The formula for the mass that remains:

m₀ - the initial mass, t - time, T - the half-life

The answer is c. 1.25 g.
Answer:0.061
Explanation:
Given

Temperature of soup 
heat capacity of soup 
Here Temperature of soup is constantly decreasing
suppose T is the temperature of soup at any instant
efficiency is given by



integrating From
to 


![W=c_v\left [ T-T_C\ln T\right ]_{T_H}^{T_C}](https://tex.z-dn.net/?f=W%3Dc_v%5Cleft%20%5B%20T-T_C%5Cln%20T%5Cright%20%5D_%7BT_H%7D%5E%7BT_C%7D)
![W=c_v\left [ \left ( T_C-T_H\right )-T_C\left ( \ln \frac{T_C}{T_H}\right )\right ]](https://tex.z-dn.net/?f=W%3Dc_v%5Cleft%20%5B%20%5Cleft%20%28%20T_C-T_H%5Cright%20%29-T_C%5Cleft%20%28%20%5Cln%20%5Cfrac%7BT_C%7D%7BT_H%7D%5Cright%20%29%5Cright%20%5D)
Now heat lost by soup is given by

Fraction of the total heat that is lost by the soup can be turned is given by

![=\frac{c_v\left [ \left ( T_C-T_H\right )-T_C\left ( \ln \frac{T_C}{T_H}\right )\right ]}{c_v(T_C-T_H)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bc_v%5Cleft%20%5B%20%5Cleft%20%28%20T_C-T_H%5Cright%20%29-T_C%5Cleft%20%28%20%5Cln%20%5Cfrac%7BT_C%7D%7BT_H%7D%5Cright%20%29%5Cright%20%5D%7D%7Bc_v%28T_C-T_H%29%7D)




Answer:
0.8895m
Explanation:
Cable diameter = 0.0125m
Mass of elevator = 6450kg
Young Modulus(E) = 2.11*10¹¹N/m
∇l (change in length) =
L = 362m
A = Πr², but r = d / 2 = 0.0125 / 2 = 0.00625m
A = 3.142 * (0.00625)² = 1.227*10^-4m²
Young Modulus (E) = Tensile stress / Tensile strain
E = (F / A) / ∇l / L
F = mg = 6450 * 9.8 = 63210N
2.11*10¹¹ = (63210 / 1.22*10^-4) / (∇l / 362)
2.11*10¹¹ = 5.18*10⁸ / (∇l / 362)
2.11*10¹¹ = (5.18*10⁸ * 362) / ∇l
2.11*10¹¹ = 1.875*10¹¹ / ∇l
∇l = 1.875*10¹¹ / 2.11*10¹¹
∇l = 0.8895m
The change in length is 0.8895m
The instantaneous velocity of the object is its speed and direction at that instant.
Answer:
β = 114 db
Explanation:
The intensity of sound in decibles is
β = 10 log 
in most cases Io is the hearing threshold 1 10-12 W / cm²
let's calculate the intensity of each instrument
I / I₀ = 10 (β / 10)
I = I₀ 10 (β / 10)
trumpet
I1 = 1 10⁻¹² 10 (94/10)
I1 = 2.51 10⁻³ / cm²
Thrombus
I2 = 1 10⁻¹² 10 (107/10)
I2 = 5.01 10-2 W / cm²
low
I3 =1 1-12 (113/10) W/cm²
I3 = 1,995 10-1 W / cm²
when we place the three instruments together their sounds reinforce
I_total = I₁ + I₂ + I₃
I_ttoal = 2.51 10-3 + 5.01 10-2 + 1.995 10-1
I_total = 0.00251 + 0.0501 + 0.1995
I_total = 0.25211 W / cm²
let's bring this amount to the SI system
β = 10 log (0.25211 / 1 10⁻¹²)
β = 114 db