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LForNotKnowingMath
01.06.2021 •
Business
During the first quarter of the operating year, Computer Corp began construction of its new building at a cost of $60,000,000. The building will initially be financed with 30% internal equity (9% cost of equity) with the remainder from a $30,000,000 construction loan (three annual $10,000,000 payments plus interest at 6%) and its general debt facilities (8% weighted average interest rate.) Assuming that Computer incurred average accumulated expenses of $54,000,000 pertaining to the building construction during the year and had actual borrowing costs of $2,440,000, what amount of capitalized interest cost would be recognized by the company at year-end
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Ответ:
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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