AboutPaul Klarreich Expertise All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions.
I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.
Experience I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.
Question hi
i've some questions regarding to cal. 3
1- Find an equation of the sphere that passes through the origin and whose center is (7, 4, -7).
2-Find the equation of a sphere if one of its diameters has endpoints: (-3, 7, -11) and (3, 13, -5).
3-Find an equation of the largest sphere with center (10, 4 , 8) that is contained completely in the first octant.
4- Suppose u= (3,0) and v=(3,-6) are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are
Your help is very much appreciated.
Answer Questioner: meme
Country: Qatar
Category: Calculus
Private: No
Subject: cal. III
Question: hi
i've some questions regarding to cal. 3
1- Find an equation of the sphere that passes through the origin and whose center is (7, 4, -7).
2-Find the equation of a sphere if one of its diameters has endpoints: (-3, 7, -11) and (3, 13, -5).
3-Find an equation of the largest sphere with center (10, 4 , 8) that is contained completely in the first octant.
4- Suppose u= (3,0) and v=(3,-6) are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are
Your help is very much appreciated.
.............................................
Hi, meme,
This looks like you whole homework assignment, so I'll just get you started and you can finish up.
1- Find an equation of the sphere that passes through the origin and whose center is (7, 4, -7).
You have a standard equation that looks like : (x - x0)^2 + ... = r^2. And you have a distance formula. The radius goes from (7, 4, -7) to (0,0,0).
....................................
2-Find the equation of a sphere if one of its diameters has endpoints: (-3, 7, -11) and (3, 13, -5).
Use the midpoint formula (look up your basic geometry) to get C, use the distance formula to find the diameter.
...................................
3-Find an equation of the largest sphere with center (10, 4 , 8) that is contained completely in the first octant.
Each coordinate is the distance to a plane: 10 is the distance to the yz-plane, etc. So your minimum is 4, I suppose.
...................................
4- Suppose u= (3,0) and v=(3,-6) are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are
One diagonal is the vector sum, the other is the vector difference. That should do it.
