What is the angle between the given vector and the positive direction of the x-axis?8i + 6j.

The between the given vector and the positive direction of the x-axis is approximately 41.186º.

Step-by-step explanation:

Let be and (Positive direction of the x-axis), the angle between both vectors can be determined from definition of dot product:

Angle is cleared:

The norms of and are found by Pythagorean Theorem:

The dot product between both vectors is:

The angle is now calculated:

The between the given vector and the positive direction of the x-axis is approximately 41.186º.

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.