A photocopy machine is machine is bought for K85000. It's useful life is 10 years after which it will be sold for a crap value of K5000. What is the flat rate at which the machine depreciates?
To calculate the flat rate at which the machine depreciates, we need to determine the total depreciation over its useful life and divide it by the initial cost of the machine.
The total depreciation can be calculated by subtracting the scrap value from the initial cost:
Total depreciation = Initial cost - Scrap value
Total depreciation = K85000 - K5000
Total depreciation = K80000
Now, we divide the total depreciation by the useful life of the machine to find the annual depreciation:
Annual depreciation = Total depreciation / Useful life
Annual depreciation = K80000 / 10
Annual depreciation = K8000
Finally, we divide the annual depreciation by the initial cost and multiply by 100 to express it as a percentage:
Depreciation rate = (Annual depreciation / Initial cost) * 100
Depreciation rate = (K8000 / K85000) * 100
Depreciation rate = 0.0941 * 100
Depreciation rate = 9.41%
Therefore, the flat rate at which the machine depreciates is 9.41%.
What is the length of the vector u = [ 1 / 7 ]
The vector u = [ 1 / 7 ] has only one component, 1/7. Since this is a one-dimensional vector, its length can be calculated as the absolute value of its component.
To find the length of the vector u, we take the absolute value of 1/7:
|1/7| = 1/7
Therefore, the length of the vector u = [ 1 / 7 ] is 1/7.
To calculate the flat rate at which the machine depreciates, we need to find the annual depreciation amount.
The initial cost of the machine is K85000, and its useful life is 10 years. At the end of 10 years, it will be sold for K5000.
Therefore, the total depreciation over 10 years is K85000 - K5000 = K80000.
To find the annual depreciation amount, we divide the total depreciation by the useful life:
Annual depreciation amount = Total depreciation / Useful life
= K80000 / 10
= K8000.
So, the machine depreciates at a flat rate of K8000 per year.