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WARRIOR [948]
2 years ago
11

one pump can empty the pool in 5 days, whereas a second pump can empty the pool in 7 days. how long it will take the two pumps,

working together, to empty the pool?
Mathematics
1 answer:
PtichkaEL [24]2 years ago
7 0
4 days jfjdhsbsiegebehehebeihrhe
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PLEASE HELP!<br>Calculate $40^{13} \pmod{85}.$
SVEN [57.7K]
In this type of calculations, we decompose 13 by checking the lowest powers of the base, that is 40. for example we check 40^2, or 40^3 and compare it to 85

Notice

40*40*40=64,000

so we check how many time does 85 fit into 64,000:

64,000/85=752.94

85*753=64,005;       64000-64,005=-5

this means that 

40^{3} =-5\pmod{85}

thus

40^{13} =40^{3*4+1}={(40^{3})}^{4}*40=(-5)^{4}*40 \pmod{85}=\\\\625*40\pmod{85}=(7*85+30)*40\pmod{85}=30*40\pmod{85}\\\\=1200\pmod{85}=(14*85+10)\pmod{85}=10\pmod{85}


Answer: 10 (mod85)

Remark, the set of all solutions is:

{......-75, 10, 95, .....}, that is 85k +10
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What is the undefined term that mathematically uses parallel lines
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Step-by-step explanation:

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20% in fraction form is....
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Rectangle EFGH is translated according to the rule T–5, 9(x, y). If the coordinates of the pre-image of point H are (–2, –3), wh
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T-5 .9(×,y)

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Step-by-step explanation:

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