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
Olenka [21]
3 years ago
13

Find an equation of the sphere with center (4, −12, 8) and radius 10. use an equation to describe its intersection with each of

the coordinate planes. (if the sphere does not intersect with the plane, enter dne.) intersection with xy-plane intersection with xz-plane intersection with yz-plane
Mathematics
1 answer:
xxMikexx [17]3 years ago
6 0
<span>Sphere: (x - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100 Intersection in xy-plane: (x - 4)^2 + (y + 12)^2 = 36 Intersection in xz-plane: DNE Intersection in yz-plane: (y + 12)^2 + (z - 8)^2 = 84 The desired equation is quite simple. Let's first create an equation for the sphere centered at the origin: x^2 + y^2 + z^2 = 10^2 Now let's translate that sphere to the desired center (4, -12, 8). To do that, just subtract the center coordinate from the x, y, and z variables. So (x - 4)^2 + (y - -12)^2 + (z - 8)^2 = 10^2 (x - 4)^2 + (y - -12)^2 + (z - 8)^2 = 100 Might as well deal with that double negative for y, so (x - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100 And we have the desired equation. Now for dealing with the coordinate planes. Basically, for each coordinate plane, simply set the coordinate value to 0 for the axis that's not in the desired plane. So for the xy-plane, set the z value to 0 and simplify. So let's do that for each plane: xy-plane: (x - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100 (x - 4)^2 + (y + 12)^2 + (0 - 8)^2 = 100 (x - 4)^2 + (y + 12)^2 + (-8)^2 = 100 (x - 4)^2 + (y + 12)^2 + 64 = 100 (x - 4)^2 + (y + 12)^2 = 36 xz-plane: (x - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100 (x - 4)^2 + (0 + 12)^2 + (z - 8)^2 = 100 (x - 4)^2 + 12^2 + (z - 8)^2 = 100 (x - 4)^2 + 144 + (z - 8)^2 = 100 (x - 4)^2 + (z - 8)^2 = -44 And since there's no possible way to ever get a sum of 2 squares to be equal to a negative number, the answer to this intersection is DNE. This shouldn't be a surprise since the center point is 12 units from this plane and the sphere has a radius of only 10 units. yz-plane: (x - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100 (0 - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100 (-4)^2 + (y + 12)^2 + (z - 8)^2 = 100 16 + (y + 12)^2 + (z - 8)^2 = 100 (y + 12)^2 + (z - 8)^2 = 84</span>
You might be interested in
If a 3 hats cost $24.30 how much would 1 hat cost
777dan777 [17]

Answer:

I believe it would be $8.10!

Step-by-step explanation:

Just do $24.30÷3!

8 0
3 years ago
What is the answer?
Ivan

Answer:

the answer to thos is probably the last one

8 0
3 years ago
Please help! Simplify the rational expression. State any restrictions on the variable.
alukav5142 [94]

Step-by-step explanation:

t^2-4xt-12/t-8

= -(t^2-4-6)/4

= -t^2+4+6/4

=<u> -t^2+6</u>


6 0
3 years ago
Solve the equation.<br><br> q+59=16<br> Thx!
e-lub [12.9K]

Answer:q= -43

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Suppose a system of linear equations has a 3 5 augmented matrix whose fifth column is a pivot column. is the system consistent?
likoan [24]

Answer:

The system will be inconsistent.

Step-by-step explanation:

We are given that a system of linear equations has a 3×5 augmented matrix whose fifth column is a pivot column.

Then such a system is not consistent because since the augmented matrix has a pivot in fifth column it means that the new column added to the matrix A will lead to increase in the rank as that of matrix  A.

Hence the rank of A and Augment A will not remain same and hence the system will be inconsistent.

7 0
2 years ago
Other questions:
  • The pattern of numbers is an arithmetic sequence 14, 24, 34, 44, 54. Which of the followings statements describes the recursive
    15·1 answer
  • 3n - 24<br> How to factor out the coefficient of the variable
    7·1 answer
  • What is the answer to this : Expand y(y + 10)
    10·1 answer
  • What’s the cost after discount is applied
    8·2 answers
  • Please help me idk this
    7·2 answers
  • The level of water in a tank is 16 feet. The level decreases steadily, and the tank is emptied in 8 hours. What was the change i
    7·1 answer
  • I need help(This is due in a few hours)
    11·1 answer
  • What is the y-intercept of the following equation? y = 3x - 1
    5·2 answers
  • A lawn-care company loses $130 as a result of a delay. The 4 owners of the company must share the loss equally. Which expression
    8·1 answer
  • Is this relation a function? ​{(1,4), (-5,2), (4,1), (1,6)}
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!