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Nastasia [14]
3 years ago
6

Nick types 275 words in 2.5 minutes. At this rate, how many hours would it take for him to type 9900 words?

Mathematics
1 answer:
ioda3 years ago
5 0
3/5 of an hour (0.6 hours)



First, find how many words Nick types in an hour by multiplying 275 * 60.

Nick types 16,500 words per hour.

Now just divide 9,900 by 16,500.

It takes Nick 3/5 of an hour to type 9,900 words. (0.6 hours)



Please consider marking this answer as Brainliest to help me advance.

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You're minimizing d(x,y,z)=\sqrt{(x-4)^2+y^2+(z+5)^2} subject to the constraint f(x,y,z)=x+y+z=1. Note that d(x,y,z) and d(x,y,z)^2 attain their extrema at the same values of x,y,z, so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.

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\begin{cases}\dfrac{\partial L}{\partial x}=2(x-4)+\lambda=0\\\\\dfrac{\partial L}{\partial y}=2y+\lambda=0\\\\\dfrac{\partial L}{\partial z}=2(z+5)+\lambda=0\\\\\dfrac{\partial L}{\partial\lambda}=x+y+z-1=0\end{cases}\implies\begin{cases}2x+\lambda=8\\2y+\lambda=0\\2z+\lambda=-10\\x+y+z=1\end{cases}

Adding the first three equations together yields

2x+2y+2z+3\lambda=2(x+y+z)+3\lambda=2+3\lambda=-2\implies \lambda=-\dfrac43

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The squared distance is then d\left(\dfrac{14}3,\dfrac23,-\dfrac{13}3\right)^2=\dfrac43, which means the shortest distance must be \sqrt{\dfrac43}=\dfrac2{\sqrt3}.
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