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harkovskaia [24]

3 years ago

11

What is the area of rectangle ABCD?

2 answers:

lina2011 [118]3 years ago

8 0

Multiply the length by the width and your answer will be there.

Artist 52 [7]3 years ago

6 0

Answer: 104 units squared

Step-by-step explanation: Yes, I effing love you, you're welcome!! <3

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Geometric Sequence S = 1.0011892 + ... + 1.0012 + 1.001 + 1

leva [86]

Answer:

<em /> $S_{1893} =5632.98$ <em />

<em />

Step-by-step explanation:

The correct form of the question is:

$S = 1.001^{1892} + ... + 1.001^2 + 1.001 + 1$

Required

Solve for Sum of the sequence

The above sequence represents sum of Geometric Sequence and will be solved using:

$S_n = \frac{a(1 - r^n)}{1 - r}$

But first, we need to get the number of terms in the sequence using:

$T_n = ar^{n-1}$

Where

$a = First\ Term$

$a = 1.001^{1892}$

$r = common\ ratio$

$r = \frac{1}{1.001}$

$T_n = Last\ Term$

$T_n = 1$

So, we have:

$T_n = ar^{n-1}$

$1 = 1.001^{1892} * (\frac{1}{1.001})^{n-1}$

Apply law of indices:

$1 = 1.001^{1892} * (1.001^{-1})^{n-1}$

$1 = 1.001^{1892} * (1.001)^{-n+1}$

Apply law of indices:

$1 = 1.001^{1892-n+1}$

$1 = 1.001^{1892+1-n}$

$1 = 1.001^{1893-n}$

Represent 1 as $1.001^0$

$1.001^0 = 1.001^{1893-n}$

They have the same base:

So, we have

$0 = 1893-n$

Solve for n

$n = 1893$

So, there are 1893 terms in the sequence given.

Solving further:

$S_n = \frac{a(1 - r^n)}{1 - r}$

Where

$a = 1.001^{1892}$

$r = \frac{1}{1.001}$

$n = 1893$

So, we have:

$S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{1 -\frac{1}{1.001} }$

$S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{\frac{1.001 -1}{1.001} }$

$S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{\frac{0.001}{1.001} }$

$S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001^{1893}})}{\frac{0.001}{1.001} }$

Simplify the numerator

$S_{1893} =\frac{1.001^{1892} -\frac{1.001^{1892}}{1.001^{1893}}}{\frac{0.001}{1.001} }$

$S_{1893} =\frac{1.001^{1892} -1.001^{1892-1893}}{\frac{0.001}{1.001} }$

$S_{1893} =\frac{1.001^{1892} -1.001^{-1}}{\frac{0.001}{1.001} }$

$S_{1893} =(1.001^{1892} -1.001^{-1})/({\frac{0.001}{1.001} })$

$S_{1893} =(1.001^{1892} -1.001^{-1})*{\frac{1.001}{0.001}}$

$S_{1893} =\frac{(1.001^{1892} -1.001^{-1}) * 1.001}{0.001}$

Open Bracket

$S_{1893} =\frac{1.001^{1892}* 1.001 -1.001^{-1}* 1.001 }{0.001}$

$S_{1893} =\frac{1.001^{1892+1} -1.001^{-1+1}}{0.001}$

$S_{1893} =\frac{1.001^{1893} -1.001^{0}}{0.001}$

$S_{1893} =\frac{1.001^{1893} -1}{0.001}$

$S_{1893} =5632.97970294$

Hence, the sum of the sequence is:

<em /> $S_{1893} =5632.98$ <em> ----- approximated</em>

4 0

3 years ago

sara spent $ 2.30 on sweets , $ 3.20 on a pencil and $ 9.15 on an excerise book . What steps would you use to find out much less

user100 [1]

2.30 plus 3.20 and 9.15 is 14.65 .

8 0

3 years ago

Here is a picture of an older version of the flag of Great Britain. There is a rigid transformation that takes Triangle 1 to Tri

Ainat [17]

Answer:

The side lengths are the same.

Step-by-step explanation:

A rigid transformation does not change any dimensions. The side lengths are the same.

8 0

4 years ago

Read 2 more answers

How do you convert 0.991 into a fraction

inn [45]

991 / 1000 . The decimal is in the thousandths place, so you put it over one thousand

7 0

3 years ago

Read 2 more answers

Find the greatest possible error for each measurement.<br> 12.3 L

melisa1 [442]

Answer:

the GPE is 1/2 the unit of measure used to make the measurement or you say 1/2 the most precise unit

12.3 L has 0.1 as the most precise unit of measure, so 1/2 of 0.1 is 0.05 L which is c. above

look at it this way: 12.3 can be any number between 12.25 and 12.34 rounded to the nearest tenth

any number from 12.25 to 12.34 rounded to the nearest tenth gives you 12.3, so the GPE that you can possibly make is 0.05; if the number was 12.24 it would round down to 12.2 not up to 12.3 and if the number was 12.35 it would round up to 12.4 not round down to 12.3, so again the greatest possible error that you can make is 0.05

6 0

2 years ago