Find an equation of the sphere with center s23, 2, 5d and radius 4. what is the intersection of this sphere with the yz-plane?

Equation:

Intersection:

Step-by-step explanation:        

We are asked to write an equation of the sphere with center center and radius 4.    

We know that equation of a sphere with radius 'r' and center at is in form:

Since center of the given sphere is at point , so we will substitute , , and in above equation as:

Therefore, our required equation would be .

To find the intersection of our sphere with the yz-plane, we will substitute in our equation as:

Therefore, the intersection of the given sphere with the yz-plane would be .

rx and sx

step-by-step explanation:

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!