Answer:
Step-by-step explanation:
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line but that need not be straight. Thus, a curve is a generalization of a line, in that its curvature need not be zero.
Answer:

Step-by-step explanation:
The slope of a line can be seen as:

Rise over run is the change in the y values over the change in x values. For example, in this graph, you would start on one of the points given. From there, you would move up first. After moving up a certain number of spaces, you would move to the side until you reach the other point.
In the graph, you would move up until you are in line with one of the other points. Starting at (-4,5), move up one space, then to the left 4 spaces to reach the point (0,6). Using the spaces moved in the rise over run:

Therefore, the slope is
.
This is true for any two points on the line.
:Done
*When you move up, the number will be positive
. If you move down, the number will be negative
. If you move left, the number will be positive
. If you move right, the number will be negative
. Keep this in mind. It is very important.
**Always <em>move along the y-axis first</em>, then move along the x-axis. If you do it the other way, the slope will be wrong.
Answer:
Common Difference = 2.
Step-by-step explanation:
An AP can be written as a1, a1 + d, a1 + 2d, a1 + 3d, a1 + 4d, a1 + 5d, a1 + 6d , a1 + 7d.
where a1 = first term and d is the common difference.
Here first term = a1 = 8
3rd term = a1 + 2d = 8 + 2d
5th term = a1 + 4d = 8 + 4d
8th term = 8 + 7d
First 3 terms of a GP are a , ar and ar^2
So from the given information:
a = 8 + 2d
ar = 8 + 4d
ar^2= 8 + 7d
Dividing the second equation by the first we have
r = (8 + 4d)/(8 + 2d)
Dividing the third by the second:
r = (8 + 7d) / (8 + 4d)
Therefore, eliminating r we have:
(8 + 4d)/(8 + 2d) = (8 + 7d)/(8 + 4d)
(8 + 4d)^2 = (8 + 2d)(8 + 7d)
64 + 64d + 16d^2 = 64 + 72d^ + 14d^2
2d^2 - 8d = 0
2d(d^2 - 4) = 0
2d = 0 or d^2 = 4, so
d = 0, 2.
The common difference can't be zero so it must be 2.
Answer:

Step-by-step explanation:
A = the area of the region outside the semicircle but inside the rectangle
w = the width of the rectangle or diameter of the semicircle
Since "A" is determined by "w", therefore, "A" is a function of "w" = A(w).
A(w) = (area of rectangle) - (area of semicircle)

Where,
lenght of rectangle (l) = w + 5
width of rectangle (w) = w
r = ½*w = 
Plug in the values:


Simplify




