Zadanie 9a
Express z₁z₂ in Cartesian form.
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Express z₁z₂ in Cartesian form.
Hence find b when .
Initially all five containers must occupy consecutive slots. Count the arrangements.
They are rearranged with at least one empty slot between F and every other container. The other four need not be consecutive or separated from one another. Count the arrangements.
Prove by contradiction that 3x3 + 6x2 + 9x + 2 = 0 has no integer root.
How many codes have all digits distinct?
How many have distinct digits in increasing order?
Suppose it is geometric. (i) Show that . (ii) Show that both choices give a convergent series. (iii) For p>0 and infinite sum , find x.
Now suppose the series is arithmetic with common difference d. (i) Show that p=3/4. (ii) Write d as a rational multiple of ln x. (iii) If the sum of its first n terms is , find n.
Sketch y=f(x), labelling both endpoints.