[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 503

 

x1+x2=b/a

x1*x2=c/a

abc=x1

a+b+c=x2

or vice versa. Hastened my answer again.

 
grell:

x1+x2=b/a

x1*x2=c/a

abc=x1

a+b+c=x2

or vice versa. Hastened my answer again.

That's understandable, but what's next? =)
 
ilunga:
That's understandable, but what's next? =)

I'm just saying that I was too hasty with the discriminant:)
 

Vasya and Petya also almost killed me for posting their trade results without asking their permission.

The thermometer has already been pulled out by a concerted effort. Here's another thought, a physical one. It's an odd task:

Between pins "1" and "2", to which a constant voltage source
is connected, an electrical circuit is assembled, consisting only of
resistors. The voltage across one of the resistors is U0. Resistance
of this resistor was changed, as a result the voltage on this resistor
became U1, voltages on other resistors of the circuit also changed.
Can there be a resistor in this circuit, where voltage change
will be more than |U1 - U0| ?

2010

 
There were 8 weights of 1, 2, . . ., 8 g. One of them was lost,
and the others were lined up in order of increasing mass. There is a scale with a light bulb,
which can be used to check whether two groups of weights
have the same mass. How can you tell which weight is which in 3 checks

lost?

2010

 

During the ball, each young man danced a waltz with a girl either prettier than the previous dance or smarter, and at least one danced with a girl both prettier and smarter. Could this be the case? (There were equal numbers of boys and girls at the ball.)

1994

 
Mathemat:

Vasya and Petya also almost killed me for posting their trade results without asking their permission.

The thermometer has already been pulled out by a concerted effort. Here's another thought, a physical one. It's an odd task:

Between pins "1" and "2", to which a constant voltage source
is connected, an electrical circuit is assembled, consisting only of
resistors. The voltage across one of the resistors is U0. Resistance
of this resistor was changed, as a result the voltage on this resistor
became U1, voltages on other resistors of the circuit also changed.
Can there be a resistor in this circuit, where voltage change
will be more than |U1 - U0| ?

2010

It can't. Proof to the contrary. If it could, it means you could build an amplifier with passive elements.
 
But how would you prove this to schoolchildren who have only heard of amplifiers?
 
Mathemat:
But how would you prove this to schoolchildren who have only heard of amplifiers?
It's easy to calculate the series and parallel connection.
 
The problem also shows that it is not necessary that U1>U0. It can also be less.