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chubhunter [2.5K]
3 years ago
12

The distance travelled in (m) by a ball dropped from a height are 128/9,32/3,8,6,...

Mathematics
1 answer:
Allushta [10]3 years ago
7 0

Answer: it will trave 56.89 meters before coming to rest.

Step-by-step explanation:

This is a geometric progression since the distance travelled (height) by the ball is reducing by a constant ratio, r. Since the number of times that the ball will bounce is infinite, then we would apply the formula for determining the sum of the terms in a geometric progression to infinity which is expressed as

S = a/(1 - r)

where

S = sum of the distance travelled by the ball

a = initial distance or height of the ball

r = common ratio

From the information given,

a = 128/9

r = (32/3)/(128/9) = 0.75

Therefore,

S = (128/9)/(1 - 0.75) = 56.89 meters

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Step-by-step explanation:

A. Since there are 26 different letters and 10 different numbers, there are 36 characters we can type. If characters can be repeated then, there is 2176782336 different passwords, since on all six number there are 36 possibilities each. So, 36 x 36 x 36 x 36 x 36 x 36 or 36^6 is to evaluated to find the answer. If characters are not to be repeated, there are 1402410240 different passwords, since on the first number there are 36, second has 35, third has 34, fourth has 33, fifth has 32, and sixth has 31. So, 36 x 35 x 34 x 33 x 32 x 31 is to be evaluated to solve this.

B. Since all characters that are letters can be repeated, then there are 26 letters to use forever and 10 numbers you can use with a limit. So, 36 x 35 x 34 x 33 x 32 x 31 which is to be solved if only numbers were to be used, which is 1402410240. Then, you add that with 36 x 35^5 and 36 x 35 x 34^4 and 36 x 35 x 34 x 33^3 and 36 x 35 x 34 x 33 x 32^2. which will be 7964171460. If the password must contain one digit, then you must multiply 10 with 26^5. Since, there is 10 different digits to use for the first number and 26 letters to choose from for the other five. So, it will be 26^5 times 10 which is 118813760.

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