How many solutions are there2x - y = 1- 4x + y = 1

Mathematics

2 answers:

Bezzdna [24]3 years ago

8 0

infinitely many solutions

allsm [11]3 years ago

5 0

There are many solutions

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A welder drops a piece of red-hot steel on the floor. The initial temperature of the steel is 2,500 degrees Fahrenheit. The ambi

sergey [27]

Answer: After 18.05 minutes, the temperature of steel becomes 100 degrees.

Step-by-step explanation:

Since we have given that

Initial temperature = 2500

At t = 0,

we get that

$f(t)=Ce^{-kt}+80\\\\2500=C+80\\\\2500-80=C\\\\2420=C$

After 2 minutes, the temperature of the steel is 1500 degrees.

so, it becomes,

$1500=2420e^{-2k}+80\\\\1500-80=2420e^{-2k}\\\\\dfrac{1420}{2420}=e^{-2k}\\\\0.587=e^{-2k}\\\\\ln 0.587=-2k\\\\-0.533=-2k\\\\k=\dfrac{0.533}{2}\\\\k=0.266$

So, We need to find the number of minutes when the temperature of steel would be 100 degrees.

So, it becomes,

$100=2420e^{-0.266t}+80\\\\100-80=2420e^{-0.266t}\\\\20=2420e^{-0.266t}\\\\\dfrac{20}{2420}=e^{-0.266t}\\\\\ln \dfrac{20}{2420}=-0.266t\\\\-4.8=-0.266t\\\\t=\dfrac{4.8}{0.266}\\\\t=18.05$

Hence, after 18.05 minutes, the temperature of steel becomes 100 degrees.

7 0

3 years ago

A population of geese grow in such a way that each generation is simply 2.2 times the previous generation. There were 3 geese in

lapo4ka [179]

First generation: 3

Second generation: $3\times2.2$

Third generation: $3\times2.2\times2.2=3\times2.2^2$

Fourth generation: $3\times2.2\times2.2\times2.2=3\times2.2^3$

And so on. The general formula for the $n$ th generation is $3\times2.2^{n-1}$ . So by the 15th generation, you should expect around $3\times2.2^{15-1}\approx186655$ geese.