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3 years ago

14

Find the area of a sector of a circle with radius 6 centimetre if angle of sector is 60 degree

1 answer:

Gnesinka [82]3 years ago

6 0

Answer:

Step-by-step explanation:

$area=\frac{\pi r^2 \times\theta}{360} =\frac{\pi 6^2 \times 60}{360} =6 \pi \approx 18.85~ cm^2$

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For each of the following, use logic laws to decide whether the statement is a tautology contradiction, or neither. a (a) (A B)

spayn [35]

Answer:

The statement $(A\rightarrow \lnot B)\land (B\rightarrow A)$ is a contingency.

The statement $(P\rightarrow \lnot P)\land P$ is a contradiction.

Step-by-step explanation:

A tautology is a proposition that is always true.

A contradiction is a proposition that is always false.

A contingency is a proposition that is neither a tautology nor a contradiction.

a) To classify the statement $(A\rightarrow \lnot B)\land (B\rightarrow A)$ , you need to use the logic laws as follows:

$(A\rightarrow \lnot B)\land (B\rightarrow A) \equiv$

$\equiv (\lnot A \lor\lnot B)\land(\lnot B \lor A)$ by the logical equivalence involving conditional statement.

$\equiv (\lnot B\lor \lnot A )\land(\lnot B \lor A)$ by the Commutative law.

$\equiv \lnot B \lor (\lnot A \land A)$ by Distributive law.

$\equiv \lnot B \lor (A \land \lnot A)$ by the Commutative law.

$\equiv \lnot B \lor F$ by the Negation law.

Therefore the statement $(A\rightarrow \lnot B)\land (B\rightarrow A)$ is a contingency.

b) To classify the statement $(P\rightarrow \lnot P)\land P$ , you need to use the logic laws as follows:

$(P\rightarrow \lnot P)\land P \equiv$

$\equiv (\lnot P \lor \lnot P)\land P$ by the logical equivalence involving conditional statement.

$\equiv P \land (\lnot P \lor \lnot P)$ by the Commutative law.

$\equiv (P \land \lnot P) \lor (P \land \lnot P)$ by Distributive law.

$\equiv F \lor F \equiv F$ by the Negation law.

Therefore the statement $(P\rightarrow \lnot P)\land P$ is a contradiction.

8 0

3 years ago

Least to greatest 1/2, 2/5, 6/10

Elza [17]

Answer : 2/5, 1/2, 6/10

7 0

3 years ago

Read 2 more answers

Plz help..................

Mama L [17]

The answer is 9, 40, 41

5 0

3 years ago

Solve by substitution<br> 3x-4y=-4<br> y=2x-4

dybincka [34]

Answer:

x=4 and y=4

Step-by-step explanation:

From first function we have:

$3x - 4y = - 4 \\ 4y = 3x + 4$

And from the second one:

$y = 2x - 4 \\ 4y = 8x - 16$

Substitute them:

$4y = 3x + 4 \\ 4y = 8x - 16 \\ \\ 0 = - 5x + 20 \\ x = 4 \\ y = 4$

7 0

2 years ago

Solve for c. a (c−b) = d a. c = d - ab / a b. c = ab - d / a c. c = d ab / a d. c = d - ab / a

Nitella [24]

A(c - b) = d
ac - ab = d
ac = d + ab
c = (d + ab)/a

7 0

3 years ago