A solution composed of 50% ethanol, 10% methanol, and 40% water is fed at the rate of 100 kg/hr into a separator that produces one stream at the rate of 60 kg/hr with the composition of 80% ethanol, 15% methanol and 5% water, and the second stream of unknown composition. What is the mass fraction of ethanol in the unknown stream?

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Four hundred years after the invention of this device, the telescope has become an essential scientific instrument, an icon of science.

But it is more than just an extension of our senses — the telescope is an instrument of thought as well. Throughout its 400-year history, the telescope has changed our view of the universe and our view of ourselves.

Never more so than at the very beginning. News of Hans Lippershey's 1608 patent reached Galileo Galilei the following year. Within one day, he had made his own telescope, and, in 1610, published a short, still very readable, book, Siderius Nuncius, (The Starry Messenger). This remarkable work changed everything.

Galileo's telescope made clear that the universe was far larger than had been imagined — and our place in it far smaller than had been imagined.

The public impact was immediate. The poet John Donne, in 1611, wrote of "Galileo … who of late hath summoned the other world, the stars to come nearer to him, and give him an account of themselves." But this new other world, as Donne also saw, had a negative side. The old universe of unity and proportion, crowned by a perfect heaven scaled to human proportion, was threatened: "New philosophy calls all in doubt."

Today you can buy a better telescope than Galileo's for under a hundred dollars, and a careful replica of his telescope for a great deal more. An ordinary pair of binoculars will show just about all that he saw (DON'T try to use them to see the sunspots!). But you can only imagine how unsettling this modest instrument was in the early 17th century.

We now take for granted that science gives us otherwise invisible worlds. We have wonderful instruments that do this — the telescope, the microscope, fMRI brain scans, the Large Hadron Collider. We now see many invisible worlds: tiny bacteria in our water, shifting patterns of blood flow in the brain, submicroscopic particles (some hope) that haven't been seen since the first microseconds of the universe.

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