(1 point) Find an equation of the largest sphere with center (5,3,5)(5,3,5) and is contained in the first octant. Be sure that y
1 answer:
Answer:
x^2+y^2+z^2-10x-6y-10z +50 =0
Step-by-step explanation:
Given that a sphere is contained in the first octant
Centre of the sphere is given as (5,3,5)
Since this is contained only in the first octant radius should be at most sufficient to touch any one of the three coordinate planes
When it touches we can get the maximum sphere
We find that y coordinate is the minimum of 3 thus radius can be atmost 3 so that then only it can touch y =0 plane i.e. zx plane without crossing to go to the other octants.
Hence radius =3
Equation of the sphere would be
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The first step is to name the equations to make the process of solving them easy.
The second step is to multiply each of the equations by the coefficient of the x term in the other equation. In this case, we will multiply equation (1) by 5 to get equation (3) and then multiply equation (2) by 6 to get equation (4).
The next step is to add equation equation(3) and (4) together to get equation (5) as shown below;
The next step is to take the value of y and substitute it into any of the equations above. For this solution, I pick equation (1). The work done to solve for x is shown below.;
The solution for this system of equations is
Answer: D.
Step-by-step explanation:
1. You have the following expression given in the problem above:
÷5
2. By definition, two expression are equivalent when they are the same even though they they are written in a different form.
3. Keeping this on mind, you can rewrite the division of those two numbers as a fraction, as you can see below:
3. Then, is the equivalent expression to 4h ÷ 5.