Find the equation of the plane through the point (1,1,1) which is perpendicular to the line of intersection of the two planes x−y−3z=−1 and x−3y+z= 2.

In: Advanced Math

Solve the 4 degree polynomial equation \( x^4 − 2x^3 + 4x^2+ 6x − 21 = 0 \), given that the sum of two its roots is zero.

In: Advanced Math

Find the values of sin θ, cos θ, and tan θ for the given right triangle. Give the exact values.

In: Advanced Math

Which of the following sets are not well defined? Explain.

**a. **The set of wealthy school teachers

**b. **The set of great books

**c. **The set of natural numbers greater than 100

**d. **The set of subsets of \(\{1,2,3,4,5,6\}\)

**e. **The set \(\{x \mid x \neq x\) and \(x \in N\}\)

In: Advanced Math