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Olin [163]
3 years ago
11

Find an equation of the sphere through the point (4,3,-1) and has center (3,8,1).

Mathematics
1 answer:
sleet_krkn [62]3 years ago
6 0

Answer:

(x - 3)^{2} + (y - 8)^{2} + (z - 1)^{2} = 30

Step-by-step explanation:

The general equation of a sphere is as follows:

(x - x_{c})^{2} + (y - y_{c})^{2} + (z - z_{c})^{2} = r^{2}

In which the center is (x_{c}, y_{c}, z_{c}, and r is the radius.

In this problem, we have that:

x_{c} = 3, y_{c} = 8, z_{c} = 1

So

(x - 3)^{2} + (y - 8)^{2} + (z - 1)^{2} = r^{2}

through the point (4,3,-1)

This leads us to find the radius.

(4 - 3)^{2} + (3 - 8)^{2} + (-1 - 1)^{2} = r^{2}

r^{2} = 1 + 25 + 4

r^{2} = 30

So the equation of the sphere is:

(x - 3)^{2} + (y - 8)^{2} + (z - 1)^{2} = 30

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Simplify: (3x2 − 5xy + 2y2) − (7x2 − 3xy − 3y2)
svlad2 [7]

Answer:

-4x² - 2xy + 5y²

Step-by-step explanation:

Step 1: Write expression

(3x² - 5xy + 2y²) - (7x² - 3xy - 3y²)

Step 2: Distribute negative

3x² - 5xy + 2y² - 7x² + 3xy + 3y²

Step 3: Combine like terms

-4x² - 2xy + 5y²

4 0
3 years ago
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Solve for the variable c in this equation:<br><br> a(c – b) = d
Natalka [10]

Answer:

c = (d/a) + b

Step-by-step explanation:

a(c-b)=d --> Divide by a

c-b = (d/a) --> add b to both sides

c = (d/a) + b

5 0
3 years ago
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Numeşte câte un sinonim pentru sensul din text al cuvintelor: despărţire, patimă.
solong [7]

Answer:

1) A synonym for the word 'parting' is separation.

A synonym for the word 'passion' is determination.

2) I'm not going to lie, the 'thought' of this pandemic never ending has crossed my mind a couple of times already!

1) Un sinonim pentru cuvântul „despărțire” este separarea.

Un sinonim pentru cuvântul „pasiune” este determinarea.

2) Nu o să mint, „gândul” acestei pandemii care nu se termină niciodată mi-a trecut prin minte de câteva ori!

Step-by-step explanation:

English Translation

1) Name a synonym for the meaning in the text of the words: parting, passion.

2) Construct a statement in which to use a phrase / expression that contains the noun thought.

Solution

1) Parting

The word 'parting' meansthe serperation of two or more quantities/substances/humans (etc.) that were once together.

The synonyms of the word include Separation, farewell, division etc.

Passion

'Passion' means a strong, powerful, intense emotion.

The synonyms of the word include determination, zeal, fervor, ardor etc

2) A statement that contains the use of the noun thought

I'm not going to lie, the 'thought' of this pandemic never ending has crossed my mind a couple of times already!

In Romanian/In limba romana

1) Împărțire

Cuvântul „despărțire” înseamnă serperarea a două sau mai multe cantități / substanțe / oameni (etc.) care au fost odată împreună.

Sinonimele cuvântului includ Separarea, adio, divizare etc.

Pasiune

„Pasiune” înseamnă o emoție puternică, puternică, intensă.

Sinonimele cuvântului includ determinarea, râvna, fervoarea, ardoarea etc.

2) O enunț care conține utilizarea substantivului gândit

Nu o să mint, „gândul” acestei pandemii care nu se termină niciodată mi-a trecut prin minte de câteva ori!

Hope this Helps!!!

Sper că acest lucru vă ajută!!!

3 0
3 years ago
Opposite reciprocal of -9/1 and 11/-7
PtichkaEL [24]

Answer:

1/9 and 7/11

Step-by-step explanation:

hope this is helpful :)

7 0
2 years ago
A pronghorn running up a steep cliff to escape its predator covered 45 miles in 1 hour and 45 minutes.
Dmitriy789 [7]

Answer:

25 . 71 mph

Step-by-step explanation:

45 miles in 1.75 hr

45 miles / 1.75 hr = 25.71 mph

5 0
2 years ago
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