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zimovet [89]
3 years ago
15

How do I write an explicit rule for this sequence?

Mathematics
2 answers:
Vaselesa [24]3 years ago
8 0

Answer:

next should be 2250 if my math is correct

jeyben [28]3 years ago
4 0

Answer:

a_{n} = 10(5)^{n-1}

Step-by-step explanation:

Note that consecutive terms have a common ratio, that is

50 ÷ 10 = 250 ÷ 50 = 1250 ÷ 250 = 5

This indicates that the sequence is geometric with n th term ( explicit rule )

a_{n} = a(r)^{n-1}

where a is the first term and r the common ratio,

Here a = 10 and r = 5, thus

a_{n} = 10(5)^{n-1} ← explicit rule

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Sinx = 1/2, cosy = sqrt2/2, and angle x and angle y are both in the first quadrant.
Leviafan [203]

Answer:

Option D. 3.73​

Step-by-step explanation:

we know that

tan(x+y)=\frac{tan(x)+tan(y)}{1-tan(x)tan(y)}

and

sin^{2}(\alpha)+cos^{2}(\alpha)=1

step 1

Find cos(X)

we have

sin(x)=\frac{1}{2}

we know that

sin^{2}(x)+cos^{2}(x)=1

substitute

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

cos^{2}(x)=1-\frac{1}{4}

cos^{2}(x)=\frac{3}{4}

cos(x)=\frac{\sqrt{3}}{2}

step 2

Find tan(x)

tan(x)=sin(x)/cos(x)

substitute

tan(x)=1/\sqrt{3}

step 3

Find sin(y)

we have

cos(y)=\frac{\sqrt{2}}{2}

we know that

sin^{2}(y)+cos^{2}(y)=1

substitute

sin^{2}(y)+(\frac{\sqrt{2}}{2})^{2}=1

sin^{2}(y)=1-\frac{2}{4}

sin^{2}(y)=\frac{2}{4}

sin(y)=\frac{\sqrt{2}}{2}

step 4

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tan(y)=sin(y)/cos(y)

substitute

tan(y)=1

step 5      

Find tan(x+y)

tan(x+y)=\frac{tan(x)+tan(y)}{1-tan(x)tan(y)}

substitute

tan(x+y)=[1/\sqrt{3}+1}]/[{1-1/\sqrt{3}}]=3.73

7 0
3 years ago
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3 0
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Ostrovityanka [42]

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Answer :-52/75

4 0
3 years ago
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