The position function of a particle is given by:
The velocity function is the derivative of the position:
The particle will be at rest when the velocity is 0, thus we solve the equation:
The coefficients of this equation are: a = 2, b = -9, c = -18
Solve by using the formula:
Substituting:
We have two possible answers:
We only accept the positive answer because the time cannot be negative.
Now calculate the position for t = 6:
Answer:
Number of dimes = 34
Number of nickels = 13
Step-by-step explanation:
Total number of coins = 47
Coins are in the form of nickels and dimes.
Value of a nickel = 5 cents
Value of a dime = 10 cents
Total value of coins = $4.05 or 405 cents
To find:
Number of nickels and dimes?
Solution:
Let number of nickels =
Money value of nickels = 5
Let number of dimes =
Money value of dimes = 10
Total value of coins =
This value is given as equal as 405.
As per question statement, the equations can be written as:
Multiplying equation (2) with 5 and subtracting from equation (1):
Number of dimes = 34
Number of nickels = 47 - 34 = 13