Answer:
Step-by-step explanation:
Consider the graphs of the 
and 
.
By equating the expressions, the intersection points of the graphs can be found and in this way delimit the area that will rotate around the Y axis.
then 
o 
. Therefore the integration limits are:
and 
The inverse functions are given by:
and 
. Then
The volume of the solid of revolution is given by:
![\int\limits^{64}_ {0} \, [2\sqrt{y} - \frac{y}{4}]^{2} dy = \int\limits^{64}_ {0} \, [4y - y^{3/2} + \frac{y^{2}}{16} ]\ dy = [2y^{2} - \frac{2}{5}y^{5/2} + \frac{y^{3}}{48} ]\limits^{64}_ {0} = 546.133 u^{2}](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B64%7D_%20%7B0%7D%20%5C%2C%20%5B2%5Csqrt%7By%7D%20-%20%5Cfrac%7By%7D%7B4%7D%5D%5E%7B2%7D%20%20dy%20%3D%20%5Cint%5Climits%5E%7B64%7D_%20%7B0%7D%20%5C%2C%20%5B4y%20-%20y%5E%7B3%2F2%7D%20%2B%20%5Cfrac%7By%5E%7B2%7D%7D%7B16%7D%20%5D%5C%20%20dy%20%3D%20%5B2y%5E%7B2%7D%20-%20%5Cfrac%7B2%7D%7B5%7Dy%5E%7B5%2F2%7D%20%2B%20%5Cfrac%7By%5E%7B3%7D%7D%7B48%7D%20%5D%5Climits%5E%7B64%7D_%20%7B0%7D%20%3D%20546.133%20u%5E%7B2%7D)
Answer:
Choice C is correct.
Step-by-step explanation:
put point A in (x+1,y-3)
now (-6,4) becomes (-5,1).
put point C in (x+1,y-3)
now (2,1) becomes (3,-2)
put point B in (x+1,y-3)
now (-3,-2) becomes (-2,-5).
9514 1404 393
Answer:
65 feet
Step-by-step explanation:
The problem involves finding the perimeter of a rectangle, then making adjustments to remove parts of the perimeter that aren't wanted.
The perimeter of a rectangle is given by the formula ...
P = 2(L+W)
For Aubrey's 12' × 8' room, the perimeter is ...
P = 2(12' +8') = 40'
This is the length of the border Aubrey needs at the ceiling.
__
At "waist-high", we need to subtract the total width of all the windows and doors. That total is ...
3' + 4' + 3' + 5' = 15'
So, the waist-high border is 40' -15' = 25'.
__
The total amount of border Aubrey needs is ...
ceiling border + waist-high border = 40' + 25' = 65'.
Aubrey needs 65 feet of border.
Answer:
The duty he has to pay is 156.25$.
Step-by-step explanation:
We know that for foreign-made vehicles imported into the U.S., whether new or used, either for personal use or for sale, are generally dutiable at the following rates: Cars: 2.5%.
From task we know that the Fiat car abroad that cost him $6,250.
We have the following proportion:
The duty he has to pay is 156.25$.
You can answer it in fraction or decimal.
Fraction: In fraction, write 9 above 917 like this: 9/917. That is the answer in fraction.
Decimal: In decimal, do the long-division algorithm. You should get 0.009815.
