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....
Basically each part of the first complex number gets multiplied by each part of the second complex number. You are multiplying 2 binomials.
(15 + 56i(7 + 4i)
= 105 + 60i + 392i + 224i^2
= 105 + 452i - 224 ( because i^2 = -1)
= - 119 + 452i
Answer:
(Abbys slope 2/3) (Brandons slope 2/3) Abby is correct both triangles have the same slope.
Step-by-step explanation:
Answer:
600 cubic feet of water
Step-by-step explanation:
If the pool is filled 4 feet and the pool is 5 feet deep, that leaves 1 foot of depth left to fill. This makes the volume equation 30 x 20 x 1 which equals 600.
The amount of interest for $5000 investment that earns 4% per year such that 1$ is $1.040742 a the end of the year will be as follows:
A=P(1+r/100)^n
P=principple
r=rate
n=time
Thus
Amount at the end of the year will be:
A=5000(1+4/100)^1=5200
thus interest earned will be:
5200-5000
=$200
