How many days should it take the remaining 3 workers to build a barn?

Mathematics

1 answer:

Anna [14]3 years ago

8 0

9514 1404 393

Answer:

15 days
7 workers

Step-by-step explanation:

The effort required to complete a task is often estimated in terms of person·days. Amy's barn-building task takes an effort of ...

(5 workers)(9 days) = 45 worker·days

If there are only 3 workers, the time required is ...

time = (45 worker·days)/(3 workers) = 15 days

If the barn is to be build in 7 days, the number of workers required is ...

(45 worker·days)/(7 days) = 6 3/7 workers

A minimum of 7 workers are required to build the barn in 7 days or less. (6 workers will take 7 1/2 days, so aren't enough.)

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The acceleration of the particle is given by the formula mentioned below:

$a=\frac{d^2s}{dt^2}$

Differentiate the position vector with respect to t.

$\begin{gathered} \frac{ds(t)}{dt}=\frac{d}{dt}\sqrt[]{\mleft(t^3+1\mright)} \\ =-\frac{1}{2}(t^3+1)^{-\frac{1}{2}}\times3t^2 \\ =\frac{3}{2}\frac{t^2}{\sqrt{(t^3+1)}} \end{gathered}$

Differentiate both sides of the obtained equation with respect to t.

$\begin{gathered} \frac{d^2s(t)}{dx^2}=\frac{3}{2}(\frac{2t}{\sqrt[]{(t^3+1)}}+t^2(-\frac{3}{2})\times\frac{1}{(t^3+1)^{\frac{3}{2}}}) \\ =\frac{3t}{\sqrt[]{(t^3+1)}}-\frac{9}{4}\frac{t^2}{(t^3+1)^{\frac{3}{2}}} \end{gathered}$

Substitute t=2 in the above equation to obtain the acceleration of the particle at 2 seconds.