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3 years ago

Find the length of arc QS

Mathematics

1 answer:

ss7ja [257]3 years ago

4 0

Answer:

QS ≈ 4.71 units

Step-by-step explanation:

The arc QS is calculated as

QS = circumference of circle × fraction of circle

= 2πr × $\frac{90}{360}$ ( r is the radius )

= 2π × 3 × $\frac{1}{4}$

= 6π × 0.25 ≈ 4.71 units ( to the nearest hundredth )

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Svet_ta [14]

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To find the area under the curve for the second equation:

$A_{2} = \int\limits^3__-3}{2x + 12} \, dx$

To find the total area:

$A = A_{2} -A_{1} = \int\limits^3__-3}{2x + 12} \, dx -\int\limits^3__-3}{x^{2} + 2x + 3} \, dx$

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Note: The reason the area is equal to the area two minus area one is that the line, area 2, is above the region of interest (see image).

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