Determine whether the conjecture is true or false. Give a counterexample for any false conjecture. Given: points A, B, C, and D

Conjecture: A, B, C, and D are coplanar.

Question 16 options:

False; the four points do not have to be in a straight line.

True

False; two points are always coplanar but four are not.

False; three points are always coplanar but four are not.

False; three points are always coplanar but four are not.

Step-by-step explanation:

We are given points A, B, C and D. We say that a set of points are coplanar if there exists a plane that coints all the points. Consider A,B, C ,D points in a 3 dimensional space. It is true, by euclidean geometry, that given any 3 points in a 3 dimensional space, they are coplanar.

However, this is not true for 4 points.

Consider the points A=(1,0,0), B=(0,1,0), C=(0,-1,0) and D=(0,0,1). In this case, A,B and C are in the plane (x,y,0) and D is not coplanar to points A,B,C

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere