F$1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of interest, i, earned by the deposit in the first n years is given by the formula
i = 1,000 ( (1 + r/100)^n - 1 ),
where r percent is the annual interest rate paid by the bank. is the annual interest rate paid by the bank greater than 8 percent?
(1) the deposit earns a total of $210 in interest in the first two years.
(2) ( 1 + r/100 )^2 > 1.5

(1) The annual interest rate is 10%, that is greater than 8%

(2) The annual interest is bigger than 22.47% and that is greater than 8%

Step-by-step explanation:

We have the equation:

Where I is the earns in interest, n is the number of years and r is the annual interest rate.

For the first case, we can replace I by $210 and n by 2 as:

Solving for r, we get:

So, for the first case, the interest rate paid by the bank is 10% and it is greater than 8%

For the second case, we need to take the equation and solve for r as:

So, for the second case the rate need to be bigger than 22.47% and that is bigger than 8%

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.