A)<span>

dQ = ρ(r) * A * dr = ρ0(1 - r/R) (4πr²)dr = 4π * ρ0(r² -
r³/R) dr

which when integrated from 0 to r is

total charge = 4π * ρ0 (r³/3 + r^4/(4R))

and when r = R our total charge is

total charge = 4π*ρ0(R³/3 + R³/4) = 4π*ρ0*R³/12 = π*ρ0*R³ / 3

and after substituting ρ0 = 3Q / πR³ we have

total charge = Q ◄

B) E = kQ/d²

since the distribution is symmetric spherically

C) dE = k*dq/r² = k*4π*ρ0(r² - r³/R)dr / r² = k*4π*ρ0(1 -
r/R)dr

so

E(r) = k*4π*ρ0*(r - r²/(2R)) from zero to r is

and after substituting for ρ0 is

E(r) = k*4π*3Q(r - r²/(2R)) / πR³ = 12kQ(r/R³ - r²/(2R^4))

which could be expressed other ways.

D) dE/dr = 0 = 12kQ(1/R³ - r/R^4) means that

r = R for a min/max (and we know it's a max since r = 0 is a
min).

<span>E) E = 12kQ(R/R³ - R²/(2R^4)) = 12kQ / 2R² = 6kQ / R² </span></span>

Responda:

400 g

Explicação:

Dado o seguinte:

Deixe Mass (m1) = m em t1 = 45 ° C

Massa (m2) = 200g em t2 = 15 ° C

Equilíbrio térmico (T) = 35 ° C

Usando a relação:

m1 * C * ΔT = m2 * C * ΔT

Onde m1 e m2 são as massas; C = capacidade de calor específico da água e ΔT é a mudança de temperatura

m1 * ΔT = m2 * ΔT

m * (45 ° C - 35 ° C) = 200 * (35 ° C - 15 ° C)

10 * m = 200 * 20

10 * m = 4000

m = 4000/10

m = 400g

The power rating on the motor is the maximum power it's ABLE to deliver. It can run with LESS power output than the rating, but if you try to run it with MORE than it's rated, the motor will overheat and eventually burn out.

" 10 watts " means " 10 Joules of enrgy per second ".

If the motor is operated at its full maximum rated capacity, then

(500 joules) / (10 joules/sec) = <em>**50 seconds**</em>

**Answer:**

Final speed of security car v = 65 m/s

**Explanation:**

**Given:**

Speed of race car u1 = 35m/s

Speed of security car u2 = 5 m/s

Acceleration = 5 m/s²

**Find:**

Final speed of security car v

**Computation:**

Assume, they chase S meter

So

S = u1t + [1/2]at²

S = 35t

S = u2t + [1/2]at²

so,

35t = 5t + [1/2](5)t²

t = 12 s

So

v = u + at

v = 5 + 5(12)

**Final speed of security car v = 65 m/s**