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shtirl [24]
3 years ago
10

Find the exact value of tan 15 degrees

Mathematics
1 answer:
pentagon [3]3 years ago
4 0
<span>tan(15) = 
sin(15) / cos(15) = 
sin(45 - 30) / cos(45 - 30) = 
[ sin(45)cos(30) - sin(30)cos(45) ] / [ cos(45)cos(30) + sin(45)sin(30)] 

Since sin(45) = cos(45) = √2/2, you can just factor that out from the top and bottom 
[ cos(30) - sin(30) ] / [ cos(30) + sin(30)] 
[ √3/2 - 1/2 ] / [ √3/2 + 1/2] 
(√3 - 1) / (√3 + 1) 
(√3 - 1)^2 / (√3+1)(√3 - 1) 
(√3 - 1)^2 / (3 - 1) 
(3 - 2√3 +1) / 2 
2 - √3 

There's also a formula for tan(a-b), but I couldn't remember it off hand.</span>
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3 years ago
Hats and mittens are on sale at the store! One woman was able to buy 5 hats and 4 pairs of mittens for $30.
aalyn [17]

The price of one hat is $2 and one pair of mittens is $5

Step-by-step explanation:

Hats and mittens are on sale at the store!

  • One woman was able to buy 5 hats and 4 pairs of mittens for $30
  • Another woman purchased 3 pairs of mittens and 2 hats for $19
  • The price of one hat is x
  • The price of one pair of mittens is y

We need to find x and y

∵ One woman was able to buy 5 hats and 4 pairs of mittens for $30

∵ The price of one hat is x

∵ The price of one pair of  mittens is y

- Multiply 5 hats by x and 4 pairs of mittens by y and equate

  their sum by 30

∴ 5x + 4y = 30 ⇒ (1)

∵ Another woman purchased 3 pairs of mittens and 2 hats for $19

- Multiply 2 hats by x and 3 pairs of mittens by y and equate

  their sum by 19

∴ 2x + 3y = 19 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -2 and equation (2) by 5 to eliminate x

∵ -10x - 8y = -60 ⇒ (3)

∵ 10x + 15y = 95 ⇒ (4)

- Add equations (3) and (4)

∴ 7y = 35

- Divide both sides by 7

∴ y = 5

Substitute the value of y in equation (1) or (2) to find x

∵ 2x + 3(5) = 19

∴ 2x + 15 = 19

- Subtract 15 from both sides

∴ 2x = 4

- Divide both sides by 2

∴ x = 2

The price of one hat is $2 and one pair of mittens is $5

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#LearnwithBrainly

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3 years ago
The number of penguins in Antarctica decreased by 30% between last year and this year. Last year there were 650 penguins. What i
goblinko [34]

9514 1404 393

Answer:

  455

Step-by-step explanation:

The decrease was 30% of 650, or ...

  0.30 · 650 = 195

So, the population this year is ...

  650 -195 = 455

3 0
3 years ago
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If 2/8 of a class has a pencil and 2/6 of the class has pins but no pencils, how many more students have pins then pencils?
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Answer:

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Step-by-step explanation:

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