The area= (20x14)/2
So, 20 times 14, divided by 2.
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
Answer:
222! thats your answer!
Step-by-step explanation:
1.The second industrial revolution refers to the changes in manufacturing and building, and the new inventions brought about by the introduction of inexpensive steel. After the Second Industrial Revolution cites were overcrowded because of the need of jobs for people. The streets of cities were overcrowded which had sanitation issues so, lots of people were getting sick as a result. Crime grew as a result of not enough police and because it was easy to lose the police in crowds of people. Devices such as cars, electric lights, and telephones made the middle class's life more enjoyable. People who did urban planning reforms such as trolly parks made it so the working class could spend their extra time and money on something enjoyable.
2.One of the largest effects that we still deal with all over the war is Slavery. The Atlantic Slave Trade is a well-known trade route used to trade slaves and items through Africa.Through the trade and conquering of Africa by the Europeans, weapons and processed items were traded with the Africans.The trade of items allowed major groups to prosper and continue to grow. This eventually resulted in large African kings defending their lands against the powerful Europeans when they attacked.
3.Nationalism is patriotic feelings towards your country. Nationalism can cause terror or hate to other nations that you see as a threat to your way of life. I'll give you one example so as not to do the work for you. The Nazi's were a great example of strong nationalism.
The vertex is in essence the turning point of the parabola y = x²<span> − 10x + 2
the x coordinate of the turning point = </span>
=
= 5
when x = 5, y = (5)² - 10(5) + 2
= -23
Thus coordinate or vertex is ( 5, -23)
