Nannie Mack

2020-12-29

Describe in words the region of ${R}^{3}$ represented by the equation(s) or inequality.

${x}^{2}+{y}^{2}=4$

tafzijdeq

Skilled2020-12-30Added 92 answers

Concept:

The equation ${x}^{2}+{y}^{2}={r}^{2}$ represents a circle with its center on the z-axis.

Given:

${x}^{2}+{y}^{2}=4$

3) Calculation:

The given equation is

${x}^{2}+{y}^{2}=4$

The equation ${x}^{2}+{y}^{2}=4$

is a set of all the points in ${R}^{3}\text{}lying\text{}on\text{}circle\text{}{x}^{2}+{y}^{2}=4.$

That is,

$(x,y,z)|{x}^{2}+{y}^{2}=4,x\in R,y\in R,z\in R$

Here is no restriction on z-coordinate, so a point in the region must lie on a circle with radius 2 and centre on z-axis but it could be any horizontal plane $z=k$ (parallel to xy - plane)

Therefore, the region consists of all points on the circle ${x}^{2}+{y}^{2}=4,z=k$

That is, a circular cylinder with radius 2 whose axis is the z - axis

Therefore, the given equations represents the region in ${R}^{3}$ consisting of all possible citcles of radius 2 and centre on z -axis that 1s a circular cylinder with radius 2 whose axis is the z - axis.

Conclusion:

The given equations represents the region in ${R}^{3}$ consisting of all possible circles of radius 2 and centre on z - axis that is a circular cylinder with radius 2 whose axis is the z - axis.

The product of the ages, in years, of three (3) teenagers os 4590. None of the have the sane age. What are the ages of the teenagers???

Use the row of numbers shown below to generate 12 random numbers between 01 and 99

78038 18022 84755 23146 12720 70910 49732 79606

Starting at the beginning of the row, what are the first 12 numbers between 01 and 99 in the sample?How many different 10 letter words (real or imaginary) can be formed from the following letters

H,T,G,B,X,X,T,L,N,J.Is every straight line the graph of a function?

For the 1s orbital of the Hydrogen atom, the radial wave function is given as: $R(r)=\frac{1}{\sqrt{\pi}}(\frac{1}{{a}_{O}}{)}^{\frac{3}{2}}{e}^{\frac{-r}{{a}_{O}}}$ (Where ${a}_{O}=0.529$ ∘A)

The ratio of radial probability density of finding an electron at $r={a}_{O}$ to the radial probability density of finding an electron at the nucleus is given as ($x.{e}^{-y}$). Calculate the value of (x+y).Find the sets $A$ and $B$ if $\frac{A}{B}=\left(1,5,7,8\right),\frac{B}{A}=\left(2,10\right)$ and $A\cap B=\left(3,6,9\right)$. Are they unique?

What are the characteristics of a good hypothesis?

If x is 60% of y, find $\frac{x}{y-x}$.

A)$\frac{1}{2}$

B)$\frac{3}{2}$

C)$\frac{7}{2}$

D)$\frac{5}{2}$The numbers of significant figures in $9.1\times {10}^{-31}kg$ are:

A)Two

B)Three

C)Ten

D)Thirty oneWhat is positive acceleration?

Is power scalar or vector?

What is the five-step process for hypothesis testing?

How to calculate Type 1 error and Type 2 error probabilities?

How long will it take to drive 450 km if you are driving at a speed of 50 km per hour?

1) 9 Hours

2) 3.5 Hours

3) 6 Hours

4) 12.5 HoursWhat is the square root of 106?