There are several possibilities. Here are a few that occur to me:

-- If Point-A is the summit of Pike's Peak, he may feel somewhat
short of breath.

-- If Point-A is his grandmother's house, he may feel a great sense
of pleasant anticipation.

-- If Point-A is his office on Monday morning, then he may feel
a tightening sensation in his chest.;

-- If Point-A is his home on Friday afternoon, then he feels the
effects of a slow and steady drop in his blood pressure.

I finer point might be put to it if we had any idea of where
Point-A is, and what it represents in the grand scheme
of things.

5 0

2 years ago

Electric charge is distributed over the disk x2 + y2 ≤ 4 so that the charge density at (x, y) is rho(x, y) = 4x + 4y + 4x2 + 4y2

maw [93]

Answer:

Q=185.84C

Explanation:

We have to take into account the integral

$Q=\int \rho dV$

In this case we have a superficial density in coordinate system.

Hence, we have for R: x2 + y2 ≤ 4

$Q=\int_{-2}^2\int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}}\rho dydx$

but, for symmetry:

$Q=4\int_0^2\int_0^{\sqrt{4-x^2}}\rho dydx\\\\Q=4\int_0^2\int_0^{\sqrt{4-x^2}}(4x+4y+4x^2+4y^2) dydx\\\\Q=4\int_0^{2}[4x\sqrt{4-x^2}+2(4-x^2)+4x^2\sqrt{4-x^2}+\frac{4}{3}(4-x^2)^{3/2}]dx\\\\Q=4[46.46]=185.84C$