Answer:
An ellipse and a rectangle.
Step-by-step explanation:
If Jamal cuts the right circular cylinder anywhere but its extremities, the resulting shapes on both pieces will be an ellipse.
If he cuts precisely in a perpendicular way in relation to the ends, he will then form two new right circular cylinders, then the ellipses obtained would be circles.
If Jamal cuts the right circular cylinder lengthwise, going from one end to the other, even if it's not perpendicular to the base, he will obtain a rectangular shape.
Answer:
10
Step-by-step explanation:
Given
Add these two equations:
Substitute it into the first equation:
Then
Fill the 5-liter container, pour water from that into the 3 liter container until that is full, You will now have 2 liters left in the 5 liter container.
Empty the 3-liter container, and then transfer the 2 liters from the 5-liter container into it.
Now fill the 5-liter container again, then pour water carefully from the 5-liter container into the 3-liter container until it is full - exactly one more liter.
The 5-liter container now has 4 liters in it.
Answer:
4 cm
Step-by-step explanation:
Take the 11 cm on the bottom and subtract the 7 cm right above it.
Imagine the bottom half of this shape as a rectangle, the bottom and top side are of the same length. The top side would have to be 11 cm in length as well, so just subtract 11-7 to get the missing part.
When integrating using shells, the first step is to plot the graph. I personally plotted it with the x and y axis switched, because it aids me in picturing the graph. The integral ranges from 9 to 11, since those are the limits from the two lines y = 9 and y = 11. The reason that these are the limits is because it is rotating around the x, not the y.
Now that you have the limits of the integral, you have to find what goes inside it.
Because you are integrating using shells, you need to remember to include the
Again, there is a y here instead of an x, because you are rotating around the x axis. Then you just need to input the function f(y). If you look at the graph that you (hopefully) plotted, you can see that this function ranges between the y axis and the curve
. Put together the pieces, and you have the integral
After substituting in
, you get
Simplified, this is
Integrating, we get
Therefore, the solution is
Note: I didn't spend very much time reviewing these integrals, so I may be incorrect.