When an spherical balloon volume is increasing at the rate of $3ft^3/min$ then the diameter of the balloon is increasing $\frac{3}{2\pi }ft /min$

How can we find the rate of change of balloon's diameter ?

The volume of a spherical balloon is $v=\frac{4}{3} \pi r^3$

In form of diameter we can write as

$v=\frac{4}{3} \pi (\frac{D}{2} )^3\\=\frac{1}{6} \pi D^3$

Now we will differentiate both sides wrt to $t$ we get

$\frac{dv}{dt} =\frac{1}{6} \pi 3D^2 \frac{dD}{dt} \\\frac{dD}{dt} =\frac{2}{\pi D^2} \frac{dv}{dt} \\\\when r=1\\D=2ft$

Given in the question $\frac{dv}{dt} =3ft^3/min$

thus when we substitute the values we get

$\frac{dD}{dt} =\frac{2}{\pi *2^2} (3)\\\frac{dD}{dt}=\frac{3}{2\pi } ft/min$

Learn more about the differentiation here:

brainly.com/question/28046488

#SPJ4

3 0

2 years ago

4. The town of Euclid started a voluntary recycling program. The first year it was utilized by 1500 residents.

V125BC [204]

Answer:

170,070 residents

Step-by-step explanation:

Original population = 1500 residents

Total population after 6 years is calculated using the formula

A = P(1+r)^t

r is the rate = 120% = 1.2

t is the time = 6 years

P is the original population

A = 1500(1+1.2)^6

A = 1500(2.2)^6

A = 1500(113.379904)

A = 170,069.856

4 0

3 years ago

If 80% of the 400 students at Washington Junior High School passed the ISTEP test, how many students did not pass the ISTEP test

nlexa [21]

Answer:

80 students

Step-by-step explanation:

400/80%=320

400-320=80

8 0

3 years ago