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Nitella [24]
3 years ago
6

Find the exact value of tan(pi/12) using the sum and difference formulas

Mathematics
2 answers:
kari74 [83]3 years ago
7 0
Π/12 is half of π/6, which is 30 degree
tan(α/2)=(1-cosα)/sinα)
plug in the values: tan(π/12)=(1-cosπ/6)/sin(π/6)=(1-√3/2)/(1/2)=2-√3
JulsSmile [24]3 years ago
4 0

Answer:

A

Step-by-step explanation:

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What is the name of the shape of the graph of a quadratic function?
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Is this a multiple choice or no
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3 years ago
A ball was dropped from a height of 60m. Each time it hit the ground, it bounced up 1/2 (half) of the height that it dropped. Ho
asambeis [7]

Answer:

The ball traveled 116.25 m when it hit the ground for the fifth term

Step-by-step explanation:

This is a geometric progression exercise and what we are asked to look for is the sum of a GP.

The ball was dropped from a height of 60 m. This means that the initial height of the ball is 60 m.

First value, a = 60

Each time it hit the ground, it bounced up 1/2 (half) of the height that it dropped.

This is the common ratio, r = 1/2 = 0.5

The number of terms it hits the ground is the number of terms in the GP.

number of terms, n = 5

The distance traveled by the ball when it hit the ground for the fifth term will be modeled by the equation:

S_n = \frac{a(1 - r^n) }{1 - r} \\S_5 =  \frac{60(1 - 0.5^5) }{1 - 0.5}\\S_5 =  \frac{58.125}{0.5} \\S_5 = 116.25 m

4 0
3 years ago
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Veronika [31]

Answer:

A. England = 56000000

B. 1.046 * 10^7

C. 9.7 to 2sf

Step-by-step explanation:

A. England = 5.60*10000000

=56000000

B. Wale = 3.14*1000000 = 3140000

Scotland = 5.44*1000000 = 5440000

Northern Ireland = 1.88*1000000 =1880000

Total = 10460000

In standard form =1.046*10^7

C. Total population as at 2018 = 66460000

expected population by 2041 = 72900000

increase or change = (72900000 - 66460000) = 6440000

% change = (6440000/66460000)*100

= 0.0969003912 * 100

= 9.69003912

= 9.7 to 2sf

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3 years ago
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marin [14]

Answer:

Horizontal shift of 1 unit to the right, a vertical shift upward of 6 units, and a vertical stretch by a factor of 3 ..

Step-by-step explanation:

Given function is:

3[|x-1|+2]

Can also be written as:

3|x-1|+6

As we can see that the -1 is grouped with x which means it is a horizontal shift of 1 unit to the right.

Now, 6 is added to the function and it is not grouped with x which means that there is a vertical shift of 6 units upward.

Lastly, 3 is multiplied with the term containing x which means that there is a vertical stretch of 3 units.

Hence, the correct option is:

Horizontal shift of 1 unit to the right, a vertical shift upward of 6 units, and a vertical stretch by a factor of 3 ..

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