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Answer:
The equation of the sphere that passes through the point (7,1,-3) and center at (5, 6, 5) is
.
Step-by-step explanation:
Any sphere centered at
in an Euclidean space with a radius
is represented by the following formula:

If
and
, the radius of the sphere is obtained:



The equation of the sphere that passes through the point (7,1,-3) and center at (5, 6, 5) is
.
Answer: 
Step-by-step explanation:
For this exercise it is important to remember that, by definition, the length of the minor arc can be calculated wih the following formula:

In this case , according to the data given in the exercise, you know that:

Therefore, susbtituting those values into the formula, you get that length of AB is the following:

Answer:
x=55
Step-by-step explanation:
The 3 angles of a triangle add up to 180 degrees
<A + < B + <C = 180
x + 75+ 50 = 180
x + 125 = 180
subtract 125 from each side
x = 180-125
x = 55
Answer:
y =
x + 
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (1, 5)
m =
=
, hence
y =
x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (1, 5 ), then
5 =
+ c ⇒ c = 5 -
= 
y =
x +
← in slope-intercept form