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3 years ago

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Buses to Acton leave a bus station every 24 minutes. Buses to Barton leave a bus to Barton every 20 minutes A bus to Acton and a

bus to Barton both leave the bus station at 9:00am When will a bus to Acton and a bus to Barton next leave the bus station at the same time?

1 answer:

Oduvanchick [21]3 years ago

5 0

Answer:

11 am

Step-by-step explanation:

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Determine whether or not f is a conservative vector field. if it is, find a function f such that f = ∇f. (if the vector field is

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$\mathbf f(x,y)=(ye^x+\sin y)\,\mathbf i+(e^x+x\cos y)\,\mathbf j$ is continuous, so $\mathbf f(x,y)$ is indeed conservative. So we know there is some scalar function $f(x,y)$ such that $\nabla f(x,y)=\mathbf f(x,y)$ .

$\dfrac{\partial f}{\partial x}=ye^x+\sin y$
$\displaystyle\int\frac{\partial f}{\partial x}\,\mathrm dx=\int(ye^x+\sin y)\,\mathrm dx$
$f(x,y)=ye^x+x\sin y+g(y)$

$\dfrac{\partial f}{\partial y}=\dfrac{\partial(ye^x+x\sin y+g(y))}{\partial y}$
$e^x+x\cos y=e^x+x\cos y+g'(y)$
$0=g'(y)$
$\implies g(y)=C$

So we have

$f(x,y)=ye^x+x\sin y+C$

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