<h3><u>Answer;</u></h3>
A.75°C
<h3><u>Explanation</u>;</h3>
Let the change in temp of cold water be x degrees,
while that of hot water be 100 - x degrees.
Heat exchange = mcΔt
Ice
Δt = x
m = 0.50 kg
c = 4.18 kJ/kg*°C
Hot water
Δt = 100 - x
m = 1.5 kg
c = 4.18
But;
Heat lost = heat gained
0.50 * c * x = 1.5 * c * (100 - x)
0.50 *x = 1.5*(100 - x)
0.5x = 150 - 1.5x
0.5x + 1.5x = 150 - 1.5x + 1.5x
2x = 150
x = <u>75° C</u>
Hence; the equilbrium temperature will be 75° C
Answer
The rate at which the magnetic field is changing is ![[\frac{dB}{dt} ] = 0.000467 T/s](https://tex.z-dn.net/?f=%5B%5Cfrac%7BdB%7D%7Bdt%7D%20%5D%20%3D%20%200.000467%20T%2Fs)
Explanation
From the question we are told that
The electric field strength is 
The radius is 
The rate of change of the magnetic field is mathematically represented as
Where 
is change of a unit length
Where A is the area which is mathematically represented as
So
where L is the circumference of the circle which is mathematically represented as
So
![E (2 \pi r ) = (\pi r^2 ) [\frac{dB}{dt} ]](https://tex.z-dn.net/?f=E%20%282%20%5Cpi%20r%20%29%20%3D%20%20%28%5Cpi%20r%5E2%20%29%20%5B%5Cfrac%7BdB%7D%7Bdt%7D%20%5D)
![E = \frac{r}{2} [\frac{dB}{dt} ]](https://tex.z-dn.net/?f=E%20%20%3D%20%20%20%5Cfrac%7Br%7D%7B2%7D%20%20%5B%5Cfrac%7BdB%7D%7Bdt%7D%20%5D)
![[\frac{dB}{dt} ] = \frac{E}{ \frac{r}{2} }](https://tex.z-dn.net/?f=%5B%5Cfrac%7BdB%7D%7Bdt%7D%20%5D%20%3D%20%5Cfrac%7BE%7D%7B%20%5Cfrac%7Br%7D%7B2%7D%20%7D)
substituting values
![[\frac{dB}{dt} ] = \frac{3.5 *10^{-3}}{ \frac{15}{2} }](https://tex.z-dn.net/?f=%5B%5Cfrac%7BdB%7D%7Bdt%7D%20%5D%20%3D%20%5Cfrac%7B3.5%20%2A10%5E%7B-3%7D%7D%7B%20%5Cfrac%7B15%7D%7B2%7D%20%7D)
Answer:
F = 2.6692 x 10⁻⁹ N
Explanation:
Given,
The mass of the rock, m = 10 kg
The mass of the boulder, M = 100 kg
The distance between them, d = 5 m
The gravitational force between the two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. It is given by the formula
<em> F = GMm/d² newton</em>
Where,
G - Universal gravitational constant
Substituting the given values,
F = 6.673 x 10⁻¹¹ x 100 x 10 / 5²
F = 2.6692 X 10⁻⁹ N
Hence, the force between the two bodies is, F = 2.6692 X 10⁻⁹ N
Answer:
Total distance traveled = 9 m
Explanation:
Given:
Distance travel towards north = 3 meter
Distance travel towards south = 6 meter
Find:
Total distance traveled
Computation:
Total distance traveled = Sum of total distance
Total distance traveled = Distance travel towards north + Distance travel towards south
Total distance traveled = 3 m + 6 m
Total distance traveled = 9 m
