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Ugo [173]
3 years ago
9

Predict the next three numbers in the pattern 10,7,4,1

Mathematics
2 answers:
bazaltina [42]3 years ago
7 0
Since the pattern is subtracting 3 each time, the next three numbers would be; -2, -5, and -8.
Anettt [7]3 years ago
6 0
-2, -5, -8. The pattern shows that the numbers decrease by 3.
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Svetradugi [14.3K]

Answer:

3

Step-by-step explanation:

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5 0
3 years ago
Find the point(s) on the surface z^2 = xy 1 which are closest to the point (7, 11, 0)
leonid [27]
Let P=(x,y,z) be an arbitrary point on the surface. The distance between P and the given point (7,11,0) is given by the function

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
d^*(2,10,2\sqrt5)=46
d^*(2,10,-2\sqrt5)=46

So the two points on the surface z^2=xy closest to the point (7,11,0) are (2,10,\pm2\sqrt5).
5 0
3 years ago
The three interior angle measures of this triangle are x = <br> °, y = <br> °, and z =
tankabanditka [31]

check the picture below.


recall that a flat-line is always 180°, and the sum of all interior angles in a triangle is 180°.

3 0
3 years ago
What are the solutions of x2=-5+8
AveGali [126]

Answer:

x² = -5 + 8

x² = 3

x  = √3 ≈ 1.73

5 0
3 years ago
Number 5? Pre Cal- A small airplane is cruising at an airspeed of 235 kph heading in a direction of 45° (measured from the posit
larisa86 [58]

Answer:

c

Step-by-step explanation:

c

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2 years ago
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