The chords intersect at point U. What is the value of y? <br> 2<br> 4<br> 6<br> 8

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

Help plz thank you so much

Anit [1.1K]

Answer:

(x, y) --> (y, x)

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Riya and her friends want to rent a flat. They want the flat to be lower than the 5th floor. They want a flat that costs between

abruzzese [7]

Answer:

They want the flat to be lower than the 5th floor. They want a flat that costs between £875 and £925 per month. Riya finds information about flats to rent.

Step-by-step explanation:

it's not a sure answer, please

don't be sure about it

8 0

2 years ago

Matthew is 3 times as old as jenny. in 7 years, he will be twice as old as she will be then. how old is each now? Explain how to

Nataliya [291]

Let m and j be the current ages of Matthew and Jenny, respectively.

Now, Matthew is 3 times as old as Jenny, so the variables are in the following relation:

$m=3j$

In 7 years, both of them will be 7 years older, i.e. their ages will be m+7 and j+7, and Matthew will be twice as old:

$m+7=2(j+7)$

Now, remembering that m=3j, we can rewrite the second equation as

$3j+7=2j+14 \iff j = 7$

So, Jenny is 7 and Matthew is 21 (he's 3 times older).

In fact, in 7 years, they will be 14 and 28, and Matthew will be twice as old.

7 0

3 years ago

Sabe-se que no inventário periódico, o registro contábil do estoque de mercadorias ocorrerá apenas no final de um determinado pe

DedPeter [7]

Answer:

It is known that in the periodic inventory, the accounting record of the stock of goods will occur only at the end of a certain period with the physical count of the existing quantities. Consider the following CVM information = 500.00; Initial Inventory = 700.00 and Purchases = 800.00. Applying the concept of periodic inventory and applying the formula for calculating the CMV, determine the value of the final stock.

ALTERNATIVES

Final stock of 2,000.00.

Final stock of 1,500.00.

Final stock of 1,300.00.

Final stock of 1,200.00.

Final stock of 1,000.00.

Final Stock (EF) = 1,000.00

Step-by-step explanation:

Alternative E - Final stock of 1,000.00.

Given That,

CMV = 500,00

Initial Stock (EI) = 700.00

Purchases (C) = 800.00

Final Stock (EF) = ?

Formula

CMV = Initial Stock (EI) + Purchases (C) - Final Stock (EF)

CMV = EI + C - EF

500 = 700 + 800 - EF

500.00 = 700.00 + 800.00 -X

500 = 1500- EF

500.00 = 1,500.00-X

EF = 1500-500

X = 1,000.00

EF = 1,000.00

Therefore, the final stock is 1,000

3 0

3 years ago

The chords intersect at point U. What is the value of y? 2 4 6 8