1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ohaa [14]
3 years ago
13

Find the equation of the sphere centered at (-9,9, -9) with radius 5. Normalize your equations so that the coefficient of x2 is

1. -0.
Give an equation which describes the intersection of this sphere with the plane z = 0.
Mathematics
1 answer:
olganol [36]3 years ago
6 0
<h2><u>Answer</u>:</h2>

(a) x² + y² + z² + 18(x - y + z) + 218 = 0

(b) (x + 9)² + (y - 9)² + 56 = 0

<h2><u>Step-by-step explanation:</u></h2>

<em>The general equation of a sphere of radius r and centered at C = (x₀, y₀, z₀) is given by;</em>

(x - x₀)² + (y - y₀)² + (z - z₀)² = r²               ------------------(i)

<em>From the question:</em>

The sphere is centered at C = (x₀, y₀, z₀) = (-9, 9, -9) and has a radius r = 5.

<em>Therefore, to get the equation of the sphere, substitute these values into equation (i) as follows;</em>

(x - (-9))² + (y - 9)² + (z - (-9))² = 5²

(x + 9)² + (y - 9)² + (z + 9)² = 25      ------------------(ii)

<em>Open the brackets and have the following:</em>

(x + 9)² + (y - 9)² + (z + 9)² = 25

(x² + 18x + 81) + (y² - 18y + 81) + (z² + 18z + 81) = 25

x² + 18x + 81 + y² - 18y + 81 + z² + 18z + 81 = 25

x² + y² + z² + 18(x - y + z) + 243 = 25

x² + y² + z² + 18(x - y + z) + 218 = 0    [<em>equation has already been normalized since the coefficient of x² is 1</em>]

<em>Therefore, the equation of the sphere centered at (-9,9, -9) with radius 5 is:</em>

x² + y² + z² + 18(x - y + z) + 218 = 0

(2)  To get the equation when the sphere intersects a plane z = 0, we substitute z = 0 in equation (ii) as follows;

(x + 9)² + (y - 9)² + (0 + 9)² = 25

(x + 9)² + (y - 9)² + (9)² = 25

(x + 9)² + (y - 9)² + 81 = 25        [<em>subtract 25 from both sides</em>]

(x + 9)² + (y - 9)² + 81 - 25 = 25 - 25

(x + 9)² + (y - 9)² + 56 = 0

The equation is therefore, (x + 9)² + (y - 9)² + 56 = 0

You might be interested in
\angle a∠aangle, a and \angle b∠bangle, b are complementary angles. \angle a∠aangle, a measures 64^\circ64
Archy [21]

Answer:

If angle a and b are complementary angles, and angle a is 64, complementary equals 90, so 90-64= 26 degrees for angle b.

6 0
3 years ago
Read 2 more answers
Tomas is making trail mix using granola and walnuts. He can spend a total of $12 on the ingredients. He buys 3 pounds of
spin [16.1K]

Answer:

The first error that Tomas made was added 6 to both sides of the equation instead of subtracting 6

Step-by-step explanation:

Let

x ----> represents the number of pounds of granola

y ----> represents the number of pounds of walnuts

we know that

The linear equation that represent this scenario is

2x+6y=12 -----> equation A

x=3 -----> equation B

substitute equation B in equation A and solve for y

2(3)+6y=12

6+6y=12

Subtract 6 both sides

6+6y-6=12-6

6y=6

Divide by 6 both sides

6y/6=6/6

y=1

so

The number of pounds of walnuts is 1

therefore

The first error that Tomas made was added 6 to both sides of the equation instead of subtracting 6

8 0
3 years ago
Read 2 more answers
Betty and Sally are 28 miles apart on a path when they start moving toward each other. Betty runs at a constant speed of 6 miles
andreev551 [17]

Answer:

3.5 hours

Step-by-step explanation:

if you multiply 6 and 2 by 3.5, then add them you get 28

4 0
3 years ago
Wath is six hundred ninety- two thousand,four
ki77a [65]
692,004 is the answer

3 0
2 years ago
Read 2 more answers
Find the x - and y -intercepts of the following equation. <br>2 x + 3 y = − 24
sattari [20]

Answer:

(2,3)

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • Gary earned a gross pay of $1,047.30 last week. Using the fact that Social Security tax is 6.2% of gross pay, determine the amou
    6·2 answers
  • The two fastest times in the past 20 years for the girls 200-meter fun at Clarksville elementary school are 27.97 seconds and 27
    5·1 answer
  • 6 mg of 20 mg is what​
    10·1 answer
  • HIGH SCHOOL LEVEL) <br>SUPER EASY I JUST AM DUMB, PLEASE HELP
    8·1 answer
  • Help me fast in need it
    9·2 answers
  • A shirt that cost $5 is marked up 20% what is the markup​
    9·1 answer
  • Give two examples of organism that has cell structure similar to cell of permanent alide​
    8·1 answer
  • Tisha tried to evaluate an expression. Here is her work: 490÷729–23 = 490÷499–23 Step 1 = 109–23 Step 2 = 90–23 Step 3 = 883 Ste
    11·1 answer
  • 5.
    10·1 answer
  • Drug Name Half-life
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!