Answer:
Step-by-step explanation:
<u>Slope-intercept </u><u>form</u>
y= mx +c, where m is the slope and c is the y-intercept
Line p: y= -8x +6
slope= -8
The product of the slopes of perpendicular lines is -1. Let the slope of line q be m.
m(-8)= -1
m= -1 ÷(-8)
m= ⅛
Substitute m= ⅛ into the equation:
y= ⅛x +c
To find the value of c, substitute a pair of coordinates that the line passes through into the equation.
When x= 2, y= -2,
-2= ⅛(2) +c
Thus, the equation of line q is 
.
That is a 45 degree angle on the side
The longest piece is 24 ft and the smallest piece is 4 ft
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....
