Ineed with parts 3, 6, and 7 you can ignore the graphing parts you!
a cart weighs 8 pounds is attached to the wall by a spring with spring constant k = 2 lb/ft. the cart is pulled 1 ft in the direction away from the wall, and released with the given initial velocity 2 ft/sec.
assuming there's no friction/air resistance (no dumping) , write down the ode
solve the ode and graph it in desmos
what are its natural frequency, period and amplitude?
case a: assuming friction/air resistance (dumping) exists and it's measured as 10 lb/ft proportional to the cart's speed.
write down ode
solve the ode and graph it in desmos
case b: assuming friction/air resistance (dumping) exists and it's measured as 8 lb/ft proportional to the cart's speed.
write down ode
solve the ode and graph it in desmos
case c: assuming friction/air resistance (dumping) exists and it's measured as 2 lb/ft proportional to the cart's speed.
write down ode
solve the ode and graph it in desmos
case d: back to the no dumping case, however a periodic external force latex: f\left(t\right)=2\: \sin\left(4t\right) f(t)=2sin⁡(4t)is applied to the cart
write down the ode
solve the ode

55/i dont know i do it for the points

step-by-step explanation:

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

a) 0,0; 1,1; and 2,2

step-by-step explanation:

these have the exact same coordinates, thus they are the correct function.

this is a good question! i’ll do some research and what i find, i’ll contact you asap when i have something! ✊