Choose region 2 from the Explore & Test page that is bounded by the curves y = (x − 3)2 when x ≥ 3, x = 0, y = 4. Set the axis of revolution to be the y-axis and use the first slider to rotate the region around the y-axis. The solid generated resembles a coffee cup without a handle. Move the second slider to see how the volume of the disks can be used to approximate the volume of the coffee cup.

V= 76 π cubic units

Step-by-step explanation:

y= ----->

Here we will apply the risk method.

Risk method: consider a strip of length x and width dy as

a) Radius= R(y) = x =

[We rotate this disc about y-axis to get a disk]

b) Cross-section area = A(y)= π

                                    = A(y)= π (y+9+6 )

--------> Volume of the disc = A(y) x dy

c) Required volume= v = A(y) x d(y)

                         V=  π (y + 9 + 6 ) dy

                         V=  π [

                          V= 76  π cubic units.

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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46.2+112.3

step-by-step explanation: