The radius of the circle, in cm, after t seconds would be 50t
The area, A, of the circle after t seconds is expressed in the equation: A = pi * r^2
A = pi * (50T)^2 = pi*2500*t^2
The change of area per unit time is obtained by differentiating the equation
A' = pi*2500*2*t A' = pi*5000*t
when t = 3 secondsA' = pi*5000*3 = 47122 cm2/s
Displacement = distance and direction from the start-point
to the end-point, regardless of the route followed on the way.
From the throw to the 'plop', the displacement is 5 meters down.
Explanation:
<h3>p = mv</h3>
- <em>p</em> denotes momentum
- <em>m</em> denotes mass
- <em>v</em> denotes velocity
→ p = 3 kg × 3 m/s
→ <u>p</u><u> </u><u>=</u><u> </u><u>9</u><u> </u><u>kg</u><u>.</u><u>m</u><u>/</u><u>s</u>
<u>Option</u><u> </u><u>D</u><u> </u><u>is</u><u> </u><u>corre</u><u>ct</u><u>.</u>
Answer:
Tt = 70 + 135e^-0.031t
13 minutes
Explanation:
Given that :
Initial temperature, Ti = 205°
Temperature after 2.5 minutes = 195°
Temperature of room, Ts= 70
Using the relation :
Tt = Ts + Ce^-kt
Temperature after time, t
When freshly poured, t = 0
205 = 70 + Ce^-0k
205 = 70 + C
C = 205 - 70 = 135°
T after 2.5 minutes to find proportionality constant, k
Tt = Ts + Ce^-kt
195 = 70 + 135e^-2.5k
125 = 135e^-2.5k
125 / 135 = e^-2.5k
0.9259 = e^-2.5k
Take In of both sides :
−0.076989 = - 2.5k
k = −0.076989 / - 2.5
k = 0.031
Equation becomes :
Tt = 70 + 135e^-0.031t
t when Tt = 160
160 = 70 + 135e^-0.031k
90 = 135e^-0.031t
90/135 = e^-0.031t
0.6667 = e^-0.031t
In(0.6667) = - 0.031t
−0.405465 = - 0.031t
t = 0.405465/ 0.031
t = 13.071
t = 13 minutes
