Almost periodic equations and conditions of Ambrosetti-Prodi by Ortega R., Tarallo M.

By Ortega R., Tarallo M.

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Anton has started to cover each face with blue and white triangular tiles. He can fit 11 blue tiles along each edge. 1. How many tiles (blue and white) does Anton need to completely cover the tetrahedron? 42 Patterns and Figures Additional Practice You can paste two tetrahedra together as shown in the figure. 2. How many tiles are needed to completely cover this new shape? Dot Pattern: Pattern Number: 2 3 3. Study the dot pattern above and draw the pattern for n ‫ ؍‬4. You can split each pattern in a triangle and a rectangle so that the base of the triangle has as many dots as the right side of the rectangle.

Additional Practice 39 Additional Practice Section B Sequences Joey and Alice collect old magazines for their school. Joey has currently collected 24 magazines. Each week he gets three more old magazines. 1. Make a number strip that begins with 24 and gives the number of magazines Joey has at the end of each week. 2. How many magazines will Joey have after n weeks? Alice currently has 39 magazines. Each week she collects two magazines. 3. How many magazines will Alice have after n weeks? 4. How many magazines will Joey and Alice collect together after n weeks?

You can keep starting the sequence later by adding one more to n each time, as shown below. Sequence Formula, where n starts at 0 in each case 0, 1, 4, 9, 16, 1, 4, 9, 16, 4, 9, 16, 9, 16, n2 ‫ ؍‬n2 (n ؉ 1)2 ‫ ؍‬n 2 ؉ 2n ؉ 1 (n ؉ 2)2 ‫ ؍‬n 2 ؉ 4n ؉ 4 (n ؉ 3)2 ‫ ؍‬n 2 ؉ 6n ؉ 9 18. By looking at patterns, predict what the equivalent expression for (n ؉ 4)2 would be. Where does the sequence start? 19. Find an equivalent expression for (2n ؉ 1)2. Explain your method and how you know it is correct. Section C: Square Numbers 25 C Square Numbers The square of a number is the number multiplied by itself.

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