1. Which of the following sets are convex and which are not (hint - you may...
Prove that each of the following sets is convex (a) {(x1, 22, x3) E R3 | 0 < 띠, x2, 23 and x1 + 2x2 + 3x3 6)
Question 4 1 pts Which sets of molecules may interact by hydrogen-bonding? Select all that apply. Hint: you may need to draw the structures. O NH3 and H2O Cl2 and H2 O NH3 and HF OCH4 and H-H ONF3 and 02 O H2 and H2
2. Which of the following sets are convex? (a) A slab, i.e., a set of the forn {rE Rn l α-ar-β} (b) A rectangle, i.e., a set of the forin {2. E Rn | Qi-Z'i is sometimes called a hyperrectangle when n > 2. ,n). A rectangle A, i = 1, (d) The set of points closer to a given point than a given set, i.e., where SCR (e) The set of points closer to one set than another, i.e.,...
1. Draw a convex set S. Explain briefly how you know S is convex. Then break that set into two sets Sį and S2 such that Si U S2 = S and Sin S2 = 0 and neither Si nor S2 is convex. 2. Consider a sphere S. Lines on the sphere are taken to be great circles. On the sphere, does the Plane Separation Postulate hold? Give a short explanation to back up your claim that considers the various...
Let A and B be two arbitrary sets. Which one of the following propositions may not be true? a. AE P(A) What condition(s) are required to ensure that all propositions (a, b, c and d) in Problem 6 are true?
List all of the following sets to which each number belongs. A number may belong to more than one set. complex numbers nonreal complex numbers pure imaginary numbers real numbers Drag each set above to the number(s) that belong to the set below. Items may be used more than once. 1. 1+3 i 2.-81 3. V3 5. 7-9 6. - 7-10
1.You use a CONVEX lens of focal length f= 5 cm to concentrate the rays of the sun to set fire to (an unfortunate) leaf a) Draw a picture of the rays through the lens b) Label the OBJECT DISTANCE (o), IMAGE DISTANCE (i), and determine their NUMERICAL VALUES (with UNITS of course). (HINT: use 1/o + 1/1-1/f.)
(4) 2. Which of the sets of vectors in 1-(a) through 1(d) form a basis for R3? Explain why. Hint Use your answers in question (1).
3) Devise a synthesis of the following compound using the given compounds (you may use each one more than once if needed). You may also use any needed inorganic or organic reagents but all of the carbons in the target molecule must come from the given starting materials. Hint: this synthesis will require you to use ozonolysis and a reaction that starts with the letter DI
Which of the following objects are NOT convex? 1. A frisbee 2. A table 3. An open laptop 4. A bowl 5. A mattress 6. A hockey puck 7. A chair 8. A closed laptop 9. A bathtub 10. A paperback book