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2 years ago

Describe in words the region of R3 reperesented by the equations or inequalities x2+y2=4,z=-1

Mathematics

1 answer:

Roman55 [17]2 years ago

8 0

Answer:

It represents a circle of radius 2, centered in the origin of the plane xy and transversal to the z-axis in z=-1.

Step-by-step explanation:

The first thing to notice is that

$x^2+y^2=2^2$

<u>represents a circle of radius 2</u>, with its center in the origin of a plane xy, of cartesians coordinates.

Starting from here, we have to put the coordinate z, to complete the space R³. <em>Then, the cirlce will "live" into the plane xy, where z=-1</em>.

Finally, we have that this region is a circle of radius 2, centered in the origin of the plane xy, and transversal to z=-1.

You might be interested in

If triangle ABC is dilated by a scale factor of 2 with a dilation center of A, what will be the coordinates of point b’?

mojhsa [17]

Answer:

In the given figure the sides of triangle measures as follows:

AB= 4 units,

BC= 6 units,

Since triangle ABC is right angled triangle, to find AC we will have to use Pythagorean theorem,

AB² + BC² = AC²

Plugging the values of AB and BC to find AC,

4² + 6² = AC²

16+36=AC²

AC = 7.48

Now if the triangle is dilated by a scale factor of 2, each side will be multiplied by 2 to get the new triangle A'B'C'

side A'B' = 2* AB = 2*4= 8 units

side B'C' = 2* BC = 2*6 =12 units

side A'C' = 2*AC = 2*7.48 = 14.96 units

Perimeter of triangle = sum of three sides

Perimeter of triangle A'B'C' = A'B' + B'C' + A'C'= 8+12 + 14.96 = 34.96 units.

Perimeter of triangle ABC = AB+BC + AC = 4+6+7.48 = 17.48 units.

Perimeter of triangle A'B'C' = 2* Perimeter of triangle ABC

The perimeter of new triangle A'B'C' is 34.96 units which is twice that of triangle ABC.

Answer : A) The perimeter of A'B'C' is 2 times the perimeter of ABC.

8 0

3 years ago

A jewelry box containes 3 rings, 7 necklaces, 4 earrings, 5 braceletes and 1 tiara. If 1 piece of jewlery is selected at radom,

Brums [2.3K]

Answer:

C and D

Step-by-step explanation:

Hope this helps!

6 0

3 years ago

Read 2 more answers

What is 9.286 as a mixed number

marshall27 [118]

9.286

[To change to mixed number, count the number of digits after the decimal point. There are 3 digits, so the denominator will be 1000]

$9.286 = 9 \frac{286}{1000}$

Then we simplify the fraction
(286 ÷ 2)/(1000÷2) = 143/500

Therefore,
$9.286 = 9 \frac{286}{1000}$
$9.286 = 9 \frac{143}{500}$

8 0

3 years ago

Read 2 more answers

212.35 into a fraction

Alla [95]

Answer: 212 7/20

Step-by-step explanation: We know that 212 is the whole number. So we need to convert .35 into a fraction in simplest form. Any decimal that has a hundredths place will be divided by 100 to get the fraction. In this case that fraction would be 35/100. And to convert that into simplest form, you need to find the least (or lowest) common denominator which is 5. Then you divide the numerator and denominator by 5 and get 7/20, so your answer is 212 7/20

5 0

3 years ago

Describe the translation of the function from the parent function f(x) = x².

kkurt [141]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\

\begin{array}{rllll} 
% left side templates
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}$

$\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\

\end{array}\\$

$\bf \begin{array}{llll}
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\\\
\qquad if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}
\end{array}
$

now, notice the template above... now let's see your function $\bf y=x^2+4\implies 
\begin{array}{llllll}
y=&1(&1x&+&0)^2+&4\\
&A&B&&C&D
\end{array}$

so.. what do you think was the shift then?

8 0

3 years ago