Question

Show that the equation x^{2}+y^{2}+z^{2}
= 7 has no integer solutions.

(Using mod)

Answer #1

Show that the equation x2+y2+z2
= 7 has no integer solutions.
(Without mod)

write the equation of the cone z2=x2+y2 in sperical form

Which of the following congruences have solutions?
a) x2 Congruent 7(mod 53)
b) x2 Congruent 14(mod 31)
c) x2 Congruent 53(mod 7)
d) x2 Congruent 25(mod 997)
All of them please!!

Write the equation of the sphere in standard form.
x2 +
y2 + z2 +
4x − 6y − 2z
= 22
Find its center and radius.
center
(x, y, z)
=
radius

Write the equation of the sphere in standard form.
x2 +
y2 + z2 +
2x − 4y − 2z
= 10
Find its center and radius.
center
(x, y,
z)
=
radius

A) Show that the equation represents a sphere, find its center
and radius:
x2+y2+z2-2x-4y+8z=15
B) Find the equation of the sphere if one of its diameters is
between the points (2,0,0) and (0,6,0)
C) Describe in words or with a drawing the region represented by
x2+y2=9, z= -2
D) Find the length of the sides of the triangle that passes
through the following points and determine if it is a rectangle,
isosceles, equilateral: (5,3,4), (7,1,3), (3,5,3)

Find all solutions in positive integers of the Diophantine
equation x2 + 3y2 = z2

Substances X2,
Y2, and Z2 can all act as oxidizing agents.
In solution X2 is green, Y2 is yellow, and
Z2 is red. In the reactions in which they participate,
they are reduced to X–, Y–, and Z–
ions, all of which are colorless. A solution of X2 is
mixed with one containing Y– ions. The color changes
from green to yellow.
a. Write the net
equation for the reaction.
b. Which species
is oxidized?
c. Which species
is the...

Find the surface area of the cone x2 + y2
= z2 that lies inside the sphere x2 +
y2 + z2 = 6z by taking integrals.

Calculate ∫ ∫S f(x,y,z)dS for the given surface and function.
x2+y2+z2=144, 6≤z≤12; f(x,y,z)=z2(x2+y2+z2)−1.

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