Lewis Harvey
2021-09-20
Answered

Describe the given set with a single equation or with a pair of equations.The set of points in space equidistant from the origin and the point (0, 2, 0)

You can still ask an expert for help

Asma Vang

Answered 2021-09-21
Author has **93** answers

Step 1

Let the points are given by (x,y,z)

Step 2

Given that (x,y,z) is equidistant from the origin and the point (0, 2, 0).

So we equate both distances and make an equation.

$\sqrt{{(x-0)}^{2}+{(y-0)}^{2}+{(z-0)}^{2}}=\sqrt{{(x-0)}^{2}+{(y-2)}^{2}+{(z-0)}^{2}}$

$\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}=\sqrt{{x}^{2}+{(y-2)}^{2}+{z}^{2}}$

$x}^{2}+{y}^{2}+{z}^{2}={x}^{2}+{(y-2)}^{2}+{z}^{2$ (square both sides)

$y}^{2}={(y-2)}^{2$

y=2-y (because y=y-2 is not possible)

2y=2

y=1

Answer: y=1 plane

Let the points are given by (x,y,z)

Step 2

Given that (x,y,z) is equidistant from the origin and the point (0, 2, 0).

So we equate both distances and make an equation.

y=2-y (because y=y-2 is not possible)

2y=2

y=1

Answer: y=1 plane

asked 2020-10-18

Find a least squares solution of Ax=b by constructing and solving the normal equations.

$A=\left[\begin{array}{cc}3& 1\\ 1& 1\\ 1& 4\end{array}\right],b\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]$

$\stackrel{\u2015}{x}=$ ?

asked 2021-09-23

Find an equation for the plane that contains the two lines

${l}_{1}:x=t+2,y=3t-5,z=5t+1$

and

${l}_{2}:x=5-t,y=3t-10,z=9-2t$

and

asked 2021-10-01

Determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify.

asked 2021-09-21

Solve each system of equations using substitution. State whether the system is inconsistent or consistent with dependent equation.

asked 2021-09-20

(a) Find a system of two linear equations in the variables x and y whose solution set is given by the parametric equations x = t and y = 3- 2t.

(b) Find another parametric solution to the system in part (a) in which the parameter is s and y =s.

(b) Find another parametric solution to the system in part (a) in which the parameter is s and y =s.

asked 2021-09-30

Solve the equation.

$5{x}^{2}=2x-3$

asked 2021-05-08

Use elimination to solve the system of equation:

2x+2y=-2

3x-2y=12

2x+2y=-2

3x-2y=12