Observe that the given vector field is a gradient field:
Let , so that
Integrating the first equation with respect to , we get
Differentiating this with respect to gives
Now differentiating with respect to gives
Putting everything together, we find a scalar potential function whose gradient is ,
It follows that the curl of is 0 (i.e. the zero vector).
Gas giant are plants with mass 10 times bigger than the mass of the Earth. They are also called outer planets. There are four gas giant planets in our solar system: Jupiter, Saturn, Uranus and Neptune. The farther away from the Sun they are (the distance from the Sun is increased) the longer they orbit the Sun because of the great distance.
negative acceleration- deceleration
Electromagnetic waves<span> differ from mechanical </span>waves<span> in that they </span>do<span> not require a </span>medium<span> to propagate. This means that electromagnetic </span>waves<span> can </span>travel<span> not only </span>through<span> air and solid materials, but also </span>through<span> the vacuum of space.</span>
Answer:
1) R1 + ((R2 × R3)/(R2 + R3))
2) 0.5 A
3) 3.6 V
Explanation:
1) We can see that resistors R2 and R3 are in parallel.
Formula for sum of parallel resistors; 1/Rt = 1/R2 + 1/R3
Making Rt the subject gives;
Rt = (R2 × R3)/(R2 + R3)
Now, Resistor R1 is in series with this sum of R2 and R3. Thus;
Total resistance of circuit = R1 + ((R2 × R3)/(R2 + R3))
2) R_total = R1 + ((R2 × R3)/(R2 + R3))
We are given;
R1 = 7.2 Ω
R2 = 8 Ω
R3 = 12 Ω
R_total = 7.2 + ((8 × 12)/(8 + 12))
R_total = 7.2 + 4.8
R_total = 12 Ω
Formula for current is;
I = V/R
I = 6/12
I = 0.5 A
3) since current through the circuit is 0.5 and R1 is 7.2 Ω.
Thus, potential difference through R1 is;
V = IR = 0.5 × 7.2 = 3.6 V