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4 years ago

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Calculate the length of a minor arc OP in terms of π

2 answers:

Zarrin [17]4 years ago

5 0

Answer: $\bold{\dfrac{16}{3}\pi}$

<u>Step-by-step explanation:</u>

arc length (s) = radius (r) × θ (in radians)

radius (r) = 6 cm

major arc OP is 200°, so minor arc is 160°.

$\text{Convert degrees into radians}:\\\dfrac{\pi}{180}=\dfrac{\theta}{160}\\\\\\\dfrac{160\ \pi}{180}=\theta\\\\\\\dfrac{8\pi}{9}=\theta$

$s=r\times \theta\\\\.\ =6\times \dfrac{8\pi}{9}\\\\\\.\ =\dfrac{2\times 8\pi}{3}\\\\\\.\ =\dfrac{16}{3}\pi$

Tanzania [10]4 years ago

3 0

Answer:

arc length = radius * angle in degrees * (PI / 180)

arc length = 6 * 160 * (PI/180)

arc length = PI * 960 / 180

arc length = PI * 5 + (60/180)

arc length = (16/3) * PI

Step-by-step explanation:

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Step-by-step explanation:

<u>Step 1: Solve using the first point</u>

<em>(2, 28)</em>

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<u>Step 2: Solve using the second point</u>

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<em>(4, 220)</em>

$220 = a(4)^3 + b(4)^2 + c(4) + d$

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<u>Step 4: Solve using the fourth point</u>

<em>(-2, -20)</em>

$-20 = a(-2)^3 + b(-2)^2 + c(-2) + d$

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<u>Step 5: Combine the first and fourth equations</u>

<u /> $28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d$

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$8 - 8b = 8b - 8b + 2d$

$(8 -8b)/2 = 2d/2$

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<u>Step 6: Solve for c in the second equation</u>

$-5 + 5 = -a + b - c + d + 5$

$0 + c = -a + b - c + c + d + 5$

$c = -a + b + d + 5$

<u>Step 7: Substitute d with the stuff we got in step 5</u>

$c = -a + b + (4 - 4b) + 5$

$c = -a + b + 4 - 4b + 5$

$c = -a - 3b + 9$

<u>Step 8: Substitute d and c into the first equation</u>

<u /> $28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)$

$28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b$

$28 - 22 = 6a - 6b + 22 - 22$

$6 / 6 = (6a - 6b) / 6$

$1 + b = a - b + b$

$1 + b = a$

<u>Step 9: Substitute a, b, and c into the third equation</u>

$220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)$

$220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b$

$220 - 100 = 60b + 100 - 100$

$120 / 60 = 60b / 60$

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<u>Step 10: Find a using b = 2</u>

$a = b + 1$

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<u>Step 11: Find c using a = 3 and b = 2</u>

$c = -a - 3b + 9$

$c = -(3) - 3(2) + 9$

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