Question

В цистерне находилась концентрированная серная кислота, содержащая 2 т воды. После того как эту кислоту смешали с 10т воды, ее концентрация понизилась на 16%. Сколько концентрированной серной кислоты находилось в цистерне?

Answer 1

X/(x+2)-x/(x+12)=0.16
10x/((x+2)(x+12))=4/25
250x=4(x+2)(x+12)
250x=4x^2+56x+96
-4x^2+194x-96=0
D=194^2-4(-4)(-96)=36100
x1=(√36100-194)/(2(-4))=0.5
x2=(-√36100-194)/(2(-4))=48
ответ: в цистерне могло быть как 0,5 тонн, так и 48 тонн  концентрированной кислоты ( правильны оба результата )

Answer 2

Calculation of Concentrated Sulfuric Acid in the Tank

To calculate the amount of concentrated sulfuric acid in the tank, we need to consider the change in concentration after it is mixed with water.

Given: - The tank initially contains concentrated sulfuric acid with 2 tons of water. - After mixing this acid with 10 tons of water, its concentration decreases by 16%.

Let's denote the initial concentration of the acid as C (in tons) and the final concentration after mixing as C' (in tons).

According to the given information, the concentration of the acid decreases by 16%. This means that the final concentration is 84% of the initial concentration.

Mathematically, we can represent this as:

C' = 0.84 * C To find the initial concentration C, we can set up an equation using the information given:

C + 2 = C' + 10 Substituting the value of C' from equation into equation we get:

C + 2 = 0.84 * C + 10

Simplifying the equation:

0.16 * C = 8

C = 8 / 0.16

C = 50

Therefore, the initial concentration of the concentrated sulfuric acid in the tank is 50 tons.

Now, to find the amount of concentrated sulfuric acid in the tank, we can subtract the amount of water from the total weight of the mixture.

Initially, the tank contains 2 tons of water. After mixing with 10 tons of water, the total weight of the mixture is 12 tons.

Therefore, the amount of concentrated sulfuric acid in the tank is:

50 - 12 = 38 tons

So, there were 38 tons of concentrated sulfuric acid in the tank.

Please note that the sources provided did not directly answer the question. The calculation was done based on the given information and mathematical reasoning.