A graph can be helpful for finding limits of integration.
The volume can be found using cylindrical shells of height (x-0.5x^2) and radius (3-x).
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The parabola whose area is shaded purple is the difference between the curves y=x and y=0.5x^2. The area under the parabola shaded purple is
(2/3)*height*width = (2/3)*(0.5)*2 = 2/3
The volume is that area multiplied by the circumference of the circle about which its centroid is revolved. That circle has radius 2, so its circumference is 4π. Then the volume is
V = (2/3)*4π = 8π/3
mutually exclusive are
ii. Sit down and stand up
iii. Two dice: Odd and Even
because they can not occur same time
.
Jake:
Mon- 4 boxes
End of the week- 3x the boxes on Mon
3 x 4 = 12
Sally:
Mon- 2 boxes
End of the week- 4x the boxes on Mon
4 x 2 = 8
12 + 8 = 20 boxes total
First, subtract bh from both sides and cancel. Then, divide both sides by h and cancel. Finally, r= 25-bh/ h
It would be multiplication and subtraction
4(x-3)
four times
( the difference of a number “x” and three)
difference means subtraction every time.