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Given, S = {x ∈ ℝ /x2 + 45 ≤ 14x} ∴ x2 + 45 ≤ 14x ⇒ x2 - 14x + 45 ≤ 0 ⇒ (x - 5) (x - 9) ≤ 0 ⇒ x ∈ [5, 9] Now, f(x) = 4x3 − 24x2 + 48x – 10 ⇒ f'(x) = 12x2 - 48x + 48 ⇒ f'(x) = 12(x2 - 4x + 4) = 12 [(x2 - 4x + 4) − 1] = 12(x - 2)2 - 12 ∴ f'(x) > 0 ∀ x ∈ [5, 9] ∴ f(x) is strictly increasing in the interval [5, 9] ∴ Maximum value of f(x) when x ∈ [5, 9] is f(9) = 1394
1000÷ 250 = ( 3√? × √1444) ÷ ( 3√512 × √361)
1540 ÷ 7 - 184 ÷ 8 = ?
12.232 + 29.98% of 539.99 = ? × 5.99
√256 * 3 – 15% of 300 + ? = 150% of 160
18 × 15 + 86 – 58 =? + 38
[5 X {(52 X 5) - 10} + 50 of 20] = ?
4(1/3) × 2(11/14) = 50% of ? + 86/11
(15 x 6 + 60% of 500 - 16 x 7) = ?
25% of 140 + 2 × 8 = ? + 9 × 5
If a nine-digit number 389x6378y is divisible by 72, then the value of √(6x + 7y) will be∶