What's the sum for 329+252

Find an equation of the sphere containing all surface points P = (x, y, z) such that the distance from P to A(−3, 6, 3) is "twic

Marina86 [1]

Answer:

Equation of Sphere = $x^{2}$ + $y^{2}$ + $z^{2}$ - 18x - 4/3y +10z + 142/3 = 0

Step-by-step explanation:

Data Given:

P = (x,y,z)

Distance from P to A (-3,6,3) = Twice the distance from P to B(6,2,-3)

Solution:

Find the equation of the sphere:

It is given that:

PA = 2PB

Squaring both sides:

$(PA)^{2} = (2PB)^{2}$

$(PA)^{2} = 4 (PB)^{2}$

$(x - (-3))^{2}$ + $(y - 6)^{2}$ + $(z-3)^{2}$ = 4 x $(x-6)^{2}$ + $(y-2)^{2}$ + $(z-(-3))^{2}$

Solving the above equation:

$(x + 3))^{2}$ + $(y - 6)^{2}$ + $(z-3)^{2}$ = 4 x { $(x-6)^{2}$ + $(y-2)^{2}$ + $(z + 3))^{2}$ }

$x^{2}$ + 9 + 6x + $y^{2}$ + 36 - 12y + $z^{2}$ + 9 - 6z = 4 { $x^{2}$ + 36 - 12x + $y^{2}$ + 4 - 4y + $z^{2}$ + 9 + 6z}

$x^{2}$ + 9 + 6x + $y^{2}$ + 36 - 12y + $z^{2}$ + 9 - 6z = 4 $x^{2}$ + 144 - 48x +4 $y^{2}$ + 16 - 16y + 4 $z^{2}$ + 36 + 24z

Putting the right hand side = 0 and solving the equation:

$x^{2}$ - 4 $x^{2}$ + $y^{2}$ - 4 $y^{2}$ + $z^{2}$ - 4 $z^{2}$ + 6x + 48x - 12y +16y -6z - 24z + 9 + 36 + 9 -144 - 16 - 36 = 0

-3 $x^{2}$ - 3 $y^{2}$ -3 $z^{2}$ + 54x + 4y -30z -142 = 0

Taking (-) common

- ( 3 $x^{2}$ + 3 $y^{2}$ + 3 $z^{2}$ - 54x - 4y +30z + 142) = 0

3 $x^{2}$ + 3 $y^{2}$ + 3 $z^{2}$ - 54x - 4y +30z + 142 = 0

dividing the whole equation by 3

$x^{2}$ + $y^{2}$ + $z^{2}$ - 54/3x - 4/3y +30/3z + 142/3 = 0

$x^{2}$ + $y^{2}$ + $z^{2}$ - 18x - 4/3y +10z + 142/3 = 0

7 0

3 years ago

What is the area of the triangle?

mestny [16]

Answer:

height ×base divided by two

7 0

3 years ago

How would I find k , L , and M. Giving Brainly

SSSSS [86.1K]

Angle L is equal to angle N, so angle L is equal to 119. Angle k and angle L is equal to 61.

8 0

3 years ago

Which mathematical property is demonstrated?

RSB [31]

Answer:

The commutative property states that you can rearrange the order of the numbers and get the same result. The commutative property states that you can rearrange the order of the numbers and get the same result. The addition properties are the exact same, but replace multiply with add. Your answer is D.

Step-by-step explanation:

All the problem is doing is switching the numbers to different sides of the equation. You will still get the same answer.

5 0

3 years ago

Read 2 more answers

g Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether event

vagabundo [1.1K]

Answer:

There is not sufficient evidence to support the claim.

Step-by-step explanation:

The claim to be tested is:

The mean respiration rate (in breaths per minute) of students in a large statistics class is less than 32.

To test this claim the hypothesis can be defined as follows:

H₀: The mean respiration rate of students is 32, i.e. μ = 32.

Hₐ: The mean respiration rate of students is less than 32, i.e. μ < 32.

The sample mean respiration rate of students is 31.3.

According to the claim the sample mean is less than 32.

The sample mean value is not unusual if the claim is true, and the sample mean value is also not unusual if the claim is false.

Thus, there is not sufficient evidence to support the claim.

7 0

3 years ago