Answer:
Slope=-1
Step-by-step explanation:
Slope=y1-y2/x1-x2
Where (X1,y1)(0,8) and (X2,y2) (4,4)
Slope=8-4/0-4
=4/-4
=-1
So slope is -1
1) The graph consists of three horizontal segments, with discontinuities (jumps) at x = 1, x = 2, and x = 3.
A horizontal segment at y = - 2 for the values x = 0 to 1.
A horizontal segment at y = - 1 for values x = 1 to 2
A horizontal segment at y = 0 for values x - 2 to 3.
2) To know whether the end points of a segment are defined by the left or the right values you have to look for the circle at the extreme of the segment: if it is a solid dot, means that the end is included, if is is an open circle (white inside) then the end is not included in that segment.
3) That function is based on the function named integer part because if relates y with the integer part of x.
The integer value function is [x] and it makes correspond y values witht he integer values of x.:
y = 0 witht the integer value of x for x between 0 and 1, excluding 1.
y = 1 with the integer value of x between 1 and 2 (excluding 2)
y = 2 with the integer value of x between 2 and 3 (excluding 3)
y = 3 with the integer value of x between 3 and 4 (excluding 4)
But our function is two units below, so it is [x] - 2
Step-by-step explanation:
We start with Left hand side
We know that csc(x) = 1/ sin(x)
So csc(2x) is replaced by 1/sin(2x)
Also we use identity
sin(2x) = 2 sin(x) cos(x)
4 divide by 2 is 2
Now we multiply top and bottom by sin(x) because we need tan(x) in our answer
We know that sinx/ cosx = tan(x)
Also 1/ sin(x)= csc(x)
so it becomes 2csc^2(x) tan(x) , Right hand side
Hence verified
A. Let x = cheese and
y = chocolate
2x + y = 25
x + y = 20
B. Subtract the second equation from the first.
2x + y = 25
-(x + y = 20)
-—————
x = 5
Plug 5 back in to the second equation and solve for y.
x + y = 20
5 + y = 20
Subtract 5 from both sides.
y = 15
5 cheese and 15 chocolate
Used elimination method because coefficients on the y values were both 1 so it was easy to subtract the equations and eliminate the y variable.
