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Misha Larkins [42]

2 years ago

14

Mady has an infinite number of balls and empty boxes available to her. The empty boxes, each capable of holding four balls, are

arranged in a row from left to right. At the first step, she places a ball in the first box of the row. At each subsequent step, she places a ball in the first box of the row that still has room for a ball and empties any previous boxes. How many balls in total are in the boxes as a result of Mady's 2010th step

1 answer:

True [87]2 years ago

3 0

Answer:

The number of balls in the box at 2010th step is 6 balls

Explanation:

Since the boxes are arranged from left to right, and since the empty boxes are capable of holding 4 balls at once.

Therefore, her steps would follow this pattern ;

00001 - 1st Step

0002 - 2nd Step

0003 - 3rd Step

0004 -4th Step

0010 - 5th Step

0011 - 6th Step

0021 - 7th step

0031 - 8th step

0041 - 9th step

Looking at this pattern, it is obvious this digits are in base 5 because once we count to 4 in a unit, we move to the next at 1.

Thus,at Mady's 2010th step, we'll convert to base 5,thus 2010 in base 5 is calculated as;

2010 ÷ 5 = 402 r 0, so Base 5 is now: _ _ _ _ 0.

402 ÷ 5 = 80 r 2, so Base 5 is now: _ _ _ 2 0.

80 ÷ 5 = 16 r 0, so Base 5 is now:

_ _ 0 2 0.

16 ÷ 5 = 3 r 1, so Base 5 is now: _ 1 0 2 0.

3 ÷ 5 = 0 r 3, so Base 5 is now: 3 1 0 2 0.

So 2010 in base 10 is 31020 in base 5. Thus,the number of balls in the box at 2010th step is equal to 3 + 1 + 0 + 2 + 0 = 6balls

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3 years ago

Read 2 more answers

Space pilot Mavis zips past Stanley at a constant speed relative to him of 0.800c. Mavis and Stanley start timers at zero when t

inna [77]

Answer:

Explanation:

a. The equation of Lorentz transformations is given by:

x = γ(x' + ut')

x' and t' are the position and time in the moving system of reference, and u is the speed of the space ship. x is related to the observer reference.

x' = 0

t' = 5.00 s

u =0.800 c,

c is the speed of light = 3×10⁸ m/s

Then,

γ = 1 / √ (1 - (u/c)²)

γ = 1 / √ (1 - (0.8c/c)²)

γ = 1 / √ (1 - (0.8)²)

γ = 1 / √ (1 - 0.64)

γ = 1 / √0.36

γ = 1 / 0.6

γ = 1.67

Therefore, x = γ(x' + ut')

x = 1.67(0 + 0.8c×5)

x = 1.67 × (0+4c)

x = 1.67 × 4c

x = 1.67 × 4 × 3×10⁸

x = 2.004 × 10^9 m

x ≈ 2 × 10^9 m

Now, to find t we apply the same analysis:

but as x'=0 we just have:

t = γ(t' + ux'/c²)

t = γ•t'

t = 1.67 × 5

t = 8.35 seconds

b. Mavis reads 5 s on her watch which is the proper time.

Stanley measured the events at a time interval longer than ∆to by γ,

such that

∆t = γ ∆to = (5/3)(5) = 25/3 = 8.3 sec which is the same as part (b)

c. According to Stanley,

dist = u ∆t = 0.8c (8.3) = 2 x 10^9 m

which is the same as in part (a)

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3 years ago

Two men standing on the same side of wall and at the same distance from It, such that they are 4oom apart when one fires a gun t

Mamont248 [21]

Answer:

1. 571.43m/s

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Explanation:

1.Take the difference in time.

1.2-0.7=0.7 seconds

Take the distance between them and divide with differnce in time.

400÷0.7=571.43 seconds.

2.Take the time of the two men and divide by two.

0.5÷2= 0.25 secs

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multiply each with the velocity.

0.25×571.43=142.9m

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1 year ago

A rocket car on a horizontal rail has an initial mass of 2500 kg and an additional fuel mass of 1000 kg. At time t0 the rocket m

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Explanation:

The expression used will be as follows.

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$\int_{t_{o}}^{t_{f}} \frac{dv}{dt} dt = u\int_{t_{o}}^{t_{f}} \frac{1}{M} \frac{dM}{dt} dt$

= $u\int_{M_{o}}^{M_{f}} \frac{dM}{M}$

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$v_{o} = 0$

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u = -2900 m/s

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= $2500 kg + 1000 kg - 95 kg \times t_{f}s$

= $(3500 - 95t_{f})s$

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a = $\frac{dv_{f}}{dt_{f}} = \frac{u}{M} \frac{dM}{dt}$

= $\frac{u}{3500 - 95 t} \times (-95) m/s^{2}$

= $\frac{95 \times 2900}{3500 - 95t} m/s^{2}$

At t = 10 sec,

$v_{f}$ = 918.34 m/s

and, a = 108 $m/s^{2}$

3 0

3 years ago