Answer: The field F has a continuous partial derivative on R.
Step-by-step explanation:
For the field F has a continuous partial derivative on R, fxy must be equal to fyx and since our field F is ∇f,
∇f = fxi + fyj + fzk.
Comparing the field F to ∇f since they at equal, P = fx, Q = fy and R = fz
Since P is fx therefore;
∂P ∂y = ∂ ∂y( ∂f ∂x) = ∂2f ∂y∂x
Similarly,
Since Q is fy therefore;
∂Q ∂x = ∂ ∂x( ∂f ∂y) = ∂2f ∂x∂y
Which shows that ∂P ∂y = ∂Q ∂x
The same is also true for the remaining conditions given
Step-by-step explanation:
1 pound = 16 ounces
5 pound = 16 x 5 = 80
Cost per ounce = 15
Cost of 80 ounces = 15 x 80 = 1200
Option D is the correct answer
Answer:
Step-by-step explanation:
The diagram shows right triangle with hypotenuse of 15 units and angle of 30°. This angle is opposite to the leg with length of x units.
In the right triangle, the leg opposite to the 30° angle is half of the hypotenuse, so
Answer:
$45.12
Step-by-step explanation:
($0.47 /stamp)×(8 stamps/mo)×(12 mo/yr) = $45.12 /yr
You will save $45.12 per year on stamps.
Answer:
35 pounds of $8.00 tea and 15 pounds of $6.00 tea
Step-by-step explanation:
Let x represent the pounds of tea of the $8 kind. 8x would represent the total cost of that type of tea. We can also say 50 - x is the pounds of tea of the $6 kind, so 6(50 - x) is the total cost of that type of tea. 50 * 7.4 represents the total cost of all the tea, and the expression 8x + 6(50 -x) would also represent the same thing. We can write this as an equation,
8x + 6(50 -x) = 50 * 7.4
simplify,
8x + 300 - 6x = 370
2x + 300 = 370
and solve.
2x = 70
x = 35
This means there is 35 pounds of the $8 kind.
We can subtract that from 50 to find,
50 - 35 = 15,
15 pounds is the amount of the $6 kind.
