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3 years ago

Show cos 20 * cos 40 * cos 80 =1/8

1 answer:

8 0

cos 20 cos 40 cos 80 =
= ( 2 sin 20 cos 20 cos 40 cos 80 ) / 2 sin 20 =
( multiple and divide by 2 sin 20 )
= ( sin 40 cos 40 cos 80 ) / 2 sin 20 =
= ( 1/2 sin 80 cos 80 ) / 2 sin 20 =
= ( sin 80 cos 80 ) / 4 sin 20 =
= 1/2 sin 160 / 4 sin 20 =
= sin 160 / 8 sin 20 = ( and since: sin 160 = sin 20 )
= 1 / 8

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I increase a number by 24% the answer is 6014 what number did I start with

miskamm [114]

Answer:

1443.36

Step-by-step explanation:

6014*.24=1443.36

Hope it helps

8 0

3 years ago

A box contains five slips of paper, marked $1, $1, $10, $25, and $25. The winner of a contest selects two slips of paper at rand

Arisa [49]

Answer:

w = $1 or $10 or $25

Probability distribution of w = ($1,$1 $1,$1 $1,$10 $1,$25 $1,$25 $1,$1 $1,$1 $1,$10 $1,$25 $1,$25 $10,$1 $10,$1 $10,$10 $10,$25 $10,$25 $25,$1 $25,$1 $25,$10 $25,$25 $25,$25 $25,$1 $25,$1 $25,$10 $25,$25 $25,$25)

Step-by-step explanation:

Since the winner gets the larger amount of the two slips picked, random variable 'w' which is the amount awarded could be $1 or $10 or $25.

The probability distribution of 'w' is the values that the statistic takes on. Which could be: $1,$1 $1,$1 $1,$10 $1,$25 $1,$25 $1,$1 $1,$1 $1,$10 $1,$25 $1,$25 $10,$1 $10,$1 $10,$10 $10,$25 $10,$25 $25,$1 $25,$1 $25,$10 $25,$25 $25,$25 $25,$1 $25,$1 $25,$10 $25,$25 $25,$25

6 0

3 years ago

a washer and dryer cost 750 combined the washer cost $50 more than the dryer what is the cost of the dryer?

-BARSIC- [3]

Answer:

350$ for dryer

Step-by-step explanation:

x = cost of dryer
x + 50 = cost of washer

750 = x + (x + 50)
750 = 2x + 50
700 = 2x
350 = x

3 0

2 years ago

I need help.. i really want to go sleep.. thank you so much...

Effectus [21]

Answer:

1) True 2) False

Step-by-step explanation:

1) Given $\sum\limits_{k=0}^8\frac{1}{k+3}=\sum\limits_{i=3}^{11}\frac{1}{i}$

To verify that the above equality is true or false:

Now find $\sum\limits_{k=0}^8\frac{1}{k+3}$

Expanding the summation we get

$\sum\limits_{k=0}^8\frac{1}{k+3}=\frac{1}{0+3}+\frac{1}{1+3}+\frac{1}{2+3}+\frac{1}{3+3}+\frac{1}{4+3}+\frac{1}{5+3}+\frac{1}{6+3}+\frac{1}{7+3}+\frac{1}{8+3}$ $\sum\limits_{k=0}^8\frac{1}{k+3}=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}$

Now find $\sum\limits_{i=3}^{11}\frac{1}{i}$

Expanding the summation we get

$\sum\limits_{i=3}^{11}\frac{1}{i}=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}$

Comparing the two series we get,

$\sum\limits_{k=0}^8\frac{1}{k+3}=\sum\limits_{i=3}^{11}\frac{1}{i}$ so the given equality is true.

2) Given $\sum\limits_{k=0}^4\frac{3k+3}{k+6}=\sum\limits_{i=1}^3\frac{3i}{i+5}$

Verify the above equality is true or false

Now find $\sum\limits_{k=0}^4\frac{3k+3}{k+6}$

Expanding the summation we get

$\sum\limits_{k=0}^4\frac{3k+3}{k+6}=\frac{3(0)+3}{0+6}+\frac{3(1)+3}{1+6}+\frac{3(2)+3}{2+6}+\frac{3(3)+4}{3+6}+\frac{3(4)+3}{4+6}$

$\sum\limits_{k=0}^4\frac{3k+3}{k+6}=\frac{3}{6}+\frac{6}{7}+\frac{9}{8}+\frac{12}{8}+\frac{15}{10}$

now find $\sum\limits_{i=1}^3\frac{3i}{i+5}$

Expanding the summation we get

$\sum\limits_{i=1}^3\frac{3i}{i+5}=\frac{3(0)}{0+5}+\frac{3(1)}{1+5}+\frac{3(2)}{2+5}+\frac{3(3)}{3+5}$

$\sum\limits_{i=1}^3\frac{3i}{i+5}=\frac{3}{6}+\frac{6}{7}+\frac{9}{8}$

Comparing the series we get that the given equality is false.

ie, $\sum\limits_{k=0}^4\frac{3k+3}{k+6}\neq\sum\limits_{i=1}^3\frac{3i}{i+5}$

6 0

3 years ago

{(1, -2), (-2, 0), (-1, 2), (1, 3)}

-Dominant- [34]

It is not a function because x repeats
Domain={1,-2,-1}
Range={-2,0,2,3}

Hope this helps

Have a great day/night

3 0

2 years ago