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:
Parallel slope = -8
Perpendicular slope = 1/8
I dont know i just want coins lol
plus i just dont know
A= P(1+r)^t, where P= initial value, r= interest rate in %, and t = number of years.
However, if there isa decrease in value, the formula becomes:
A= P(1-r)^t and in our case :
A = 30,000(1- 0.24)^t OR A = 30,000(0.76)^t
Answer:
B
Step-by-step explanation:
Let point N has coordinates (0,0), then figure A has vertices at points (-3,0), (-7,0), (-7,4) and (-3,4). Figure B has vertices at points (3,1), (7,1), (7,-3) and (3,-3).
1. Translation 10 units to the right has the rule
(x,y)→(x+10,y).
Then vertices of the figure A have images:
- (-3,0)→(7,0);
- (-7,0)→(3,0);
- (-7,4)→(3,4);
- (-3,4)→(7,4).
2. Translation 3 units down has the rule
(x,y)→(x,y-3).
Then images are
- (7,0)→(7,-3);
- (3,0)→(3,-3);
- (3,4)→(3,1);
- (7,4)→(7,1).
As you can see these points are exactly the vertices of the figure B.
