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3 years ago

Given that √3^n = 3^x/27^y. Express n in terms of x and y.

Mathematics

1 answer:

Radda [10]3 years ago

7 0

Answer:

Step-by-step explanation:

HEllo,

$(\sqrt{3})^n=3^{\frac{n}{2}}=\dfrac{3^x}{27^y}=3^x\times(3^3)^{-y}=3^{x-3y}\\\\\dfrac{n}{2}=x-3y\\\\\boxed{\sf \bf n= 2x-6y}$

Hope this helps

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Given the sequence 8, 16, 32, 64, ..., which expression would give the thirteenth term?

mrs_skeptik [129]

8, 16, 32, 64,…
×2 ×2 ×2

$a_{n} = a_{1} * r^{n - 1}$
$a_{n} = 8 * 2^{13 - 1}$
$a_{n} = 8 * 2^{12}$
$a_{n} = 8 * 4096$
$a_{n} = 32768$

   First Term: 8
      Second Term: 16
      Third Term: 32
      Fourth Term: 64
       Fifth Term: 128
      Sixth Term: 256
   Seventh Term: 512
   Eighth Term: 1024
   Ninth Term: 2048
      Tenth Term: 4096
   Eleventh Term: 8192
   Twelfth Term: 16384
Thirteenth Term: 32768

$The\ expression\ that\ would\ give\ the\ thirteenth\ term\ of\ the\ problem\ would\ be\ the\ equation\ of\ the\ geometric\ sequence,\ which\ is\ equal\ to\ a_{n} = a_{1} * r^{n - 1}.$

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3 years ago

Read 2 more answers

Please help ASAP! It’s due in 20 min and I have complete it! I just need the statements and reasons! Thank you

azamat

Answer:

1) <11 and <14 are Same-Side Exterior Angles causing them to be supplementary.

2. <8 and <9 are Same-Side Interior Angles causing them to be supplementary.

Step-by-step explanation:

See answer above.

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3 years ago

4. State one use of the following gases: a) Argon - b) Helium -

Aleonysh [2.5K]

Step-by-step explanation:

HELIUM: To fill air balloon

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3 years ago

The length of a rectangle is 3 cm greater than its width. the perimeter is 25 cm. what are the dimensions of the rectangle?

slega [8]

P = 2(L + W)
P = 25
L = W + 3
now we sub and solve
25 = 2(W + 3 + W)
25 = 2(2W + 3)
25 = 4W + 6
25 - 6 = 4W
19 = 4W
19/4 = W
4.75 = W <== width = 4.75 cm (or 4 3/4 cm)

L = W + 3
L = 4.75 + 3
L = 7.75 <== length = 7.75 cm (or 7 3/4 cm)

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3 years ago