i.e.
3.
By the chain rule,
4.
By the chain rule,
