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KIM [24]
3 years ago
11

Describe in words the region of R3 reperesented by the equations or inequalities x2+y2+z2≤3

Mathematics
1 answer:
Vaselesa [24]3 years ago
8 0

Answer:

The region represented by the equation is a full sphere of radius √3 centered in the origin of coordinates.

Step-by-step explanation:

<em>In a plane xy, the equation that represents a circle with center in the origin, of radius r is</em>

x^2+y^2=r^2

<em>in R³, or a space xyz, we can represent a sphere with its center in the origin, and of radius r, with the equation</em>

x^2+y^2+z^2=r^2

So, in this problem we have that

3=r^2

which means that the sphere has a radius of √3.

<u>Finally, our equation is an inequality</u>, and the sphere is equal to, and less than, the calculated radius.

Therefore, the sphere is "full" from the surface to its center.

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Calculate the average (arithmetic mean) of the list of numbers shown in the table. (rounded to the nearest tenth) A) 35.2 B) 39.
jenyasd209 [6]
<h3><u>Given Numbers:-</u></h3>
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<h3><u>To Find:-</u></h3>
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<h3><u>Solution</u>:-</h3>

\green{ \underline { \boxed{ \sf{Average = \frac{Sum \:of \: observation}{Number \:of \: observation}}}}}

\longrightarrow Here, no of observation are 9

Now,

\begin{gathered}\implies \small \sf Average =\frac{23+33+33+27+25+68+27+44+72}{9}\\\end{gathered}

\begin{gathered}\\\implies \small \sf Average =\frac{56+60+93+71+72}{9}\\\end{gathered}

\begin{gathered}\\\implies \sf Average =\frac{116+164+72}{9}\\\end{gathered}

\begin{gathered}\\\implies \sf Average =\frac{352}{9}\\\end{gathered}

\begin{gathered}\\\implies \sf Average = 39.1 \\\end{gathered}

\longrightarrowThe Average of given set of numbers is 39.1 .

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