I did it! Hope that helps and super sorry about my horrible handwriting. I lost my ipad pen!
Log 2x + log 12 = 3log 2x = 3 - log 12log 2x = 3 - 1.08log 2x = 1.922x = 10^1.922x = 83.33x = 83.33/2x = 41.67
Make the same denominator then Add which would be 4/12 + 1/12 which is 5/12
Step-by-step explanation:
The integral was obtained using cylindrical shells. The volume of each shell is:
dV = 2π r h t
where r is the radius, h is the height, and t is the thickness.
The thickness is either dx or dy. Looking at the integral, we can tell it is dy. So the solid is revolved about the x-axis (or a line parallel to the x-axis).
The radius will be y. So the height must be x = 9/(9+y²).
So the solid is obtained by rotating the region 0 ≤ x ≤ 9/(9+y²), 0 ≤ y ≤ 3 about the x-axis.
Answer:
4
Step-by-step explanation:
WA times AX = YA x YZ
8x5=40
because they have to equal each other we just have to divide 40 by 10
40/10=4 so segment YZ=4