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3 years ago

10. In ABC, if A and B are acute angles, and sin A= 10/13 what is the value of cos A ?

Mathematics

1 answer:

Margarita [4]3 years ago

5 0

Answer:

In triangle AB, A and B are acute angles so. AC and BC are right angles.

Sin A = 10/13

13 is the hypotenuse side and 10 is the opposite side.

To find cos A.

From pythagorean theorem:

Step-by-step explanation:

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Answer:

r = -8sin(theta)

Step-by-step explanation:

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A printer takes 30 minutes to print a banner and a poster. I will take 50 minutes to print a banner and three posters. How long

qwelly [4]

Answer:

It takes the printer 20 minutes to print a banner

Step-by-step explanation:

Notice that there are two unknowns in this problem: the time to print a poster and the time to print a banner. Let's assign the letter "b" to the time it takes to print a banner, and "p' the time it takes to print a poster.

So we can write the following two equations involving the total amount of time that takes to print in the two cases:

$b+p=30\\b+3p=50$

We can solve for the unknown "p" by subtracting term by term in the equation set above:

$b+3p=50\\b+p=30\\\\b-b+3p-p=50-30\\2p=20\\p=10$

So it takes 10 minutes to print each poster, we can find the time it takes to print the banner by using the value we just found in one of the equations:

$b+p=30\\b+10=30\\b=20$

So, it takes 20 minutes to print a banner.

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3 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).

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3 years ago

How to solve 3x^2+22x=-35 by factoring

Zepler [3.9K]

Answer:

x = -7/3 or -5

Step-by-step explanation:

3x^2 + 22x = -35

3x^2 + 22x + 35 = 0

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so for 3x+7:

3x+7 = 0

3x = -7

x = -7/3

So for x + 5:

x + 5 = 0

x = -5

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