The period t of a simple pendulum is given by t = 2π formula887.mml, where l is the length of the pendulum and g is the acceleration due to gravity. thus if l and t are measured, we can estimate g with g = 4π2l/t2. assume that the period is known to be t = 1.49 s with negligible uncertainty and that l is measured to be 0.559 ± 0.005 m. estimate g, and find the uncertainty in the estimate. note: when doing calculations, use pi = 3.1416.

Filling in the given numbers, you have

... g = 4(3.1416/1.49)²·0.559 ≈ 9.9403

The error is proportional to the length, so is

... ±∆g = ±(0.005/0.559)g = ±0.0889

The estimate for the value of g is 9.9403 ± 0.0889 m/s².

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

it is contrapositive

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