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Archy [21]
3 years ago
9

Prove that 25^11 - 5^19 is divisible by 31.

Mathematics
1 answer:
Stells [14]3 years ago
7 0

Answer:

See below  

Step-by-step explanation:

                                        25¹¹ - 5¹⁹

Convert to base 5       = (5²)¹¹ - 5¹⁹

                                    =  5²²   - 5¹⁹

Factor out the GCF     =  5¹⁹(5³ - 1)

                                    =  5¹⁹(125 - 1)

                                    =  5¹⁹ × 124

                                    =  5¹⁹ × 4 × 31

31 is a factor of 25¹¹ - 5¹⁹, so the expression is divisible by 31.

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The price of an item has risen to $120 today. Yesterday it was $40. Find the percentage increase.
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Answer:

200%

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If $40 is 100% then multiply it by 3 to get $120

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If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then Torricelli's Law gives the v
pochemuha

Answer:

V'(t) = -250(1 - \frac{1}{40}t)

If we know the time, we can plug in the value for "t" in the above derivative and find how much water drained for the given point of t.

Step-by-step explanation:

Given:

V = 5000(1 - \frac{1}{40}t )^2  , where 0≤t≤40.

Here we have to find the derivative with respect to "t"

We have to use the chain rule to find the derivative.

V'(t) = 2(5000)(1 - \frac{1}{40} t)d/dt (1 - \frac{1}{40}t )

V'(t) = 2(5000)(1 - \frac{1}{40} t)(-\frac{1}{40} )

When we simplify the above, we get

V'(t) = -250(1 - \frac{1}{40}t)

If we know the time, we can plug in the value for "t" and find how much water drained for the given point of t.

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4 years ago
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