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The boundary of a park is shaped like a circle. The park has a rectangular pound in the center and are flower beds, one on each side
of the playground. The tenth of the playwround ist and its width is w. The feath of each side of the flowers in which wouvent
expressions represent the total fencing material required to surround the playwound and flower bacheme that the playwound and beds
do not overlap
The total fending material required to fence the playwound and both flower beds is
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Correct  cos(α - β) = 140/221

Step-by-step explanation:

cosα = ±√(1 - sin²α) => cosα = ±√(1 - (-5/13)²) = ±√(1 - (25/169)  

cosα = ±√(169 -25)/169 = ± √144/169

cosα = ± 12/13  since it is given that α (alpha) ends in the third quadrant

we choose  cosα = - 12/13

we know that is  tanβ = sinβ/cosβ = - 8/15 or sinβ : cosβ = 8 : 15 =>

sinβ = 8k and cosβ = 15k  where k is the coefficient of proportionality

we know the basic trigonometric equality

sin²β + cos²β = 1    when we replace the coefficients we get

(8k)² + (15k)² = 1 => 64k² + 225k² = 1 => 289k² = 1 => k² = 1/289 =>

k = 1/17   now we get sinβ and cosβ

since it is given that  β (beta) ends in the second quadrant

sinβ = 8/17 and cosβ = - 15/17

As we know it is:

cos(α - β) = cosα cosβ + sinα sinβ = - 12/13 · (- 15/17) + (- 5/13) · 8/17 =>

cos(α - β) = 180/221 - 40/221 = 140/221

cos(α - β) = 140/221

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