Let a and b be coprime integers, and let m be an integer such that a | m and b | m. Prove that ab | m
. Find the Maclaurin series for f(x) = (1 + x) −3 using the definition. Find the radius of convergence.
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 121.1-cm and a standard deviation of 2.2-cm. For shipment, 26 steel rods are bundled together.
Find P91, which is the average length separating the smallest 91% bundles from the largest 9% bundles.
P91 = -cm
Enter your answer as a number accurate to 2 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Random-digit-dialing telephone surveys used to exclude cell phone numbers. If the opinions of people who have only cell phones differed from those of people who have landline service, the poll results may not represent the entire adult population. The Pew Research Center interviewed separate random samples of cell-only and landline telephone users who were less than 30 years old and asked them to describe their political party affiliation.
or goodness of fit, homogeneity or independence?
Show from first principles, i.e., by using the definition of linear independence,
that if μ = x + iy, y ̸= 0 is an eigenvalue of a real matrix
A with associated eigenvector v = u + iw, then the two real solutions
Y(t) = eat(u cos bt − wsin bt)
Z(t) = eat(u sin bt + wcos bt)
are linearly independent solutions of ˙X = AX.
Use (a) to solve the system (see image)
Find a vector function that represents the curve of intersection of the two surfaces of the cylinder x^2+y^2=4 and the surface z=xy.