Answer:
Step-by-step explanation:
1) True. This is because the divergence of F is 1, thus, F is a linear function. Orientation is given outward to the surface. Linear function double integrated over a surface with outward orientation gives volume enclosed by the surface.
2) True. This is primarily what the Divergence theorem is.
3) False. If F was 3/pi instead of div(F), then the statement would have been true.
4) False. The gradient of divergence can be anything. The curl of divergence of a vector function is 0, not the gradient o divergence.
5) False. While finding Divergence, derivatives are taken for different variables. Since the derivatives of constants are 0, therefore, both the vector functions F and G can be different constant parts of there components even if their divergences are equal.
Answer:
dx/dt = 0,04 m/sec
Step-by-step explanation:
Area of the circle is:
A(c) =π*x² where x is a radius of the circle
Applying differentiation in relation to time we get:
dA(c)/dt = π*2*x* dx/dt
In this equation we know:
dA(c)/dt = 0,5 m²/sec
And are looking for dx/dt then
0,5 = 2*π*x*dx/dt when the area of the sheet is 12 m² (1)
When A(c) = 12 m² x = ??
A(c) = 12 = π*x² ⇒ 12 = 3.14* x² ⇒ 12/3.14 = x²
x² = 3,82 ⇒ x = √3,82 ⇒ x = 1,954 m
Finally plugging ths value in equation (1)
0,5 = 6,28*1,954*dx/dt
dx/dt = 0,5 /12.28
dx/dt = 0,04 m/sec
Answer:
Provided in the picture below.
Step-by-step explanation:
Provided in the picture below.
Answer:
Step-by-step explanation:
Let x represent the number of toys that each club member donated.
There are 9 students in a service club.
If each club member donated 4 children's books for the baskets, it means that the total number of books donated by the club members would be
9 × 4 = 36
If each club member also donated an equal number of toys. It means that the total number of toys donated by the club members would be
9 × x = 9x
A total of 63 items were collected for the baskets. Therefore, the linear equation that you can use to find how many toys each club member donated would be
9x + 36 = 63
