The cpi is currently 153. if a coffee maker costs $31.90 today, how much did one cost in 1983, to the nearest cent? a. $20.85 b.
2 answers:
One coffee maker's cost in 1983 was $20.85 if the current CPI is 153 option (a) is correct.
It is given that the CPI is currently 153 if a coffee maker costs $31.90 today. It is required to find how much did one cost in 1983.
<h3>What is CPI?</h3>It is defined as the tool to measure inflation that indicates between two periods how much cost is increased. It can be represented by for the given time 't'
The formula for finding the CPI:
Where is the cost in the current market
is the cost at the given period.
We have in the question:
Putting these values in the CPI formula, we get:
Thus, one coffee maker's cost in 1983 was $20.85 if the current CPI is 153.
Learn more about the CPI here:
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Answer:
12pi(8-pi), or
183.158 to third decimal place
Step-by-step explanation:
The geometry is indicated in the attached figure.
A. by integration
We will find the volume of the solid by the method of shells, i.e. we will integrate strips parallel to the axis of rotation to form many thin shells, then integrate to get the sum of all these shells.
For each shell, of thickness dy, we integrate strips of length located at y
L(x) = y(x)
and area
L(x)dy
Each strip is at a distance of (4-y) from
for which the volume of each shell equals
dV = 2*pi*(4-y)*L(x)dy = 2*pi*(4-y)*y(x) dy
The total volume of the solid can be obtained by integrating y from 0 to pi
integral( dV ) from 0 to pi
= integral (2*pi*(4-y)*y(x) dy) for y from 0 to pi
= 12*pi(-sin(y)+y*cos(y)-4*cos(y)) for y from 0 to pi
=12(8-pi)*pi
= 183.158
B. Using Pappus theorem
Pappus theorem simplifies the calculation of volume of revolution by multiplying the area of the rotating region by 2pi times the distance between the centroid and the rotation axis.
Here the area of the figure is A=2*6=12, (2 is the area under the sine curve from 0 to pi), or
A = integral (6sin(x))dx, x from 0 to pi
= 6 cos(x), x from 0 to pi
= 6(1- (-1))
= 12
Distance from centroid to axis of rotation = (4-pi/2)
Volume = 2*pi*A*(4-pi/2) = 2*pi*12*(4-pi/2)
= 12pi(8-pi)
=183.158 as before
