The equation of a sphere is:
(x – h)^2 + (y – k)^2 + (z – l)^2 = r^2
where h, k and l are the coordinates of the center of the
sphere
Using the midpoint formula, the coordinate of the center
is:
h = (-4 + 6) / 2 = 1
k = (7 + -5) / 2 = 1
l = (6 + 7) / 2 = 6.5
so the equation becomes:
(x – 1)^2 + (y – 1)^2 + (z - 6.5)^2 = r^2
we plug in any point, in this case point P to solve for r:
(-4 -1)^2 + (7 – 1)^2 + (6 - 6.5)^2 = r^2
r^2 = 61.25
So the full equation is:
<span>(x – 1)^2 + (y – 1)^2 + (z - 6.5)^2 = 61.25</span>
Answer:
(3,0)
Step-by-step explanation:
put x-3=0 and solve for it whic hwould be x=3
Easy peasy
slope=(change in rise)/(change in run)
aka
slope between points (x1,y1) and (x2,y2) is
slope=(y2-y1)/(x2-x1) since y is rise/up and x is run/leftright
points
(-7,-9) and (-5,-8)
x1=-7
y1=-9
x2=-5
y2=-8
remember minusing a negative means addin a positive
slope=(-8-(-9))/(-5-(-7))=
(-8+9)/(-5+7)=1/2
slope=1/2
positive slopes go from bottom left to top right
since it is less than 1
it is more horizonal than vertical
You are correct. For each of the three possibilities for their second day, there are two possibilities for the third day.
The total number of possibilities is 3*2 = 6.
The value of the angles should be. (x-40°). , (x-20°), (½x-10°) , not (x-40°) + (x-20°)+(½x-10°)
Sum of all the interior angles of a triangle is 180°.
So a equation can be made by the given data,
(x-40°) + (x-20°) + (½ x-10°) = 180°
x-40°+x-20°+½x-10° = 180°
2x+½x -60°-10° = 180°
5/2 x - 70° = 180°
5/2 x = 180° + 70°
5/2 x = 250°
x = 250° × 2/5
x = 50° × 2
x = 100°
So the angles are
x-40° = 100°-40° = 60°
x-20° = 100°–20° = 80°
½x-10° = ½(100)° - 10° = 50° -10° = 40°
The answer can be checked by putting the values of the angle we got in the second statement i.e. Sum of all the interior angles of a triangle is 180°.
60° + 80° + 40° = 100° + 80° = 180°
