Answer:
Step-by-step explanation:
5 can cancel
Full Question
A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t = 0, the resulting mass—spring system is disturbed from its rest state by the force F (t) = 20 cos(8t). The force F (t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds.
Determine the spring constant k.
Answer:
Spring Constant = 1000Nm^-1
Step-by-step explanation:
Given
Mass = 10kg
Spring Extension = 9.8cm
Spring Constant K = Force/Extension
Force = Mass * Acceleration
Force = 10 * 9.8 = 9.8N
Spring Extension = 9.8 cm = 9.8 /100 = 0.098 m
Spring constant = 98 / 0.098
Spring Constant = 1000Nm^-1
Answer:
gift 1:
424 cm^2
570 cm^3
gift 2:
1420.5 cm^2
3622.5 cm^3
Step-by-step explanation:
We have to calculate the surface area of these gifts in order to know the amount of wrapping paper.
The formula for the surface area is:
A = 2*ab + 2*ac + 2*bc
Gift 1:
A = 2*6*10 + 2*6*9.5 + 2*10*9.5
A = 424 cm^2
That means that gift 1 needs 424 cm^2 of wrapping paper
Gift 2:
A = 2*14*17.25 + 2*14*15 + 2*17.25*15
A = 1420.5 cm^2
That means that gift 2 needs 1420.5 cm^2 of wrapping paper
Now, to calculate the cubic centimeters of packaging peanuts, we calculate the volume, the volume has as formula:
V = a*b*c
Gift 1:
V = 6*10*9.5
V = 570 cm^3
This means that gift 1 needs 570 cm^3 of packaging peanuts
Gift 2:
V = 14*17.25*15
V = 3622.5 cm^3
That means that gift 2 needs 3622.5 cm^3 of packaging peanuts
If compounding annually, the student will need to put $6,208.85 into the account.