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sveta [45]
3 years ago
13

Write the following as a complex number in the form a + bi square root -245

Mathematics
2 answers:
Pepsi [2]3 years ago
5 0

Answer:

Step-by-step explanation:

√(-245)=√(49×5×i^2)=7√5 i=0+7√5 i

svetoff [14.1K]3 years ago
3 0

Answer:

\sqrt{-245}  in the form a + bi is 0+7\sqrt{5}i

Step-by-step explanation:

We know that

       i=\sqrt{-1}

We need to find  \sqrt{-245}

     \sqrt{-245}=\sqrt{-1}\times \sqrt{245}=i\sqrt{245}=i\sqrt{49\times 5}=i\times 7\sqrt{5}

\sqrt{-245}  in the form a + bi is 0+7\sqrt{5}i

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Vsevolod [243]

Answer:

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Step-by-step explanation:

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andre [41]

Answer:

90⁰

Step-by-step explanation:

y=cosx

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2 years ago
Find the point(s) on the surface z^2 = xy 1 which are closest to the point (7, 11, 0)
leonid [27]
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d(x,y,z)=\sqrt{(x-7)^2+(y-11)^2+z^2}

Note that f(x) and f(x)^2 attain their extrema, if they have any, at the same values of x. This allows us to consider the modified distance function,

d^*(x,y,z)=(x-7)^2+(y-11)^2+z^2

So now you're minimizing d^*(x,y,z) subject to the constraint z^2=xy. This is a perfect candidate for applying the method of Lagrange multipliers.

The Lagrangian in this case would be

\mathcal L(x,y,z,\lambda)=d^*(x,y,z)+\lambda(z^2-xy)

which has partial derivatives

\begin{cases}\dfrac{\mathrm d\mathcal L}{\mathrm dx}=2(x-7)-\lambda y\\\\\dfrac{\mathrm d\mathcal L}{\mathrm dy}=2(y-11)-\lambda x\\\\\dfrac{\mathrm d\mathcal L}{\mathrm dz}=2z+2\lambda z\\\\\dfrac{\mathrm d\mathcal L}{\mathrm d\lambda}=z^2-xy\end{cases}

Setting all four equation equal to 0, you find from the third equation that either z=0 or \lambda=-1. In the first case, you arrive at a possible critical point of (0,0,0). In the second, plugging \lambda=-1 into the first two equations gives

\begin{cases}2(x-7)+y=0\\2(y-11)+x=0\end{cases}\implies\begin{cases}2x+y=14\\x+2y=22\end{cases}\implies x=2,y=10

and plugging these into the last equation gives

z^2=20\implies z=\pm\sqrt{20}=\pm2\sqrt5

So you have three potential points to check: (0,0,0), (2,10,2\sqrt5), and (2,10,-2\sqrt5). Evaluating either distance function (I use d^*), you find that

d^*(0,0,0)=170
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So the two points on the surface z^2=xy closest to the point (7,11,0) are (2,10,\pm2\sqrt5).
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3 years ago
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now, the triangles are just four triangles with a base of 6, and a height of 4, in red noted there.

so, just get the area of all those rectangles and the triangles, sum them up and that's the surface area of the composite,

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