Let the cold water go up x degrees.
Let the hot water go down 100 - x degrees.
The formula for heat exchange is m*c*delta t
Givens
Ice
deltat = x
m = 0.50 kg
c = 4.18
Hot water
deltat = 100 - x
m = 1.5 kg
c = 4.18
Formula
The heat up = heat down
0.50 * c * x = 1.5 * c * (100 - x) Divide both sides by c
Solution
0.50 *x = 1.5*(100 - x) Remove the brackets.
0.5x = 150 - 1.5x Add 1.5x to both sides.
0.5x + 1.5x = 150 - 1.5x + 1.5x Combine like terms
2x = 150 Divide by 2
x = 75
Answer
A
For a parallel circuit with two resistors, the total resistance is calculated from the expression:
1/R = 1/R1 + 1/R2
We are given the total resistance, R, which is 20 ohms and R2 which is 75 ohms. We calculate R1 as follows:
1/20 = 1/R1 + 1/75
1/R1 = 11/300
R1 = 27.27 ohms
Everything is in the universe.
That's what the word means.
Answer:
I = 21.13 mA ≈ 21 mA
Explanation:
If
I₁ = 5 mA
L₁ = L₂ = L
V₁ = V₂ = V
ρ₁ = 1.68*10⁻⁸ Ohm-m
ρ₂ = 1.59*10⁻⁸ Ohm-m
D₁ = D
D₂ = 2D
S₁ = 0.25*π*D²
S₂ = 0.25*π*(2*D)² = π*D²
If we apply the equation
R = ρ*L / S
where (using Ohm's Law):
R = V / I
we have
V / I = ρ*L / S
If V and L are the same
V / L = ρ*I / S
then
(V / L)₁ = (V / L)₂ ⇒ ρ₁*I₁ / S₁ = ρ₂*I₂ / S₂
If
S₁ = 0.25*π*D² and
S₂ = 0.25*π*(2*D)² = π*D²
we have
ρ₁*I₁ / (0.25*π*D²) = ρ₂*I₂ / (π*D²)
⇒ I₂ = 4*ρ₁*I₁ / ρ₂
⇒ I₂ = 4*1.68*10⁻⁸ Ohm-m*5 mA / 1.59*10⁻⁸ Ohm-m
⇒ I₂ = 21.13 mA
Answer:
(a) - 42700 m/s
(b) - 6.8 x 10^-4 m/s^2
Explanation:
initial velocity of star, u = 20.7 km/s
Final velocity of star, v = - 22 km/s
time, t = 1.99 years
Convert velocities into m/s and time into second
So, u = 20700 m / s
v = - 22000 m/s
t = 1.99 x 365.25 x 24 x 3600 = 62799624 second
(a) Change in planet's velocity = final velocity - initial velocity
= - 22000 - 20700 = - 42700 m/s
(b) Accelerate is defined as the rate of change of velocity.
Acceleration = change in velocity / time
= ( - 42700 ) / (62799624) = - 6.8 x 10^-4 m/s^2
