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adelina 88 [10]
4 years ago
14

Which equation could be used to calculate the sum of the geometric series? One-third + two-ninths + StartFraction 4 Over 27 EndF

raction + StartFraction 8 Over 81 EndFraction + StartFraction 16 Over 243 EndFraction S 5 = StartFraction one-third (1 minus (two-thirds) Superscript 5 Baseline) Over (1 minus two-thirds) EndFraction S 5 = StartFraction two-thirds (1 minus (one-third) Superscript 5 Baseline) Over (1 minus one-third) EndFraction S = StartFraction one-third Over (1 minus two-thirds) EndFraction S = StartFraction two-thirds Over (1 minus one-third) EndFraction
Mathematics
2 answers:
Troyanec [42]4 years ago
5 0

Answer:

A

Step-by-step explanation:

edge 2020

kondaur [170]4 years ago
4 0

Answer:

S 5 = StartFraction one-third (1 minus (two-thirds) Superscript 5 Baseline) Over (1 minus two-thirds) EndFraction

Step-by-step explanation:

Given the geometric series:

1/3+2/9+4/27+8/81+16/243

First we must know that the series is a finite series with just 5terms.

Before we can know the formula to calculate sum of the first five terms of the series, we must determine its common ratio (r) first.

r = (2/9)÷1/3 = 4/27÷2/9= 8/81÷4/27

r = 2/9 × 3/1

r = 2/3

Similarly;

r = 4/27×9/2

r = 2/3

Since all values of r is the as them the common ratio is 2/3.

If r< 1 in geometric series, then the formula for finding its sum is applicable

Sn = a(1-rⁿ)/1-r

a is the first term = 1/3

r is the common ratio = 2/3

n is the number of terms = 5

Substituting the values in the formula we have:

S5 = 1/3{1-(2/3)^5}/1-2/3

This gives the requires equation

S 5 = StartFraction one-third (1 minus (two-thirds) Superscript 5 Baseline) Over (1 minus two-thirds) EndFraction

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Marysya12 [62]

Equivalent expression is the expression of two equation when the way of representation of the two equation is different but the result is same.The expressions which are equivalent to the given expression are,

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Given information-

The expression given in the problem is,

\ln x+2 \ln 5 +\ln1

<h3>Equivalent expression-</h3>

Equivalent expression is the expression of two equation when the way of representation of the two equation is different but the result is same.

For given expression,

\ln x+2 \ln 5 +\ln1

As the above function is the function of <em>x. </em>Thus it can be written as,

f(x)=\ln x+2 \ln 5 +\ln1

<h3>Logarithm power rule</h3>

Logarithm power rule states that the exponent of the logarithm function can transfers to front of the logarithm and vice versa. Thus,

f(x)=\ln x+ \ln 5^2 +\ln1\\&#10;f(x)=\ln x+ \ln 25 +\ln1

Now the value of \ln 1 is equal to the zero. Thus,

f(x)=0+\ln 25 +\ln1\\&#10;f(x)=0+\ln 25 +\ln1\\&#10;f(x)=\ln 25 +\ln1\\&#10;f(x)=\ln 25 +0\\&#10;f(x)=\ln 25

Hence the expressions which are equivalent to the given expression are,

  • \ln25+\ln1
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Learn more about the equivalent expression here;

brainly.com/question/10628562

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You pay $228.50 in taxes at a rate of 10.25% to buy a new TV. How much did the tv cost original? Round your number to the hundre
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Answer:

$2229.27

Step-by-step explanation:

tax rate: 10.25%

tax amount: $228.50

price before tax: x

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0.1025x = 228.5

x = 228.5/0.1025

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Answer: $2229.27

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A model car is 5 inches long. The actual length of the car is 15 feet . What is the scale factor of the model car?
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Answer:

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Step-by-step explanation:

To obtain the scale factor, the dimensions must be in the same units.

Using the conversion

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3 years ago
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Nikitich [7]

Answer:

length is 15.5 and the width is 12.5

Step-by-step explanation:

Length rectangle = 3cm. longer than its width.

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P = 2L +2w

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Solution:

Length= 15.5 cm

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