Questions asked
A hydraulic jack is a practical use of Pascal's principle that makes it possible to lift heavy objects using much less _____ than the object's _____.
Match each MOLLUSK trait to its biological function Mantle Radula Foot Shell Protective, calcified structure Feeding organ that scrapes or cuts Secretes shell and covers organism Locomotion, arms, or tentacles
An investment has an expected return of 11.9 percent per year with a standard deviation of 20.0 percent. Assuming that the returns on this investment are roughly normally distributed, how frequently do you expect to earn between -8.1 percent and 31.9 percent? How often do you expect to earn less than -28 percent?
an executive and an engineering firm earned the monthly salary plus a Christmas bonus of 5100 if she earns a total of 96,300 per year, what is her monthly salary?
9 \[ \begin{array}{r} 3 x+4 y=-23 \\ 2 y-x=-19 \end{array} \] What is the solution \( (x, y) \) to the system of equations above? A) \( (-5,-2) \) B) \( (3,-8) \) C) \( (4,-6) \) D) \( (9,-6) \)
To evaluate the integral \( \int \frac{x+2}{(x-2)^2 \cdot (x+7)} dx \) \\ we first apply the method of partial fractions to express the integrand as a sum of simple rational functions of x: \\ \( \frac{x+2}{(x-2)^2(x+7)} = A \cdot \frac{1}{(x-2)(x+7)} + B \cdot \frac{1}{x+7} + C \cdot \frac{1}{(x-2)^2} + D \cdot 0 + E \cdot 0 \) \\ We then equate like powers of x in the numerators (use * for multiplication): \\ \( x + 2 = (A+C)x^2 + (5A+B-4C)x + (-14A+7B+4C) \) \\ and solve for the unknown coefficients to obtain the partial fraction expansion \\ \( \frac{5}{81(x-2)} + \frac{4}{9(x-2)^2} + \frac{5}{81(x+7)} \) \\ which has antiderivative \( \frac{5}{81} \ln(|x-2|) - \frac{4}{9(x-2)} - \frac{5}{81} \ln(|x+7|) + C \)
2. List all the elements of the group $S_4$ in cycle form
Solve $x\frac{dy}{dx} + 2y = \sin x$
Recall from Question 3 in this homework the table showing the approximate value of exports and imports for the United States from 1973 through 1977: \begin{tabular}{|l|l|l|} \hline Year & Exports ($, billions) & Imports ($, billions) \\ \hline 1973 & 91.2 & 89.3 \\ 1974 & 120.9 & 125.2 \\ 1975 & 132.6 & 120.2 \\ 1976 & 142.7 & 148.8 \\ 1977 & 152.3 & 179.5 \\ \hline \end{tabular} Source: U.S. Department of Commerce Which of the following statements are correct? Check all that apply. a. The value of exports (in nominal dollars) increased each year from 1973 to 1977. b. The United States ran a trade surplus in 1973. c. The United States ran consistent trade deficits between 1973 and 1977. d. Of the years listed, the United States ran its largest trade surplus (in nominal dollars) in 1973.
If the $r$, $v$, $w$ are respectively radius of the circle, instantaneous linear velocity, and the instantaneous angular velocity, then Select one: $\circ$ a. $w = vr$ $\circ$ b. $v = rw$ $\circ$ c. None $\circ$ d. $r = vw$
