makennahudson94

04.02.2020 • 

Mathematics

While staying in jerusalem, israel, you decide to visit three other cities: tel aviv, holon, and ra’anana. the following table shows the costs associated with traveling to and from each city, with all costs listed in israeli new shekalim (nis).

origin and destination
cost (nis)
jerusalem to tel aviv
269
jerusalem to holon
201
jerusalem to ra’anana
281
tel aviv to jerusalem
235
tel aviv to holon
263
tel aviv to ra’anana
203
holon to jerusalem
150
holon to tel aviv
198
holon to ra’anana
290
ra’anana to jerusalem
176
ra’anana to tel aviv
234
ra’anana to holon
218

you can choose to visit these cities in any order, but you will start and end your trip in jerusalem. if you have a budget of nis 900, which of the following routes are possible?

i. jerusalem 2007-14-01-00-00_files/i025.jpg tel aviv 2007-14-01-00-00_files/i0250001.jpg ra’anana 2007-14-01-00-00_files/i0250002.jpg holon 2007-14-01-00-00_files/i0250003.jpg jerusalem
ii. jerusalem 2007-14-01-00-00_files/i0250004.jpg holon 2007-14-01-00-00_files/i0250005.jpg tel aviv 2007-14-01-00-00_files/i0250006.jpg ra’anana 2007-14-01-00-00_files/i0250007.jpg jerusalem
iii. jerusalem 2007-14-01-00-00_files/i0250008.jpg ra’anana 2007-14-01-00-00_files/i0250009.jpg tel aviv 2007-14-01-00-00_files/i0250010.jpg holon 2007-14-01-00-00_files/i0250011.jpg jerusalem
a.
ii only
b.
i and ii
c.
i and iii
d.
none of these are possible.

Ответ:

hdolly81

17.01.2022

Mathematics

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The answer is b. I and II

Cost (NIS)
Jerusalem to Tel Aviv: J-TA = 269
Jerusalem to Holon: J-H = 201
Jerusalem to Ra’anana: J-R = 281
Tel Aviv to Jerusalem: TA-J = 235
Tel Aviv to Holon: TA-H = 263
Tel Aviv to Ra’anana: TA-R = 203
Holon to Jerusalem: H-J = 150
Holon to Tel Aviv: H-TA = 198
Holon to Ra’anana: H-R = 290
Ra’anana to Jerusalem: R-J = 176
Ra’anana to Tel Aviv: R-TA = 234
Ra’anana to Holon: R-H = 218

Options: 
I. Jerusalem - Tel Aviv - Ra’anana - Holon - Jerusalem
J-TA + TA-R + R-H + H-J = 269 + 203 + 218 + 150 = 840
840 < 900

II. Jerusalem - Holon - Tel Aviv - Ra’anana - Jerusalem
J-H + H-TA + TA-R + R-J = 201 + 198 + 203 + 176 = 778
778 < 900

III. Jerusalem - Ra’anana - Tel Aviv - Holon - Jerusalem
J-R + R-TA + TA-H + H-J = 281 + 234 + 263 + 150 = 928
928 > 900

Hence, options I and II are possible.

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Ответ:

miajay14

12.08.2020

Mathematics

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Consider this example: say we want to convert x = 11 0101 1001₂ to base 3.

The binary expansion of x is

x = 1×2⁹ + 1×2⁸ + 1×2⁶ + 1×2⁴ + 1×2³ + 1×2⁰

which in base 10 reduces to

x = 512 + 256 + 64 + 16 + 8 + 1 = 857

Recall the first several powers of 3:

3⁰ = 1; 3¹ = 3; 3² = 9; 3³ = 27; 3⁴ = 81; 3⁵ = 243; 3⁶ = 729

Now it's a matter of computing quotients and remainders. Pick the largest power of 3 that fits into the target number, then check the remainder and repeat.

• How many times does the 729 go into 857? 1 time, and it leaves a remainder of 128, or

857 = 1×729 + 128 = 1×3⁶ + 128

• How many times does 81 go into 128? Also 1 time, so

128 = 1×81 + 47 = 1×3⁴ + 47

• How many times does 27 go into 47? Also 1 time,

47 = 1×27 + 20 = 1×3³ + 20

• How many times does 9 go into 20? 2 times,

20 = 18 + 2 = 2×9 + 2 = 2×3² + 2

• How many times does 1 go into 2? Also 2 times,

2 = 2 + 1 = 2×1 + 0 = 2×3⁰

So we found

857 = 1×3⁶ + 1×3⁴ + 1×3³ + 2×3² + 2×3⁰

which is the ternary expansion of x,

x = 1 011 202₃

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