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2 years ago

The diagram below shows circle 0 with radii OA and OB. The length of a radius is 6

Mathematics

1 answer:

shepuryov [24]2 years ago

5 0

Answer:

124°

Step-by-step explanation:

We are to solve for the central angle.

In the question,

We are given

The length of the radius or radius = 6 inches

The length of the arc or the arc length (AB) = 13 inches

The formula for the Arc length of a circle = 2πr × (central angle in degree ÷ 360)

From the above formula, we can derive our formula for the measure of the central angle.

The formula for the measure of the central angle AOB =( Arc length × 360 ) ÷ 2πr

Angle AOB = (13 inches × 360) ÷ 2 × π × 6 inches

Angle AOB = 4680 ÷ 37.699111843

Angle AOB = 124.14083392°

Approximately Angle AOB to the nearest degree = 124°

Therefore, the measure of angle AOB to the nearest degree = 124°

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Given that A and B are true and X and Y are false, determine the truth value of the following proposition: ~[(A ⊃ Y) v ~(X ⊃ B)]

Anni [7]

Answer:

The value of the proposition is FALSE

Step-by-step explanation:

~[(A ⊃ Y) v ~(X ⊃ B)] ⋅ [~(A ≡ ~X) v (B ⊃ X)]

Let's start with the smallest part: ~X. The symbol ~ is negation when X is true with the negation is false and vice-versa. In this case, ~X is true (T)

~[(A ⊃ Y) v ~(X ⊃ B)] ⋅ [~(A ≡ T) v (B ⊃ X)]

Now the parts inside parenthesis: (A ⊃ Y),(X ⊃ B),(A ≡ T) and (B ⊃ X). The symbol ⊃ is the conditional and A ⊃ Y is false when Y is false and A is true, in any other case is true. The symbol ≡ is the biconditional and A ≡ Y is true when both A and Y are true or when both are false.

(A ⊃ Y) is False (F)

(X ⊃ B) is True (T)

(A ≡ T) is True (T)

(B ⊃ X) is False (F)

~[(F) v ~(T)] ⋅ [~(T) v (F)]

The two negations inside the brackets must be taken into account:

~[(F) v F] ⋅ [F v (F)]

The symbol left inside the brackets v is the disjunction, and A v Y is false only with both are false. F v (F) is False.

~[F] ⋅ [F]

Again considerating the negation:

T⋅ [F]

Finally, the symbol ⋅ is the conjunction, and A v Y is true only with both are true.

T⋅ [F] is False.

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2 years ago

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Korvikt [17]

Answer:

I noticed a pattern:

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