A bicycle tire has a diameter of 62cm. What is the distance the bicycle tire travels in 10 revolutions?

Mathematics

1 answer:

Orlov [11]3 years ago

3 0

Answer:

1948 cm

Step-by-step explanation:

First, calculate the circumference of the wheel with tire. Since C = πd, the circumference in this particular case is C = π(62 cm), or approx. 194.8 cm.

Each time the wheel turns, the bike moves forward 194.8 cm.

If the wheel turns 10 times, the bike moves forward 1948 cm.

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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

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