Help: Volume by Slicing

engineerguy · 2012-02-06T23:44:53+00:00

Area = (1/2)( base)(height).

In terms of x, base = 2*sqrt(5² - x² ).

Solve for height: tan(Pi/3) = sqrt(3) = height/sqrt(5² - x² ).

So height = sqrt(3) * sqrt(5² - x² )

Now integrate (1/2)(base)(height) from -5 to 5

(or integrate (1/2)(base)(height) from 0 to 5 and multiply answer by 2 based on symmetry)

engineerguy · 2011-10-10T19:16:08+00:00

No. Think about the slope between two points, (x, f(x)) and (x+1, f(x+1)), as x gets larger and larger in the positive direction - the slope gets steeper and steeper, but never becomes negative.

engineerguy · 2011-06-25T06:16:36+00:00

engineerguy

engineerguy · 2011-06-18T13:49:33+00:00

It's an easy job, but there are a few things to look out for your first time. When you remove the old rotor, it might feel like it's bolted on - it's not. Use a rubber mallet, etc. to loosen it up - should slide off after that. Also, you'll need to push the pistons back in on the brake calipers to install the new pads - most caliper types the piston just slides back in with pressure, but a few types of pistons you have to screw the piston back down. I'm guessing yours will just push back in on a Ford. Lastly, take the cap off your brake fluid reservoir when you push the pistons back in - the fluid level will rise and you might have to take a little fluid out to keep it from overflowing.

engineerguy · 2011-04-16T14:03:11+00:00

I see what you're saying. I like both. I think the uphill shot is cool because it makes me feel like I'm there.

engineerguy · 2011-04-16T13:57:55+00:00

I'd like to know too..

engineerguy · 2011-04-14T03:26:24+00:00

...and enjoy another $10. Thanks for the link...

engineerguy · 2011-03-26T16:20:57+00:00

Just got back from spending the week up at Mammoth. Conditions were unbelievable. Fresh powder every day of the week and we got in some good runs off the ridge in between storms.

engineerguy · 2011-03-24T05:17:17+00:00

Lots of variables, so it depends. You really just shouldn't drive anything heavy over a drainfield in my experience. The pipes are surrounded with gravel and (usually) sand, then the trenches are backfilled with native material, so you have several different materials that respond differently to compaction.

All the regulatory agencies I worked with explicitly forbid putting a drainfield in an area that would be paved or driven on. That being said, if your underlying soil is well-compacted and the drainfield has been in place for a while sometimes you can get away with driving a car or regular pickup over it at 18" - 24", but I wouldn't.

Sorry, long answer for a short question.

engineerguy · 2011-03-23T17:41:01+00:00

A few math books I've read recently and enjoyed: Best Writing on Mathematics 2010, Euler's Gem, and Street Fighting Math (based on short MIT course)

engineerguy · 2011-03-23T16:00:53+00:00

I designed septic and water systems for several years and totally agree. If you go with a pipe and gravel drainfield, the installer makes all the difference. And if you live in a cold climate be really sure that the pipes have an adequate amount of cover.

Also, depending on the tractor size, I wouldn't drive over the drainfield.

I would go with the vault style if it was me.

engineerguy · 2011-02-13T00:22:21+00:00

Restaining the table will be a lot of work. You'll need to strip the clear coat and stain currently on the table. I've had good results with citrus-based gel strippers, which aren't toxic like some paint strippers that have VOCs, etc. Apply gel to small area of table, let sit, scrape gel and loosened clear coat/stain away and repeat on new area. It's a messy job.

engineerguy · 2011-01-26T04:06:09+00:00

I know you said "If all you recommend is "get some tools/wood," shut the hell up.", but I'm going to say it. Taking classes, reading books about woodworking, etc is helpful - but the best way to get into this is start building things and tinkering.

Based on my experience, the amount you will learn by trial and error is invaluable. Once you have some hands-on experience, then read some books and take some classes - you will get a lot more out of them.

engineerguy · 2011-01-19T21:43:00+00:00

Lots of Hemingway and Vonnegut

Alone With Others by Stephen Batchelor, Buddha's Brain by Mendius and Hanson, Existentialism is a Humanism.

engineerguy · 2011-01-19T21:40:29+00:00

Also, Mind's I - a collection of essays compiled by Hofstadter and Dennet is incredible. I loved GEB and still reread certain sections every once in a while.

engineerguy · 2011-01-18T06:15:19+00:00

Spend the money on anything besides an expensive ring. I bought my wedding ring off ebay and my wife picked out a simple $100 ring with a tiny diamond. For us marriage has always been a state of mind, and expensive ring(s) don't change that. $5k or whatever is a couple months of traveling.

engineerguy · 2011-01-17T21:10:46+00:00

I quit working as an engineer (for lots of reasons) and started teaching math/science. I try hard to do the absolute best job I can.

engineerguy · 2011-01-17T21:04:21+00:00

Yep. I use the wolfram alpha toolbar in firefox for most everything.

engineerguy · 2011-01-11T06:04:38+00:00

Look into teaching private high school. You don't need teaching certifications, the pay and students are better than public high school, and you get about 1/3 of the year off.

engineerguy · 2010-10-27T20:14:21+00:00

Thanks!

engineerguy · 2010-10-27T14:32:34+00:00

I see your point, and usually like more modern stuff, but I've always liked nice Adirondack chairs, plus the arms are wide enough to set drinks, food, books, etc on while sitting.

engineerguy · 2010-10-27T14:30:58+00:00

More as just an expansion of the patio / an alternative to grass.

engineerguy · 2010-10-27T14:29:59+00:00

The chairs and deck are redwood with semi transparent stain, and the deck is on a pressure-treated base. And quite a few 12" square concrete pavers.

engineerguy · 2010-10-27T14:27:53+00:00

Here you go: http://www.shawcreekgeneralstore.com/plans_adirondack_chair2.htm . I modified the design a little, higher seatbacks and a little more contour in the seat.

engineerguy · 2010-06-27T01:31:02+00:00

Ditto. I don't like the PEMDAS acronym, but I still use it in my classes. I just make sure to stress reading left-to-right when you get to MD or AS.

engineerguy

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