Zadanie 9a
(i) Express AC in terms of α. (ii) Express AC in terms of β. (iii) Hence express α in terms of β.
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(i) Express AC in terms of α. (ii) Express AC in terms of β. (iii) Hence express α in terms of β.
Find the maximum total area of fabric required, counting both layers of triangle ADC.
Solve f(x)=0.
(i) Find f′(x). (ii) Hence find all points on the graph where f′(x) = 0, including the endpoints when appropriate.
Sketch y = ∣f(x)∣, labelling intercepts and all points whose x-coordinate satisfies f′(x) = 0.
Hence or otherwise solve ∣f(x)∣ > 1.
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Four cycles are checked in order. Find the probability that only the fourth lasts longer than 48 minutes.
A large collection contains only cycles longer than 48 minutes. (i) Find the probability that a randomly chosen cycle from this collection lasts less than 62 minutes. (ii) Twelve cycles are independently selected from the collection. Find the probability that…
Thresholds a<b satisfy P(a≤T≤b)=0.88 and P(T>b)=2P(T<a). Find the lower threshold a.