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lord [1]
3 years ago
11

If the Circumference of a circle is 12 cm, what is the circles Diameter? Please help thankss!

Mathematics
1 answer:
BARSIC [14]3 years ago
5 0

Answer:

Step-by-step explanation:

Circumference = πd = 12

d = 12/π cm

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What is the image of (-9,3)(−9,3) after a reflection over the y-axis?
nirvana33 [79]

Answer:

(9, 3 )

Step-by-step explanation:

under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

(- 9, 3 ) → (9, 3 )

3 0
2 years ago
The symbol ⊕ is used to denote exclusive or, so p ⊕ q ≡ (p v q) ^ ~ (p ^ q).
Elan Coil [88]

I'll use text forms of the logical symbols because copying/pasting on mobile is annoying.

⊕ = XOR

∨ = OR

∧ = AND

~ = NOT

↔ = IFF (meaning "if and only if")

→ = IMP (short for "implies")

and for logical equivalence I'll use a regular equal sign.

Then

p XOR q = (p OR q) AND NOT (p AND q)

(a) By definition of XOR, we have

p XOR p = (p OR p) AND NOT (p AND p)

= p AND NOT p

and this is tautologically FALSE.

(b) To rewrite XOR, first distribute the NOT over the AND using DeMorgan's law:

NOT (p AND q) = NOT p OR NOT q

Then we can interchange the AND and ORs using their respective distributive properties. That is,

p XOR q = (p OR q) AND (NOT p OR NOT q)

= (p AND (NOT p OR NOT q)) OR (q AND (NOT p OR NOT q))

= ((p AND NOT p) OR (p AND NOT q)) OR ((q AND NOT p) OR (q AND NOT q))

Both (p AND NOT p) and (q AND NOT q) are tautologically FALSE, so the truth value of either OR depends only on the other statements, so we have

p XOR q = (p AND NOT q) OR (q AND NOT p)

Recall the definition of IFF:

p IFF q = (p IMP q) AND (q IMP p)

Also recall that IMP is logically equivalent to

p IMP q = p OR NOT q

Then we have

p IFF q = (p OR NOT q) AND (q OR NOT p)

so that its negation is

NOT (p IFF q) = NOT ((p OR NOT q) AND (q OR NOT p))

= NOT (p OR NOT q) OR NOT (q OR NOT p)

= (NOT p AND q) OR (NOT q AND p)

The statements in bold match, so p XOR q is indeed equivalent to NOT (p IFF q).

3 0
3 years ago
a D.J. at a school dance plans to play dance music for 2 hours. she has 20 requests for songs. Each song plays for 3 1/2 minutes
viva [34]

So, put 2 hours into minutes. You get 120. Now, seeing how you have 20 song requests, and each one takes 3.5 minutes, multiply those two values. Now you have 70. After doing that, just subtract 70 from 120 and get 50.

tada

answer is 50

4 0
3 years ago
Compute a · (b ✕ c), where a = i − 3j + k, b = 4i + j + k and c = 9i − j + 3k.
grandymaker [24]
\mathbf a=\mathbf i-3\,\mathbf j+\mathbf k
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Umnica [9.8K]

Answer:

Step-by-step explanation:

The greatest common factor they share is 4.

4(x^3+8)

7 0
3 years ago
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