What is the distance between (-9,-6) and (-2,2)?

Mathematics

1 answer:

Firlakuza [10]2 years ago

8 0

Answer:

square root of 113

Step-by-step explanation:

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Write the equation of the sphere in standard form. x^2 + y^2 + z^2 + 2x − 4y − 6z = 22

madam [21]

The equation $x^{2} +y^{2} +z^{2} +2x-4y-6z=22$ in standard form looks like $(x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}$ .

Given equation of sphere be $x^{2} +y^{2} +z^{2} +2x-4y-6z=22$ .

We are required to express the given equation in the standard form of the equation of sphere.

Equation is basically relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation,quadratic equation, cubic equation or many more depending on the powers of variables. The standard form of the equation of sphere looks like $x^{2} +y^{2} +z^{2} =r^{2}$ .

The given equation is $x^{2} +y^{2} +z^{2} +2x-4y-6z=22$ .

We have to break 22 which is in right side into various parts according to the left side of the equation.

$x^{2} +y^{2} +z^{2} +2x-4y-6z=-1-4-9+36$

$x^{2} +y^{2} +z^{2} +2x-4y-6z+1+4+9=36$

$x^{2} +1+2x+y^{2}+4-4y+z^{2} +9-6z=36$

$x^{2} +(1)^{2} +2*1*x+y^{2} +(2)^{2} -2*2y+z^{2} +(3)^{2} -2*3z=36$

$(x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}$

Hence the equation $x^{2} +y^{2} +z^{2} +2x-4y-6z=22$ in standard form looks like $(x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}$ .

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7 0

1 year ago

Cassie is a half pound of sugar in her cabinet her cake recipe calls for two tenths of a pound of sugar how many cakes can she m

mamaluj [8]

The information's given in the question should be very minutely checked. Based on those given information's the answer to the question can easily be deduced.
Amount of sugar in the cabinet of Cassie = 1/2 pound
Amount of sugar required by Cassie to make her cake recipe = 2/10 pound
   = 1/5 pounds
Then
The number of cakes that Cassie can make = (1/2)/(1/5)
      = 5/2
      = 2 1/2
So from the above deduction we can easily conclude that Cassie can make a total of 2 cakes with the sugar she has and there will still be some sugar left.

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3 years ago

Solve the system of equations.in this form: (x, y)<br><br> -5y + 8x = -18<br><br> 5y + 2x = 58

Gre4nikov [31]

If we add the equations it looks like
-5y + 8x + 5y + 2x = -18+58
so 10x=40
so x=40/10=4
now let's replace x by 4 in the second equation
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5y=58-2*4=58-8=50
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3 years ago

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Draw a basketball with a vertical, angled, and horizontal cut

ANTONII [103]

That is what it looks like