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satela [25.4K]
2 years ago
10

Kay started a chess club, and for a while she was the only member. She planned to have each member find two new members each mon

th. By the end of the first month, she had found two new members. If her plan is carried out, how many members will the club have at the end of 6 months
Mathematics
1 answer:
Lyrx [107]2 years ago
6 0

Answer:

  127

Step-by-step explanation:

The sum of 7 terms of the series 1 +2 +4 +... with first term 1 and common ratio 2 is given by ...

  Sn = a1 × (r^n -1)/(r -1) . . . . . . first term a1, common ratio r

  S7 = 1 × (2^7 -1)/(2 -1) = (128 -1)/1 = 127

At the end of 6 months, the club will have 127 members.

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The angle θ lies in Quadrant II. sinθ=3/4 What is cosθ ?
Elden [556K]

Hello from MrBillDoesMath

Answer:

[email protected] = - sqrt(7)/ 4    

which is choice B

Discussion:

This problem can be solved by drawing triangles and looking at ratios of sides or by using the trig identity:

([email protected])^2 + (sin2)^2 = 1

If [email protected] = 3/4 , the

([email protected])^2 + (3/4)^2 = 1 =>              (subtract (3/4)^2 from both sides)

([email protected])^2 = 1 - (3/4)^2  = 1 - 9/16   = 7/16

So...... taking the square root of both sides gives

[email protected] =  +\- sqrt(7)/ sqrt(16) = +\- sqrt(7)/4

But is [email protected] positive or negative?  We are told that @ is in the second quadrant and cos(@) is negative in this quadrant, so our answer must be negative

[email protected] = - sqrt(7)/ 4    

which is choice B


Thank you,

Mr. B


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Step-by-step explanation:

hope this helps :)

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