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
What is the scale factor?
fiasKO [112]
The scale factor is 5/3

9(5/3) = 15
7 0
3 years ago
Read 2 more answers
Solve this inequality for x
r-ruslan [8.4K]

x _> 65/3


hope that helps!



4 0
3 years ago
Your delivery runs took 7 hours 12 minutes on Monday,6 hours 46 minutes on Wednesday and 6 hours 53 minutes on Friday. What was
blagie [28]
7 hours + 6 hours + 6 hours
=19 hours
12 minutes + 46 minutes + 53 minutes
=111 minutes
=1 hour 51 minutes

19 hours + 1 hour and 51 minutes is 20 hours and 51 minutes. This is the total time.

Average time = total time/number of deliveries

(20 and 51/60) divided by 3
=6.95 hours
= 6 hours and 57 minutes
5 0
3 years ago
Read 2 more answers
John Simone is buying a used car for a total cost of $11,805.00. He’s making a down payment of $1,500.00 and borrowing the remai
balu736 [363]

Answer:

Step-by-step explanation:

Given that John Simone is purchasing a used car for 11805 dollars.

Down payment = 1500

Net loan amount = 11805-1500 = 10305

Equal monthly instalments he paid = 343 dollars

Tenure =3 years

For 3 years rate of interest should be 12.2%

Then only we get for 3 years for the loan emi as 343

4 0
3 years ago
Yuvia works in a computer store, where she earns a commission of 8 percent of her sales. On Monday, her sales were $2,500. She c
tankabanditka [31]

(2,500)(0.08) = 200

On Monday, Yuvia made $200 on commission.

8 0
3 years ago
Read 2 more answers
Other questions:
  • Polygon JKLM is dilated by a scale factor of 2.5 with point C as the center of dilation, resulting in the image J′K′L′M′. If poi
    9·2 answers
  • PLZ I need help!!!!!
    5·1 answer
  • The perimeter of Raul's picture frame is 108 centimeters the length of the picture frame. Is. 18 centimeters that is. The width
    5·2 answers
  • (7+5) ÷ 6 + 10 to the second power
    9·1 answer
  • A research company surveys 8,000 people. The company expects 6,000 people to respond favorably. If there is a percent error of 2
    9·1 answer
  • Which of the following represents 12% growth per time period?
    15·1 answer
  • -12.2z - 13.4z=-179.2. <br><br>idk how to do this ​
    15·1 answer
  • Triangle ABC is a right triangle with lengths shown. What is the decimal value of cos A? Round the answer to the nearest hundred
    13·1 answer
  • ....................
    11·2 answers
  • Write an equation that represents a discount of 18% on a retail price of $55. Let p represent the new price.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!