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zimovet [89]
3 years ago
13

Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of β

if β < α. sin(3x − 27) = cos(5x + 5)
A) 14°
B) 15°
C) 75°
D) 76°
Mathematics
1 answer:
ElenaW [278]3 years ago
5 0

Answer:

A) 14°

Step-by-step explanation:

If α and β are the two angles other than 90° in a right triangle, then we have the relation between α and β as, α+β=90°.

Therefore, Sin α = Sin (90° -β) =Cos β.

So, we can write the reverse as if Sin α = Cosβ, then we have α + β =90°.

It is given that, Sin (3x-27) = Cos (5x+5).

Hence, we can write (3x-27) + (5x + 5) = 90

⇒ 8x = 90+27-5 =112

⇒ x = 14°

Therefore, option A. is correct. (Answer)

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HELP PLEASE!!
ANTONII [103]
<span>Volume of the Sphere V = 4/3pi x r^3 So when diameter d = 3 inches => r = 1.5 inches volume of the sphere = 4.188 x r^3 = 4.188 x 1.5^3 = 14.14 in So when diameter d = 8 inches => r = 4 inches volume of the sphere = 4.188 x r^3 = 4.188 x 4^3 = 268.03 in So when diameter d = 9 inches => r = 4.5 inches volume of the sphere = 4.188 x r^3 = 4.188 x 4.5^3 = 381.63 in value for option (a) is 3 x 14.14 = 42.42 inches value for option (b) is 268.03 inches value for option (c) is 381.63 / 2 = 190.815 inches So the correct option would be (b)</span>
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