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2 years ago

If X and Y are distinct digits such that the eight-digit number 7448X24Y is divisible by both 8 and 9, then find X - Y.

Mathematics

1 answer:

Talja [164]2 years ago

7 0

The value of X - Y such that the eight-digit number 7448X24Y is divisible by both 8 and 9 is 7

<h3>How to determine the distinct digits X and Y?</h3>

The eight-digit number is given as:

7448X24Y

Also, from the question

The number is divisible by 8 and 9

When a number is divisible by 8, then the last three digits of that number would be divisible by 8.

When a number is divisible by 9, the sum of the digits of the number would be divisible by 9.

So, we have:

24Y is divisible by 8

The possible value of Y from the above statement is 0

This is so because 240 is divisible by 8

The sum of the digits of the number would be divisible by 9.

This means that:

7 + 4 + 4 + 8 + X + 2 + 4 + Y = 29 + X + Y

Substitute 0 for Y

29 + X + Y = 29 + X + 0

Evaluate the sum

29 + X + Y = 29 + X

36 is divided by 9

So, we have

29 + X = 36

Subtract 29 from both sides of the equation

X = 7

So, we have

X = 7 and Y = 0

X - Y is calculated as:

X - Y = 7 - 0

Evaluate the difference in the above equation

X - Y = 7

Hence, the value of X - Y such that the eight-digit number 7448X24Y is divisible by both 8 and 9 is 7

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Read 2 more answers

When running a 100 meter race Bill reaches his maximum speed when he is 45 meters from the starting line and 5 seconds have elap

Mkey [24]

Bill's speed is constant after 5 seconds and 45 meters into the race.

Correct responses:

a. Bill's maximum speed is 8 m/s

b. 24 meters

c. 57 meters

<h3>Methods used to calculate speed and distance traveled</h3>

Given parameters are;

The distance of the race = 100 meter

Distance at which Bill reaches maximum speed = 45 meters

Speed Bill maintains after 5 seconds = The maximum speed

Time at which Bill is 85 meters from the starting line = 10 seconds after start

a. Required;

Bill's maximum speed in meters.

Solution:

Distance Bill runs at maximum speed, d = 85 m - 45 m = 40 m

Time at which Bill runs the 40 m at maximum speed, <em>t</em> = 10 s - 5 s = 5 s

$Speed = \mathbf{\dfrac{Distance}{Time}}$

Therefore;

$Bill's \ maximum \ speed = \dfrac{40 \ m}{5 \ s} = \underline{8 \ m/s}$

b. i. Required:

The distance Bill will run for 3 seconds at the maximum speed;

Solution:

Distance,<em> s</em> = Speed, <em>v</em> × Time, <em>t</em>

<em />

The distance traveled at maximum speed in 3 seconds is therefore;

Distance = 8 m/s × 3 s = 24 m

The distance Bill travels in 3 seconds at the maximum speed is 24 meters.

ii) The distance Bill travels at 8 seconds after start, is given as follows;

Distance traveled in the first 5 seconds = 45 meters

Distance traveled in the next 3 seconds = 24 meters

Therefore;

Bill's distance from the starting line 8 seconds after start is 45 meters + 25 meters = <u>69 meters</u>

c. Bill's distance 6.5 seconds after the start of the race is given as follows;

Distance traveled in the first 5 seconds = 45 meters

Distance traveled in the next 1.5 seconds = 1.5 s × 8 m/s = 12 meters

Bill's distance from the starting line 6.5 seconds after start of the race = 45 meters + 12 meters = <u>57 meters</u>

Learn more about distance, speed, time, relationship here:

https://brainly.in/question/49075584

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