Use the "mixed partials" check to see if the following differential equation is exact. if it is exact find a function f(x, y) whose differential, df(x, y) gives the differential equation. that is, level curves f(x, y) = c are solutions to the differential equation: dy _ -2x4 – 4y dx = 4x + 4y4 first rewrite as m(x, y) dx + n(x, y) dy = 0 where m(x, y) = and n(x, y) = if the equation is not exact, enter not exact, otherwise enter in f(x, y) as the solution of the differential equation here = c.

What is the equation and solution for the sentence? the sum of a number and thirty-one is one hundred thirteen. write the equation as n-31=113 and subtract 31 from both sides. the answer is 82. write the equation as n+31=113 and subtract 31 from both sides. the answer is 82. write the equation as n+31=113 and add 31 to both sides. the answer is 144. write the equation as n-31=113 and add 31 to both sides. the answer is 144.

Pam buys a sleeve of ball bearings for her skateboard. each of the bearings is 1 1/5 inches wide. the sleeve is 9 3/5 inches long. how many ball bearings are in the sleeve? show your work.

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.