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Nataly [62]
3 years ago
13

7 \sqrt{160} " alt="4 \sqrt{40} + 7 \sqrt{160} " align="absmiddle" class="latex-formula">
​
Mathematics
2 answers:
dmitriy555 [2]3 years ago
5 0

Answer:

36\sqrt{10}

Step-by-step explanation:

Using the rule of radicals

\sqrt{a} × \sqrt{b} ⇔ \sqrt{ab}

Simplifying the radicals in the expression

\sqrt{40}

= \sqrt{4(10)}

= \sqrt{4} × \sqrt{10} = 2\sqrt{10}

\sqrt{160}

= \sqrt{16(10)}

= \sqrt{16} × \sqrt{10} = 4\sqrt{10}

Thus

4\sqrt{40} + 7\sqrt{160}

= 4 × 2\sqrt{10} + 7 × 4\sqrt{10}

= 8\sqrt{10} + 28\sqrt{10}

= 36\sqrt{10}

irinina [24]3 years ago
3 0

Answer:

Step-by-step explanation:

44\sqrt{40} + 7 \sqrt{160} = 4\sqrt{2*2*2*5}  + 7\sqrt{4*4*5*2}\\  = 4*2\sqrt{10}  + 7*4\sqrt{10}\\ = 8\sqrt{10} + 28\sqrt{10} \\

= (8 + 28)√10

= 36√10

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Answer:

Step-by-step explanation:

given that a batch of 140 semiconductor chips is inspected by choosing a sample of 5 chips without replacement.

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i.e. out of 140 chips 10 are defective and 130 are good

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Expansion Numerically Impractical. Show that the computation of an nth-order determinant by expansion involves multiplications,
posledela

Answer:

  • number of multiplies is n!
  • n=10, 3.6 ms
  • n=15, 21.8 min
  • n=20, 77.09 yr
  • n=25, 4.9×10^8 yr

Step-by-step explanation:

Expansion of a 2×2 determinant requires 2 multiplications. Expansion of an n×n determinant multiplies each of the n elements of a row or column by its (n-1)×(n-1) cofactor determinant. Then the number of multiplies is ...

  mpy[n] = n·mp[n-1]

  mpy[2] = 2

So, ...

  mpy[n] = n! . . . n ≥ 2

__

If each multiplication takes 1 nanosecond, then a 10×10 matrix requires ...

  10! × 10^-9 s ≈ 0.0036288 s ≈ 0.004 s . . . for 10×10

Then the larger matrices take ...

  n=15, 15! × 10^-9 ≈ 1307.67 s ≈ 21.8 min

  n=20, 20! × 10^-9 ≈ 2.4329×10^9 s ≈ 77.09 years

  n=25, 25! × 10^-9 ≈ 1.55112×10^16 s ≈ 4.915×10^8 years

_____

For the shorter time periods (less than 100 years), we use 365.25 days per year.

For the longer time periods (more than 400 years), we use 365.2425 days per year.

8 0
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