Since all the variables cancel out and the coefficient equal to eachother, this system of equation has
<u>infinitely many solutions!</u>
In case you're not already aware, the expression 
is called the "difference quotient" and represents the average rate of change of a function 
over an interval ![[x,x+h]](https://tex.z-dn.net/?f=%5Bx%2Cx%2Bh%5D)
.
For the function 
, by substituting 
we get
Then the difference quotient is
where the last equality holds as long as 
.
I'm only going to alter the left hand side. The right side will stay the same the entire time
I'll use the identity tan(x) = sin(x)/cos(x) and cot(x) = cos(x)/sin(x)
I'll also use sin(x+y) = sin(x)cos(y)+cos(x)sin(y) and cos(x+y) = cos(x)cos(y)-sin(x)sin(y)
So with that in mind, this is how the steps would look:
tan(x+pi/2) = -cot x
sin(x+pi/2)/cos(x+pi/2) = -cot x
(sin(x)cos(pi/2)+cos(x)sin(pi/2))/(cos(x)cos(pi/2)-sin(x)sin(pi/2)) = -cot x
(sin(x)*0+cos(x)*1)/(cos(x)*0-sin(x)*1) = -cot x
(0+cos(x))/(-sin(x)-0) = -cot x
(cos(x))/(-sin(x)) = -cot x
-cot x = -cot x
Identity is confirmed
No, line graphs are used only to show change over time
Answer:
e= -2
Step-by-step explanation:
1) distribute so you get 6+0.75e=2-1.25e
2) move the variable to one side so you get 6+2e=2
3) subtract the 6: 2e=-4
4) divide by 2: e= -2
