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# Advanced Math/Linear Algebra 1

Question

spheres
We consider two spheres. The sphere of radius 3 centered at the origin (0, 0, 0).  The second sphere is tangent to the first sphere and is centered at A(3, 5, 2). Find the point of intersection P of these spheres.

Hint: The points A, P and the origin are on the same line.

This means that the line of the forms 3Ax + 5Ay + 2Az contains both the centers.
This can be seen since At A=0, it contains (0,0,0) and at A=1, it contains (3,5,2).

The length along the line from A = 0 out to A = t is
is sqrt((3t)² + (5t)² + (2t)²).

Since 3 squared, 5 squared, and 2 squared are, respectively, 9, 25, and 4,
and 9+25+4 = 38, this is the same as sqrt(38t²).

The edge of the inside sphere is then at where the equation 38t² = 3² is satisfied.
That is, t² = 9/38, or  t = 3*sqrt(38)/38.  The point is (9,15,6)*sqrt(38)/38.
That gives the value (1.4600, 2.4333, 0.9733).

Since this is almost half the distance to the outside sphere,
the radius of the outside sphere would be a little bit bigger than the inside.

It would be roughly (1.5400² + 2.5667² + 1.0267²), which is roughly 3.16.

Volunteer

#### Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.