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andreyandreev [35.5K]
3 years ago
14

Modular arithmetic Pls a little explaine it

Mathematics
1 answer:
fredd [130]3 years ago
6 0

Step-by-step explanation:

(72)¹⁴³ ≡ x (mod 7)

Since 72 ≡ 2 (mod 7),

72³ ≡ 2³ (mod 7) ≡ 1 (mod 7).

Therefore (72)¹⁴³ = (72³)⁴⁷ * (72²)

≡ 1⁴⁷ * 4 (mod 7) ≡ 4 (mod 7).

The answer is A.

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In terms of the trigonometric ratios for ΔABD, what is the length of line segment BD?
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In terms of the trigonometric ratios for ΔABD, what is the length of line segment BD?

Answer:

BD = c*sin(A)

BD = c*cos(B)

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Step-by-step explanation:

∆ABD is a right triangle.

Recall: trigonometric ratios of any right triangle can easily be understood or remembered with the acronym, SOHCAHTOA.

SOH => sin(θ) = opposite/hypotenuse

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Thus, the length of segment BD, in terms of trigonometric ratios for ∆ABD can be done as follows:

Let BD = x

AB = c

AD = b

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θ = A

Opposite = DB = x

hypotenuse = AB = c

sin(A) = \frac{x}{c}

Make x the subject of formula.

c*sin(A) = x

BD = x = c*sin(A)

=>The Cosine ratio for the length of line segment BD = x, using CAH

θ = B

Adjacent = DB = x

hypotenuse = AB = c

cos(B) = \frac{x}{c}

Make x the subject of formula.

c*cos(B) = x

BD = x = c*cos(B)

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θ = A

Adjacent = DB = x

hypotenuse = AD = b

tan(A) = \frac{x}{b}

Make x the subject of formula.

b*tan(A) = x

BD = x = b*tan(A)

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