Suppose p1 , p2 , p3 , and p4 are specific polynomials that span a two-dimensional subspace h of p5. describe how one can find a basis for h by examining the four polynomials and making almost no computations.

Lem 2 the data below are for the system ethyl propyl ether (1)-chloroform (2) at 0.5 bar. use the data to answer the following questions (all questions refer to p d 0: 5 bar). a) what are the boiling points of the pure components at 0.5 bar? b) a mixture with the overall composition z1 d 0: 1 is brought to 47.6ä±c, 0.5 bar. what is the phase? c) 100 mole of a mixture with z1 d 0: 1 (state a) is mixed with 22 mole of pure ethyl propyl ether vapor (state b). the mixing takes place at 47.6 ä±c, 0.5. bar. what is the phase of the resulting mixture (state c)? if the state is a v/l mixture report the number of moles and mole fractions in each phase. d) plot the txy graph and show states a, b and c. the graph must be done by computer and should be properly annotated. ethyl propyl ether (1) - chloroform (2) at 0.5 bar t ( ä±c) x1 y1 t ( ä±c) x1 y1 42.9 0.000 0.000 49.0 0.470 0.455 43.0 0.020 0.010 49.1 0.520 0.520 43.9 0.065 0.029 48.9 0.567 0.592 45.4 0.156 0.089 48.3 0.652 0.720 46.4 0.215 0.142 47.6 0.745 0.815 47.6 0.296 0.223 46.7 0.822 0.872 48.3 0.362 0.302 45.7 0.907 0.937 48.7 0.410 0.375 44.6 1.000

In the cathode ray tube experiment, j. j. thomson passed an electric current through different gases inside a cathode ray tube in the presence of an electric field. in which two ways did this experiment change scientists’ understanding of the atom?

Which set of characteristics best describes igneous rock? a) largest type of rock, made of organic matter, hardest type of rock b) least abundant type of rock, made of other rocks, made mostly of minerals c) found on all continents, contains wavy bands of stripes, contains fossils d) most abundant type in earth's crust, made of magma/lava, contains no fossils