G= {(-5,5), (6, 8), (-5, -5)} What is the domain and range
1 answer:
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Answer:
116,280 different leadership structures are possible
Step-by-step explanation:
The order is important.
For example, a Committee of John, Elisa, Laura and Rose means that John is the chairperson, Elisa the vice-chairperson, Laura the secretary and Rose the treasurer. If we exchange John and Elisa, their roles are also exchanged. This means that we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
How many different leadership structures are possible
Permutations of 4 elements from a set of 20. So
116,280 different leadership structures are possible
Check the picture below.
notice, the period is the length of the part in the graph that is being repeated.
Answer:
volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( x + b )² dx
Step-by-step explanation:
Given the data in the question and as illustrated in the image below;
R is in the region first quadrant with vertices; 0(0,0), A(a,0) and B(0,b)
from the image;
the equation of AB will be;
y-b / b-0 = x-0 / 0-a
(y-b)(0-a) = (b-0)(x-0)
0 - ay -0 + ba = bx - 0 - 0 + 0
-ay + ba = bx
ay = -bx + ba
divide through by a
y = x + ba/a
y = x + b
so R is bounded by y = x + b and y =0, 0 ≤ x ≤ a
The volume of the solid revolving R about x axis is;
dv = Area × thickness
= π( Radius)² dx
= π ( x + b )² dx
V = π ₀∫^a ( x + b )² dx
Therefore, volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( x + b )² dx