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anygoal [31]
3 years ago
13

Rewrite 1−2 sin ^2 (22.5∘) using a double-angle identity.

Mathematics
1 answer:
attashe74 [19]3 years ago
3 0
Using the identity :

Cos (2a) = 1-2 Sin^2(a)

Therefore :<span>1−2 sin ^2 (22.5∘) = Cos(2a)
                                                = Cos (2 * 22.5) = Cos 45</span>
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The length of a rectangle is 5959 inches greatergreater than twice the width. if the diagonal is 2 inches more than the​ length,
lorasvet [3.4K]

Length: 2w + 59

width: w

diagonal: (2w + 59) + 2  = 2w + 61

Length² + width² = diagonal²

(2w + 59)² + (w)² = (2w + 61)²

(4w² + 118w + 3481) + w²  = 4w² + 122w + 3721

5w² + 118w + 3481 = 4w² + 122w + 3721

w² + 118w + 3481 = 122w + 3721

w² - 4w + 3481 = 3721

w² - 4w - 240 = 0

a = 1, b = -4, c = -240

w = [-(b) +/- \sqrt{(b)^{2}  - 4(a)(c) }]/2(a)

 = [-(-4) +/- \sqrt{(-4)^{2}  - 4(1)(-240) }]/2(1)

   =  [4 +/- \sqrt{(16  + 960) }]/2        

  = [4 +/- \sqrt{(976) }]/2  

  = [2 +/- 4\sqrt{(61) }]/2  

  = 1 +/- 2\sqrt{(61) }

since width cannot be negative, disregard  1 - 2√61

w = 1 + 2√61  ≈ 16.62

Length: 2w + 59  =  2(1 + 2√61) + 59  = 2 + 4√61 + 59  =  61 + 4√61  ≈ 92.24

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3 years ago
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Nana76 [90]

Answer:

y = 0 and x = 6

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Step-by-step explanation:

2x+3y=12 is the equation of a straight line.

There are infinite number of solutions, but here you're probably looking for solutions where x and y are whole numbers. Trial and error will find you some, although if you examine the equation closely you see that if x is a multiple of 3 and y is a multiple of 2, then they produce terms that are the LCM (least common multiple) of 2 and 3, namely 6. That's the logic in the whole number solutions.

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