## anonymous one year ago related rate problem: i got the figure but i am confused on how it goes.. At 4:00Pm boat A left in the direction N 45degrees E. At 4:30 PM boat B left the same pier in the direction S 30 degrees E at 32mph. How fast were they separating at 5:00 Pm in mph?

1. anonymous

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2. anonymous

and then? what follows? im confused on the given values

3. ganeshie8

familiar with vectors ?

4. anonymous

5. ganeshie8

it would be easy if we use vectors

6. anonymous

how sir?

7. anonymous

How fast was boat A going?

8. anonymous

its not given sir. @SithsAndGiggles

9. anonymous

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10. anonymous

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11. anonymous

You can use the law of cosines to set up an equation relating $$z$$ to $$x$$ and $$y$$. $z^2=x^2+y^2-2xy\cos75^\circ$

12. anonymous

Differentiating with respect to $$t$$, you have $2z\frac{dz}{dt}=2x\frac{dx}{dt}+2y\frac{dy}{dt}-2y\cos75^\circ\frac{dx}{dt}-2x\cos75^\circ\frac{dy}{dt}$ We already know that $$\dfrac{dy}{dt}=32$$, but we're not given $$\dfrac{dx}{dt}$$, which I'm simply setting to be $$k$$. We'll need to find $$z$$, which isn't too hard because we have an equation for that. Once you have everything you need, you can solve for $$\dfrac{dz}{dt}$$.