By the fundamental theorem of calculus,
Now the arc length over an arbitrary interval
is
But before we compute the integral, first we need to make sure the integrand exists over it.
is undefined if
, so we assume
and for convenience that
. Then
24-8b
24-(8*b)
i don’t know the exact way it is written on your test but it is something along those lines
Part A;
There are many system of inequalities that can be created such that only contain points D and E in the overlapping shaded regions.
Any system of inequalities which is satisfied by (-4, 2) and (-1, 5) but is not satisfied by (1, 3), (3, 1), (3, -3) and (-3, -3) can serve.
An example of such system of equation is
x < 0
y > 0
The system of equation above represent all the points in the second quadrant of the coordinate system.The area above the x-axis and to the left of the y-axis is shaded.
Part B:It can be verified that points D and E are solutions to the system of inequalities above by substituting the coordinates of points D and E into the system of equations and see whether they are true.
Substituting D(-4, 2) into the system
we have:
-4 < 0
2 > 0
as can be seen the two inequalities above are true, hence point D is a solution to the set of inequalities.
Also, substituting E(-1, 5) into the system we have:
-1 < 0
5 > 0
as can be seen the two inequalities above are true, hence point E is a solution to the set of inequalities.
Part C:Given that chicken can only be raised in the area defined by y > 3x - 4.
To identify the farms in which chicken can be raised, we substitute the coordinates of the points A to F into the inequality defining chicken's area.
For point A(1, 3): 3 > 3(1) - 4 ⇒ 3 > 3 - 4 ⇒ 3 > -1 which is true
For point B(3, 1): 1 > 3(3) - 4 ⇒ 1 > 9 - 4 ⇒ 1 > 5 which is false
For point C(3, -3): -3 > 3(3) - 4 ⇒ -3 > 9 - 4 ⇒ -3 > 5 which is false
For point D(-4, 2): 2 > 3(-4) - 4; 2 > -12 - 4 ⇒ 2 > -16 which is true
For point E(-1, 5): 5 > 3(-1) - 4 ⇒ 5 > -3 - 4 ⇒ 5 > -7 which is true
For point F(-3, -3): -3 > 3(-3) - 4 ⇒ -3 > -9 - 4 ⇒ -3 > -13 which is true
Therefore, the farms in which chicken can be raised are the farms at point A, D, E and F.
Answer:
(2001, 2125), (2006, 2360)
Step-by-step explanation:
An ordered pair refers to a pair of numbers or items in a simple and orderly manner. The order in which the items are grouped is very important. In graphs an ordered pair could be the coordinates of various points on the graph in terms of x and y, that is x and y coordinate (x,y).
From the question we are to form two ordered pair in the form (year, number of heart transplants).
to do this we simply fill out the items with their corresponding numbers where the first item is the year and second is the number of heart transplants.
in year 2001 we have (2001, 2125)
in year 2006 we have (2006, 2360)
