Letf(x)∈f[x] be a polynomial of degree n≥1 and let bars denote passage to the quotient f[x]/(f(

prove that for each g(x) there is a unique polynomial g0(x)of degree≤n−1 such that g(x) =g0(x) (equivalently, the elements1,x, . . ,xn−1are a basis of the vector spacef[x]/(f(x)) overf).

The decibel level of sound is 50 db greater on a busy street than in a quiet room where the intensity of sound is watt/m2. the level of sound in the quiet room is db, and the intensity of sound in the busy street is watt/m2. use the formula , where is the sound level in decibels, i is the intensity of sound, and is the smallest sound intensity that can be heard by the human ear (roughly equal to watts/m2).

In the diagram below, tan θ = sqrt 3. what is the value of m?

Aregular pan has a length that is 4/3 the width. the total area of the pan is 432in.2. what is the width of the cake pan?