Yay Math!

[Guest]

3 hours ago, Charlie said:

Considering how much you have probably spent on insurance and registration (and perhaps on a parking spot) during the last decade just to drive 1200 miles/year (i.e., only 100 miles/month), it probably would have been cheaper--and healthier--to buy a bike.

Well, he could have health problems which preclude using a bicycle for many errands. And I suppose there are many places where bicycle use isn't feasible most of the year (I'd guess most of Canada, and perhaps even where you live in Palm Springs--can you bike when it's 104F/40C out?). That being said, you're right in that his meager use of his car should prompt reflection of the economics of the car use. At 100 miles per month, using a ride-share service would most likely be more cost-effective. 

[samhexum]

3 hours ago, Charlie said:

Considering how much you have probably spent on insurance and registration (and perhaps on a parking spot) during the last decade just to drive 1200 miles/year (i.e., only 100 miles/month), it probably would have been cheaper--and healthier--to buy a bike.

My back aches with any physical activity.  I can barely walk.  I resemble Frankenstein when I do.  I have had absolutely no quality of life for a decade.  How do you expect me to stay on a bike?

[+ Charlie]

44 minutes ago, samhexum said:

My back aches with any physical activity.  I can barely walk.  I resemble Frankenstein when I do.  I have had absolutely no quality of life for a decade.  How do you expect me to stay on a bike?

I had no way to know of your physical incapacity. However, it would still be cheaper to use an Uber. than to maintain a car.

[samhexum]

7 minutes ago, Charlie said:

I had no way to know of your physical incapacity. However, it would still be cheaper to use an Uber. than to maintain a car.

And what's the price of my freedom from the tyranny of the taxi?

[Guest]

3 hours ago, samhexum said:

And what's the price of my freedom from the tyranny of the taxi?

If you haven't tried to use Lyft or Über yet, I strongly suggest you consider doing so. I share a certain discomfort we probably have regarding taxis. There's little control over the behavior of taxi drivers, especially in most foreign countries. One risks predatory scams, being taken for a ride, and even kidnapping. However, with the rideshare companies, those risks are fairly minimized. Passengers rate drivers, and can easily report misbehavior such as discrimination (including homophobia or ethnic). Bad drivers are weeded out pretty quickly (note that drivers also rate passengers). The driver can't "take you for a ride" by taking a longer than necessary route, because the price is pre-determined. A longer route would come out of the driver's pocket. In fact, once a driver took a detour because of traffic problems, and Lyft sent me a text asking if I was OK.

When I go somewhere, I usually calculate how much it will cost me to rent a car, versus ride-share, and often find that using ride-share costs are lower. One must add up the rental agency rental fees, all silly surcharges, gas, tolls, hotel parking if needed, then add up Lyft costs. Often Lyft ends up costing less. Do the arithmetic!

There are times when a taxi is better, though. When going from my house to LAX, the ride-share services usually quote something around $45-$50. On the way back, however, they will come up with all of these "congestion surcharges" to jack up the fee to over $100. When that happens, I usually just jump into a taxi, and the fare is usually in the $85 to $90 range. Also, in Puerto Vallarta, when Über first came on the market, they were preferable, as taxis were still refusing to abide by the fixed-prices the law required (in Mexico, one confirms the fare before boarding the taxi). By the next year, though (I go to PV almost every year), the taxi drivers got wise, since they knew that if they asked for too high a fare, the passenger would just arrange for an Über. Taxi drivers don't have to have part of their fare diverted to the ride-share company, so they got their fares at or lower those Über were quoting.

Edited October 17, 2023 by Unicorn

[+ purplekow]

On 2/10/2021 at 5:33 AM, JoeMendoza said:

My calculations are off by a bit I think but the shaded area is about 1.65 and the total square is 4 making about 41% of the square shaded.

Basic numbers are. each side is 2.  top point of meeting is midpoint so top is divided to 1 and 1.  top angles are 90 degrees. lower angles are 27 degrees and 63 degrees shaded .  on the left 45 degrees both shaded and unshaded on the right     Diagonal is 5.  top angle of shashaded triangle is 72 degrees.  72 degrees.   The side of the shaded triangle are 2 2.9 along the diagonal and 1.7    Using Sin a/a.= sin b /b+ sin c /c.  gives.  sin 72/2 =  sin of 45/ b = sin of 63 / partial diagonal 

Well after some calculations by the scalene triangle area calculator, it seems my figures are off as the angles and the lengths do not fit.  So further work to be done.  

[+ nycman]

On 2/10/2021 at 5:33 AM, JoeMendoza said:

A) I hate geometry 
B) I hate myself
C) Therefore, I must solve this problem.

The key to this puzzle is knowing that the pink triangle and the small triangle above it are “identical" triangles. If you need help with figuring out how I know that….see below:

https://www.youtube.com/watch?v=I12ko_ovgwo

You must also know that ratio of the base to the height is always the same between identical triangles.

Let’s assign the sides of the square to equal 1. (It just makes the math a little easier)

Looking at the diagram, we know that base of the small triangle is 1/2 the base of the pink triangle. Therefore the height of the little triangle must be 1/2 the height of the large triangle. We also know that the height of the two triangle added together must equal 1.  Therefore the height of the small triangle must be 1/3 and the pink triangle height must be 2/3. 

Now we know the base (1) and height (2/3) of the pink triangle.

Using the formula for the area of a triangle "area = 1/2 x base x height"
We get "pink area = 1/2 x 1 x 2/3" which equals 1/3. 

Since we assumed the square is 1 x 1, we know the area of the square is 1.

Since, 1/3 of 1 is 1/3. The fraction of the square that is shaded is 1/3.

 

 

[+ purplekow]

2 hours ago, nycman said:

A) I hate geometry 
B) I hate myself
C) Therefore, I must solve this problem.

The key to this puzzle is knowing that the pink triangle and the small triangle above it are “identical" triangles. If you need help with figuring out how I know that….see below:

https://www.youtube.com/watch?v=I12ko_ovgwo

You must also know that ratio of the base to the height is always the same between identical triangles.

Let’s assign the sides of the square to equal 1. (It just makes the math a little easier)

Looking at the diagram, we know that base of the small triangle is 1/2 the base of the pink triangle. Therefore the height of the little triangle must be 1/2 the height of the large triangle. We also know that the height of the two triangle added together must equal 1.  Therefore the height of the small triangle must be 1/3 and the pink triangle height must be 2/3. 

Now we know the base (1) and height (2/3) of the pink triangle.

Using the formula for the area of a triangle "area = 1/2 x base x height"
We get "pink area = 1/2 x 1 x 2/3" which equals 1/3. 

Since we assumed the square is 1 x 1, we know the area of the square is 1.

Since, 1/3 of 1 is 1/3. The fraction of the square that is shaded is 1/3.

 

 

I started with the idea that I could find the length of the sides rather than the height.  That led me down a path of sine and cosine and actually I was doing okay but did not have a good sine table and as a result my calculations became off.  Know the height definitely makes this problem a lot easier to solve but I did not know the key to that.  Thanks for the response.    I was looking to get the area of the pink triangle and used 10 as the base as that way the area of the big square was 100 and the pink square area was the same as the percentage of coverage.  

[+ purplekow]

9 hours ago, purplekow said:

I started with the idea that I could find the length of the sides rather than the height.  That led me down a path of sine and cosine and actually I was doing okay but did not have a good sine table and as a result my calculations became off.  Know the height definitely makes this problem a lot easier to solve but I did not know the key to that.  Thanks for the response.    I was looking to get the area of the pink triangle and used 10 as the base as that way the area of the big square was 100 and the pink square area was the same as the percentage of coverage.  

I went back and looked at my calculations and indeed the angles were off by a few degrees due to misreading the sine table.  NYC man was way easier and more insightful and my hat is off to him.  

[Guest]

On 10/19/2023 at 5:20 PM, purplekow said:

I started with the idea that I could find the length of the sides rather than the height.  That led me down a path of sine and cosine and actually I was doing okay but did not have a good sine table and as a result my calculations became off.  Know the height definitely makes this problem a lot easier to solve but I did not know the key to that.  Thanks for the response.    I was looking to get the area of the pink triangle and used 10 as the base as that way the area of the big square was 100 and the pink square area was the same as the percentage of coverage.  

Strong work doc 🙌🏽👌🏽

[samhexum]

[+ jeezopete]

[mike carey]

4 hours ago, jeezopete said:

32. The text says she has 32 not she had.

[+ sync]

5 hours ago, jeezopete said:

Had it been my mother the answer would be none!  😆

[samhexum]

[MikePDNA51]

On 2/10/2021 at 2:31 AM, MysticMenace said:

width=1078pxhttps://i.insider.com/5c13f70a01c0ea0e520026b2?width=1200&format=jpeg&auto=webp[/img]

Answer: 8

[MikePDNA51]

On 2/10/2021 at 2:32 AM, MysticMenace said:

Cone=3

white ice cream=2

red=1

[samhexum]