Ask question

Ask question

All categories

Misha Larkins [42]

3 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]3 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

You might be interested in

When energy is produced in a reaction it

goblinko [34]

The correct answer is b i believe

4 0

3 years ago

a bal is launched upward with a velocity of v0 from the edge of a cliff of height D. it reaches a maximum height of H above its

lilavasa [31]

Answer:

D/H =15

Explanation:

We can find first the peak height H, taking into consideration, that at the maximum height, the ball will reach momentarily to a stop.
At this point, we can find the value of H, applying the following kinematic equation:

$v_{f} ^{2} -v_{0} ^{2} = 2* g* H (1)$

If vf=0, if we assume that the positive direction is upwards, we can find the value of H as follows:

$H = \frac{v_{0} ^{2} }{2*g} (2)$

We can use the same equation, to find the value of D, as follows:

$v_{f} ^{2} -v_{1} ^{2} = 2* g* D (3)$

In order to find v₁, we can use the same kinematic equation that we used to get H, but now, we know that v₀ = 0.
When we replace these values in (1), we find that v₁ = -v₀.
Replacing in (3), we have:

$(4*v_{0})^{2} - (-v_{0}) ^{2} = 2* g* D\\ \\ 15*v_{0}^{2} = 2*g*D$

Solving for D:

$D = \frac{15*v_{0} ^{2} }{2*g}$

From (2) we know that H can be expressed as follows:

$H = \frac{v_{0} ^{2} }{2*g}$

⇒ D = 15 * H

$\frac{D}{H} = 15$

3 0

3 years ago

Newton began his academic career in 1667. For how long was he a working scientist? Was he a very productive scientist?

rjkz [21]

Newton's 3 laws are...

inertia: things tend to continue to do what they are doing.

Change: to make something change you need a force to change it. the force needed = the mass times its acceleration

<span> Resistance: When you push on something, it pushes back.

From yahoo answers
</span>

7 0

3 years ago

1. The thin top layer of the crust is called the Crust. What are the two types of

kolbaska11 [484]

Oceanic and continental

8 0

3 years ago

Read 2 more answers

A ball is dropped off the balcony of a hotel room and it takes 2.8s to fall to the ground . how high above the ground is the bal

RideAnS [48]

The height of the ball above the ground is 38.45 m

First we will calculate the velocity of the ball when it touch the ground by using first equation of motion

v=u+gt

v=0+9.81×2.8

v=27.468 m/s

now the height of the ground can be calculated by the formula

v=√2gh

27.468=√2×9.81×h

h=38.45 m

5 0

3 years ago