Sin³ x-sin x=cos ² x
we know that:
sin²x + cos²x=1 ⇒cos²x=1-sin²x
Therefore:
sin³x-sin x=1-sin²x
sin³x+sin²x-sin x-1=0
sin³x=z
z³+z²-z-1=0
we divide by Ruffini method:
1 1 -1 -1
1 1 2 1 z=1
-------------------------------------
1 2 1 0
-1 -1 -1 z=-1
--------------------------------------
1 1 0 z=-1
Therefore; the solutions are z=-1 and z=1
The solutions are:
if z=-1, then
sin x=-1 ⇒x= arcsin -1=π+2kπ (180º+360ºK) K∈Z
if z=1, then
sin x=1 ⇒ x=arcsin 1=π/2 + 2kπ (90º+360ºK) k∈Z
π/2 + 2kπ U π+2Kπ=π/2+kπ k∈Z ≈(90º+180ºK)
Answer: π/2 + Kπ or 90º+180ºK K∈Z
Z=...-3,-2,-1,0,1,2,3,4....
Because one is negative and one is positive
Answer: Population is 960 000
Step-by-step explanation: At the beginning time is zero and
population 60 000. We can count how many doubling happens.
Adding 274 hours four times, we get 274 , 548 , 822 and 1096.
So population doubles 4 times and we get numbers
120 000 240 000 480 000 and 960 000
We are given a side of the rectangle = 11 m.
Let us assume other side of the rectangle = x meter.
We know, formula for Perimeter of the rectangle :
Periemter = 2×one side + 2× other side .
We are given perimeter = 143 m.
Therefore,
2 × 11 + 2 × x = 143
22 +2x =143.
Therefore, (d) 2x + 22 = 143 equation can be used to determine the length of the longer side of the rectangle.