The two parabolas intersect for
and so the base of each solid is the set
The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, 
. But since -2 ≤ x ≤ 2, this reduces to 
.
a. Square cross sections will contribute a volume of
where ∆x is the thickness of the section. Then the volume would be
where we take advantage of symmetry in the first line.
b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of
We end up with the same integral as before except for the leading constant:
Using the result of part (a), the volume is
c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is
and using the result of part (a) again, the volume is
Answer: 1.4
Step-by-step explanation:
Well lets look at it lets find multiples that equal 200 when multiplied first to get rid of extra work
so i just took a couple of guesses and lined them up
i got really close when i did this one
-200/30 = -6.666666667
30 + 6.666666667 = 23.33333333
see not quite there almost 25 but not far enough
so ill try to move the numbers around little by little.
-200/29.5 = -6.779661017
29.5 + -6.779661017 = 22.72033898
okay honestly after i finished this trial i wasn't sure if i was thinking straight because i completely didnt think about which way i needed to go so now i pinched myself and this time we might head the right way lol
-200/30.5 = -6.557377049
30.5 + -6.557377049 = 23.94262295
so obviously we need to move up alittle more
-200/31 = -6.451612903
31 + -6.451612903 = 24.5483871
HEY LOOK WE ARE ALMOST THERE!! lets try some more;)
-200/31.5 = -6.349206349
31.5 + -6.349206349 = 25.15079365
see we are at 25! but lets try to get rid of as many numbers behind it as possible.
-200/31.4 = -6.369426752
31.4 + -6.369426752 = 25.03057325
getting closer...
-200/31.39 = -6.371455878
31.39 + -6.371455878 = 25.01854412
what does this mean? this means we can go lower... sooo here we go
-200/31.38 = -6.373486297
31.38 + -6.373486297 = 25.0065137
i guess we can try lower..
-200/31.37 = -6.375518011
31.37 + -6.375518011 = 24.99448199
wait! before you leave! try 31.379
-200/31.379 = -6.37368941
31.379 + <span>-6.37368941 = 25.00531059
</span>okay so yes, i am taking the very long way but good comes to those with patience:D lets try making the third place after the decimal a little bit lower
-200/31.377 = -6.374095675
31.377 + -6.374095675 = 25.00290432
yes we can take it lower so lets make it the best answer
-200/31.376 = -6.374298827
31.376 + <span>-6.374298827 = 25.00170117
</span>i pray this be over soon^ lets try again....
-200/31.375 = -6.374501992
31.375 + -<span>6.374501992 = 25.00049801
</span>okay im a perfectionist... sooo lets go lower
-200/31.374 = -6.37470517
31.374 + <span>-6.37470517 = 24.99929483
</span>okay so we went to low on the third place. and of course i am moving to the fourth place...
-200/31.3749 = -6.374522309
31.3749 + <span>-6.374522309 = 25.00037769
</span>okay we can move lower on that place....
-200/31.3748 = -6.374542627
31.3748 + <span>-6.374542627 = 25.00025737
</span>lets try to move this along faster...
-200/31.3746 = -6.374583262
31.3746 +<span> -6.374583262 = 25.00001674
</span>every number counts literally so moving lower
-200/31.3744 = -6374623897
31.3744 + <span>-6374623897 = 24.9997761
we gotta put a 9 on our fifth place from our decimal sooo here we go again
-200/31.37449 = -6.374605611
31.37449 + </span><span>-6.374605611 = 24.9998439
<span>OMG DO YOU UNDERSTAND WHAT THIS MEANS!!?!?!
</span>okay that means our answer was two trials ago solved
in other words our two numbers arreee
</span><span> 31.3746
</span><span>-6.374583262
</span>hallelujah we are finished and if this is wrong i will pull my hair out.
The answer is 10x - 1380m + z
