Answer:
a) X = 17.64 m
b) X = 17.64 + 4∆t^2 + 16.8∆t
c) Velocity = lim(∆t→0)〖∆X/∆t〗 = 16.8 m/s
Explanation:
a) The position at t = 2.10s is:
X = 4t^2
X = 4(2.10)^2
X = 17.64 m
b) The position at t = 2.10 + ∆t s will be:
X = 4(2.10 + ∆t)^2
X = 17.64 + 4∆t^2 + 16.8∆t m
c) ∆X is the difference between position at t = 2.10s and t = 2.10 + ∆t so,
∆X= 4∆t^2 + 16.8∆t
Divide by ∆t on both sides:
∆X/∆t = 4∆t + 16.8
Taking the limit as ∆t approaches to zero we get:
Velocity =lim(∆t→0)〖∆X/∆t〗 = 4(0) + 16.8
Velocity = 16.8 m/s
Answer:
The time is 133.5 sec.
Explanation:
Given that,
One side of cube = 10 cm
Intensity of electric field = 11 kV/m
Suppose How long will it take to raise the water temperature by 41°C Assume that the water has no heat loss during this time.
We need to calculate the rate of energy transfer from the beam to the cube
Using formula of rate of energy


Put the value into the formula


We need to calculate the amount of heat
Using formula of heat


Put the value into the formula


We need to calculate the time
Using formula of time

Put the value into the formula


Hence, The time is 133.5 sec.
Answer:
1) true
2) false
3) false
4) true
5) true
6) true
7) true
8) false
9) true
10) false
i think these are correct if im wrong on a few im sorry. Hope this helps at least a bit. And if i do get some wrong you know just to pick the opposite answer.
Answer:

Explanation:
Since fluid is pumping in and out at the same rate (5L/min), the total fluid volume in the tank stays constant at 350L. Only the amount of salt and its concentration changed overtime.
Let A(t) be the amount of salt (g) at time t and C(t) (g/L) be the concentration at time t
A(0) = 10 g
Brine with concentration of 1g/L is pouring in at the rate of 5L/min so the salt income rate is 5 g/min
The well-mixed solution is pouring out at the rate of 5L/min at concentration C(t) so the salt outcome rate is 5C g/min
But the concentration is total amount of salt over 350L constant volume
C = A / 350
Therefore our rate of change for salt A' is
A' = 5 - 5A/350 = 5 - A/70
This is a first-order linear ordinary differential equation and it has the form of y' = a + by. The solution of this is

So 
with A(0) = 10
c + 350 = 10
c = 10 - 350 = -340
