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3 years ago

Permutations of the word "Congratulations"

Mathematics

1 answer:

Mice21 [21]3 years ago

5 0

Answer:

There are 15 letters, but if the two A's must always be together, that's the same as if they're just one letter, so our "base count" is 14! ; note that this way of counting means that we also don't need to worry about compensating for "double counting" identical permutations due to transposition of those A's, because we don't "count" both transpositions. However, that counting does "double count" equivalent permutations due to having two O's, two N's, and two T's, so we do need to compensate for that. Therefore the final answer is 14!/(23)=10,897,286,400

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Can someone tell me the answer to this please

lapo4ka [179]

Answer:

Your answer is 132 degrees

7 0

3 years ago

Read 2 more answers

Simplify the first trigonometric expression by writing the simplified form in terms of the second expression (1/1-cosx)-(cos/1+c

garik1379 [7]

$(\frac{1}{1-cos(x)})-(\frac{cos(x)}{1+cos(x)})$

cscx is 1/sinx

maybe they want us to use pythagorean identity

$cos^2(x)+sin^2(x)=1$

I notice we have 1-cos(x) and 1+cos(x), if we multiply them, we get $1-cos^2(x)$

and if we look at the pythagorean identity and minus cos^2(x) from both sides, we get

$sin^2(x)=1-cos^2(x)$

since $csc(x)=\frac{1}{sin(x)}$ , $csc^2(x)=\frac{1}{sin^2(x)}=\frac{1}{1-cos^2(x)}$

(recall that (a-b)(a+b)=a²-b²)

match the denomenators of the original fraction

multiply first fraction by $\frac{1+cos(x)}{1+cos(x)}$ and the 2nd by $\frac{1-cos(x)}{1-cos(x)}$

$(\frac{1+cos(x)}{1-cos^2(x)})-(\frac{cos(x)(1-cos(x))}{1-cos^2(x)})=$

$((csc^2(x))(1+cos(x)))-((csc^2(x))(cos(x)-cos^2(x)))=$

$csc^2(x)+csc^2(x)cos(x)-(csc^2(x)cos(x)-csc^2(x)cos^2(x)=$

$csc^2(x)+csc^2(x)cos(x)-csc^2(x)cos(x)+csc^2(x)cos^2(x)=$

$csc^2(x)+csc^2(x)cos^2(x)=$

$csc^2(x)(1+cos^2(x))$ , hmm, to get ride of those cos(x)

look to the pythagorean identity again

$sin^2(x)+cos^2(x)=1$ , force one side into form 1+cos^2(x)

$1+cos^2(x)=2-sin^2(x)$ , recall that since csc(x)=1/sin(x), sin(x)=1/csc(x) and sin^2(x)=1/(csc^2(x))

$1+cos^2(x)=2-\frac{1}{csc^2(x)}$

subsituting

$csc^2(x)(1+cos^2(x))=$

$(csc^2(x))(2-\frac{1}{csc^2(x)})=$ distributing

$2csc^2(x)-\frac{csc^2(x)}{csc^2(x)}=$

$2csc^2(x)-1$ is the simplified expression

8 0

3 years ago

At Pizza Hut they have exponential pizza, which is a 24-inch cheese pizza that costs $17.50. Each topping for the pizza costs $2

VashaNatasha [74]

So you would want to find what would add up to $29.25
So for the toppings ($2.35×5) equals $12.75
Now just add $17.50
SO your equation is:
(2.35×5)+17.50=29.25

6 0

4 years ago

What is the measure of angle X ? A. 147 B. 33 C. 100 D. 60

Musya8 [376]

Answer:

the answer is a. 147

Explaination:

A triangle always has a sum of 180°.

We already have the angle of two sides give.

10° and 23°

To find the last missing side, you add 10° and 23°, and minus the result from 180°.

10+23= 33