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madreJ [45]
2 years ago
7

0a%20_%7B6%7D%20x%20%5E%7B6%7D%20%2B%20a%20_%7B5%7D%20x%20%5E%7B5%7D%2B....%20%5C%5C%20%5Csf%20%2B%20a%E2%82%81x%20%2B%20a%20_%7B0%7D%2C%20then%20%5C%3A%20%5C%3A%20a_0%20%2B%20a%E2%82%81%20%2B%20a%E2%82%82%20%2B%20a_3%20%2B%20a_4%20%2B%20a_5%20%2B%20a_6%20%2B%20a7%20%3D%20" id="TexFormula1" title=" \sf \: If (3x-1) ^{7} = a _{7} x ^{7} + a _{6} x ^{6} + a _{5} x ^{5}+.... \\ \sf + a₁x + a _{0}, then \: \: a_0 + a₁ + a₂ + a_3 + a_4 + a_5 + a_6 + a7 = " alt=" \sf \: If (3x-1) ^{7} = a _{7} x ^{7} + a _{6} x ^{6} + a _{5} x ^{5}+.... \\ \sf + a₁x + a _{0}, then \: \: a_0 + a₁ + a₂ + a_3 + a_4 + a_5 + a_6 + a7 = " align="absmiddle" class="latex-formula">
a)0
b)1
c)128
d)64

Please solve this for me. Need step-by-step explanation. Spam free answer required. Thank you in anticipation.

​
Mathematics
2 answers:
GrogVix [38]2 years ago
6 0
Answer is c) 128

I added the step by step process in the pic attached, I don't know how to explain it very well but you can use binomial theorem for (3x-1)^7

Then you can add up all the coefficients of the calculated values as the question mentions afterwards a^7 + a^6 +..... which means it only wants you to add up the coefficients of the consecutive x terms, otherwise it would say a^7x^7 + a^6x^6 +..... and so on

Hope this helps :)

Irina-Kira [14]2 years ago
5 0

Answer:

hope it helps have a great day

Answer is option C

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Using <span>De Moivre's formula
</span>
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=================================
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Social Median  GDP (PPP), Y      X^2           Y^2            XY

usage (%), X

18085                       66         327067225 4356 1193610

15833                       56         250683889 3136 886648

6117                          47           37417689 2209 287499

6559                        42           43020481        1764 275478

9948                        40           98962704       1600 397920

15264                         41          232989696     1681 625824

17522                        50          307020484     2500 876100

4661                          34            21724921        1156 158474

9833                         54            96687889    2916 530982

5186                         22           26894596     484         114092

18579                         69            345179241    4761 1281951

19105                         67           365001025   4489 1280035

13580                         59            184416400   3481 801220

12115                           49            146773225   2401 593635

15614                          44            243796996   1936 687016

5289                           45            27973521   2025 238005

7508                           29            56370064    841 217732

11521                            43            132733441    1849 495403

2824                           32            7974976     1024 90368

3542                           27            12545764      729 95634

1855                           36            3441025        1296 66780

2056                           35            4227136        1225 71960

3142                              7            9872164           49 21994

1473                              13           2169729          169 19149

Total 227211 1007         2984944281  48077 11307509

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