Posted tagged ‘way’

SOLAR POWER IN CARS

September 10, 2011

solar-auto-carsSolar energy is one of the many renewable sources of energy that is used for fueling vehicles, running consumer products and for the efficient running of homes and business establishments. Solar power is harnessed with the help of solar cells and solar panels which are placed in the item that has to be powered.

The solar car is something that is envisioned to materialize in the future, with some countries already having solar cars racing across countries.
With this, it is proven that it is viable to indeed produce and manufacture solar power cars in bulk, in the near future so that everyone will soon own a solar power car.

Of course, once solar power cars are manufactured, it does not implicate that all other fuel sources for cars on highways will be removed. All that is done in solar power cars is the supplementation of traditional fuel with solar energy so that you save not only on your economy, but also save the environment in more ways than one every year.

The solar power cars that are used in races today run only on solar power, and thus look odd in appearance. This is because these cars are designed in such a way that they can collect maximum solar energy with which it is possible for the car to gain the required speed and desired efficiency.

The solar cells used in solar power cars are large, and usually cover the entire vehicle. However in case of commercial uses, solar cells are much smaller and designed so that the vehicle not only looks attractive, but is also efficient in its functioning. Solar cars can be used for short commutes in town as these cars can work only on solar energy.

The batteries found in the vehicle stores excess solar power so that this power can be used when solar power is not available on demand like on cloudy days and at nighttime. The engines found in these solar power cars are very much like the engines found in electric cars found today. In addition to this, the cars are lightweight, so that solar power can be used more efficiently.

At present, there are many types of solar power cars in the development stage today, which are also available for sale. However as these cars are in the developmental stage, the car is not available to the general public. With so many benefits found in solar power cars, its cost will not be much higher than the cost of the traditionally powered vehicles of today.

Another benefit of solar power cars is there is no hassle of stopping at gas stations for gas nor is there the need of getting worried of rising gasoline costs. With a solar power car, you save on the money that you would have otherwise have needed for buying fuel to run your car. In addition to this, with solar power cars you will be doing your bit in stopping global warming problems as there are no fuel emissions from solar power cars.

Daughters’ Ages

August 24, 2011

Two MIT math grads bump into each other at Fairway on the upper west side. They haven’t seen each other in over 20 years.

THE FIRST GRAD SAYS TO THE SECOND: “how have you been?”
SECOND: “great! i got married and i have three daughters now”
FIRST: “really? how old are they?”
SECOND: “well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..”
FIRST: “right, ok.. oh wait.. hmm, i still don’t know”
SECOND: “oh sorry, the oldest one just started to play the piano”
FIRST: “wonderful! my oldest is the same age!”

problem: how old are the daughters?

Solution

solution: start with what you know. you know there are 3 daughters whose ages multiply to 72. let’s look at the possibilities…

AGES:            SUM OF AGES:
1 1 72            74
1 2 36            39
1 3 24            28
1 4 18            23
1 6 12            19
1 8 9             18
2 2 18            22
2 3 12            17
2 4 9             15
2 6 6             14
3 3 8             14
3 4 6             13

after looking at the building number the man still can’t figure out what their ages are (we’re assuming since he’s an MIT math grad, he can factor 72 and add up the sums), so the building number must be 14, since that is the only sum that has more than one possibility.

finally the man discovers that there is an oldest daughter. that rules out the “2 6 6” possibility since the two oldest would be twins. therefore, the daughters ages must be “3 3 8”.

(caveat: an astute reader pointed out that it IS possible for two siblings to have the same age but not be twins, for instance one is born in january, and the next is conceived right away and delivered in october. next october both siblings will be one year old. if a candidate points this out, extra credit points to him/her.)

this question is pretty neat, although there is certainly a bit of an ahafactor to it. the clues are given in such a way that you think you are missing information (the building number), but whats important isn’t the building number, but the fact that the first man thought that it was enough information, but actually wasn’t.

even if the candidate doesn’t know the solution, they could come up with some interesting thoughts. if they just stare at you and shrug “i dunno” then thank them for their time and don’t give them afogcreek pen.

Red Marbles, Blue Marbles

August 24, 2011

Problem: you have two jars, 50 red marbles, 50 blue marbles. you need to place all the marbles into the jars such that when you blindly pick one marble out of one jar, you maximize the chances that it will be red. (when picking, you’ll first randomly pick a jar, and then randomly pick a marble out of that jar) you can arrange the marbles however you like, but each marble must be in a jar.

Solution

Chance! chance is easy if you know how to do the formula. we know that we have two choices to make. first we’ll pick a jar, and each jar will have a 1/2 chance of being picked. then we’ll pick a marble, and depending how we stack the marbles, we’ll have a (# of red marbles in jar)/(# of total marbles in jar) chance of getting a red one.

for example, say we put all the red marbles into JAR A and all the blue ones into JAR B. then our chances for picking a red one are:

1/2 chance we pick JAR A * 50/50 chance we pick a red marble
1/2 chance we pick JAR B * 0/50 chance we pick a red marble

do the math and you get 1/2 chance for a red marble from JAR A and a 0/2 chance for a red marble from JAR B. add ‘em up and you get the result = 1/2 chance for picking a red marble.

think about it for awhile and see if you can figure out the right combination. we had a 50/50 (guaranteed) chance in picking a red marble from JAR A, but we didn’t have to have 50 red marbles in there to guarantee those fantastic odds, did we? we could’ve just left 1 red marble in there and the odds are still 1/1. then we can take all those other marbles and throw them in JAR B to help the odds out there.

let’s look at those chances:

1/2 we pick JAR A * 1/1 we pick a red marble
1/2 we pick JAR B * 49/99 we pick a red marble

do the math and add them up to get 1/2 + 49/198 = 148/198, which is almost 3/4.

we can prove these are the best odds in a somewhat non-formal way as follows. our goal is to maximize the odds of picking a red marble. therefore we can subdivide this goal into maximizing the odds of picking a red marble in JAR A and maximizing the odds of picking a red marble in JAR B. if we do that, then we will have achieved our goal. it is true that by placing more red marbles into a jar we will increase the chances of picking a red marble. it is also true that by reducing the number of blue marbles in a jar we will increase the odds also. we’ve maximized the odds in JAR A since 1/1 is the maximum odds by reducing the number of blue marbles to 0 (the minimum). we’ve also maximized the number of red marbles in JAR B. if we added any more red marbles to JAR B we would have to take them out of JAR A which reduce the odds there to 0 (very bad). if we took any more blue ones out of JAR B we would have to put them inJAR A which reduce the odds there by 50% (very bad).

it wasn’t really a good proof, but QED anyway 😛