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A separate function is h(x) = 9x2/(3x + 2), x ≠ −2/3. Region R is bounded by its curve, the line y = 1, and x = 1, x = 2. (i) Establish . (ii) Hence or otherwise, calculate the area of R in the form p + qln r, with positive…
Find P(R < 990).
The highest 15% of resistances exceed r ohms. Find r to four significant figures.
What percentage of resistors pass inspection?
Find the probability that a tray contains at least 20 resistors that pass.
Find the probability that exactly three trays in a batch each contain at least 20 passing resistors.
At a second factory resistance is normal with unknown mean μ and standard deviation σ. Exactly 84% pass the same inspection thresholds. The fraction below 990 Ω is three times the fraction above 1030 Ω. Find μ.
Assume the sequence is arithmetic. (i) Find k. (ii) Hence or otherwise, find u3.
Now set k = −6. (i) Prove that the three terms form the start of a geometric sequence. (ii) Explain why the corresponding infinite geometric series has no finite sum.
The already-investigated geometric case is k = −6. A second value of k also makes the sequence geometric. (i) Show that k2 + 7k + 6 = 0. (ii) Find the first three terms for the second value. (iii) State the sum S2m of its first 2m terms.