3 years ago

A mechanic has the length of a hole 6 feet long what is the length after two inches is cut off?

Mathematics

1 answer:

Alja [10]3 years ago

4 0

The answer is 70 inches

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The radius of a spherical balloon a is increasing at a constant rate of 0.1 cm/s. another balloon, b, is being continuously defl

Dimas [21]

Let $r_A$ and $r_B$ be the respective radii of balloons A and B. If the fixed total volume is V, then

$V = \dfrac{4\pi}3\left({r_A}^3 + {r_B}^3\right)$

and knowing $r_A=10\,\rm cm$ and $r_B=9\,\rm cm$ at the start, we have V = 6916π/3 cm³. Then when $r_A=12\,\rm cm$ , the radius of the other sphere is $r_B=1\,\rm cm$ .

Differentiating both sides with respect to time t gives a relation between the rates of change of the radii:

$0 = 4\pi \left({r_A}^2 \dfrac{dr_A}{dt} + {r_B}^2 \dfrac{dr_B}{dt}\right) \implies \dfrac{dr_B}{dt} = -\left(\dfrac{r_A}{r_B}\right)^2 \dfrac{dr_A}{dt}$

We're given $\frac{dr_A}{dt} = 0.1\frac{\rm cm}{\rm s}$ the whole time. At the moment $r_A=12\,\rm cm$ , the radius of balloon B is changing at a rate of