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The time period, T, of a simple pendulum is directly proportional to the square root of the length, d, of the pendulum.

When d=6, T=5

Find the value of T when d=3

Input note: give your answer correct to 2 decimal place.

Sagot :

MrRoyal

Answer:

[tex]T = 3.54[/tex]

Step-by-step explanation:

Given

Direct Variation of T to [tex]\sqrt d[/tex]

[tex]d =6;\ when\ T = 5[/tex]

Required

Determine T when d = 3

The variation can be represented as:

[tex]T\ \alpha\ \sqrt d[/tex]

Convert to equation

[tex]T = k\sqrt d[/tex]

[tex]d =6;\ when\ T = 5[/tex]; so we have:

[tex]5 = k * \sqrt 6[/tex]

Make k the subject:

[tex]k = \frac{5}{\sqrt 6}[/tex]

To solve for T when d = 3.

Substitute 3 for d and [tex]k = \frac{5}{\sqrt 6}[/tex] in [tex]T = k\sqrt d[/tex]

[tex]T = \frac{5}{\sqrt 6} * \sqrt{3}[/tex]

[tex]T = \frac{5\sqrt{3}}{\sqrt 6}[/tex]

[tex]T = \frac{5 * 1.7321}{2.4495}[/tex]

[tex]T = \frac{8.6605}{2.4495}[/tex]

[tex]T = 3.5356[/tex]

[tex]T = 3.54[/tex] -- approximated

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