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....
Answer:
At least 4 numbers of information is needed
The four are highlighted below in the explanation section
Step-by-step explanation:
1. Given that the shape has four right angles and that all its sides are congruent then it's a quadrilateral
2. If two sides are consecutively congruent it is a quadrilateral shape
3. If a rhombus contains a right angle, then it’s a square shaped rhombus
4. If a quadrilateral is both a rectangle and a rhombus, then it’s a square
A is the only number line that correctly shows the locations of all given values.
Answer=A
***EDIT***
Okay, so if you look at the number line, you notice that the distance between one line and the next is equal to 1/4. When we move to the left, we decrease in value. When we move to the right, we increase in value.
So, knowing that, lets look at A and see if all of the numbers are correctly placed.
1/2 should be two lines to the right of 0 (since distance between one line and the next is equal to 1/4, and 1/4+1/4=2/4 or 1/2)
-4 is a relatively easy value to find, since its line is labeled.
-2 3/4 should be three lines to the right of -2 (since distance between one line and the next is equal to 1/4, and 1/4+1/4+1/4=3/4 and if you go 3/4 to the left of -2 u get -2 3/4)
(-2-3/4=-2 3/4)
1 1/4 should be three lines behind 2 (since distance between one line and the next is equal to 1/4, and 1/4+1/4+1/4=3/4 and if you go 3/4 to the left of 2 you get 1 1/4)
(2-3/4=1 1/4)
Answer:
10. x= 10 y=sqrt 200
11. x=y=450
12. x=19 y=sqrt 1083
13. x=sqrt 48 y=sqrt 12
Step-by-step explanation:
10.
x and 10 are the same
10^2+10^2=200
sqrt 200 is not a whole number so y is just sqrt 200
11.
30^2=2x^2 because x and y are the same
x^2=450
sqrt 450 is not a whole number so x and y are just sqrt 450
12.
x= 38 divided by 2=19
38^2=19^2+y^2
1444=361+y^2
y^2=1083
sqrt 1083 is not a whole number so y is just sqrt 1083
13.
x^2=(x/2)^2+36=x^2/4+36
x^2=48
sqrt 48 is not a whole number so x is just sqrt 48
y is half of x so it is sqrt 12
