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
Polly made a pinata for her sister's birthday party and wants to fill it with candy. If
devlian [24]

Answer:

The volume of candy that is needed by Polly is 1,437.3 cubic inches

Step-by-step explanation:

What we have to do here is to find the volume of the sphere with a diameter of 14 inches

If the diameter is 14 inches, then the radius is 14/2 = 7 inches

This is because the radius is half the measure of the diameter

To find the volume of the sphere, we use the formula below;

Volume of sphere

= 4/3 * pi * r^3

pi = 22/7

r = 7 inches

Volume is;

4/3 * 22/7 * 7^3

= 4/3 * 22 * 7^2 = 1437.3 cubic inches

5 0
3 years ago
Please help. I just need to get this done lol.
Mice21 [21]

Answer:

1/16

Step-by-step explanation:

6 0
3 years ago
What is the equation of the line that passes through the point (-3,-8) and has a slope of 4?
coldgirl [10]

Step-by-step explanation:

the easiest approach with a given point and the slope of the line is the point-slope form :

y - y1 = a(x - x1)

where "a" is the slope, and (x1, y1) is a point on the line.

so, we get

y - -8 = 4(x - -3)

y + 8 = 4(x + 3)

if we need the slope-intercept form

y = ax + b

we now simplify the point-slope form

y + 8 = 4x + 4×3 = 4x + 12

y = 4x + 4

3 0
2 years ago
4 bells toll together at 9 am. They toll after 7, 8. 11 and 12 seconds respectively. How many times will they toll together agai
Svetach [21]

Answer:

5 times

Step-by-step explanation:

What we need to do here is to find the lowest common multiple of 7,8,11 and 12

This is;

1848

Now, let’s calculate the number of seconds in 3 hours

In 1 hour, we have 3600 seconds

In 3 hours, this will be;

3600 * 3 = 10,800 seconds

So, to find the number of times in which all 4 will toll together, we need to know the number of 1848 seconds in 10,800 seconds

Mathematically, that will be;

10,800/1848 = 5.844

Our answer will be 5 times however

This is because the sixth time they would have sounded together would be more than the 3 hours time frame

8 0
2 years ago
Which of the following are solutions to the system graphed below.
Kisachek [45]
Weird. I think you just need to look if the point falls on the shaded area. But only (-5,5) does ...

4 0
3 years ago
Other questions:
  • Calculate the sales tax on purchases totaling $15,245. The
    6·2 answers
  • Find the square root of the<br> following numbers by prime factorisation method :<br>(iii) 3136​
    6·1 answer
  • I need to do these math problems. Can some one help?
    12·1 answer
  • Find the absolute Value<br> -8
    6·2 answers
  • What is the algebraic expression of thrice w increased by 7 is 25
    10·1 answer
  • BRAINLYEST TO WHOEVER ANSWERS FAST
    12·1 answer
  • Explain how solving -7y &gt; 161 is different from solving 7y &gt; -161.
    9·1 answer
  • A data set is normally distributed with a mean of 100 and a standard
    10·2 answers
  • Find the domain of the following piecewise function
    5·1 answer
  • Subtract (8.4 x 108) − (9.5 x 106).
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!