Acircular cloud of poison gas from a factory explosion is expanding so that t hours after the explosion the radius of the cloud is r(t)=50+20t meters. how fast is the area of the cloud increasing 4 hours after the explosion?

The area of cloud increasing 4 hours after the explosion is 16328 square meters.

Explanation:

The radius of the cloud is R(t) = 50 + 20t

We need to find how fast the area of cloud increasing when t = 4 hours.

Area of a circle A =

Now we have to find the derivative with respect to "t"

 ----------(1)

We know that r = 50 +  20t, let's find the derivative with respect to "t"

Now plugin

Now let's find . Plug in t =4, we get

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We know that the value of

So,

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Therefore, the area of cloud increasing 4 hours after the explosion is 16328 square meters.

grav forces affect all objects magnetic forces affect magnetic objects and electric currents

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day