Verify that the indicated expression is an implicit solution of the given differential equation. (dy/dx)2 + 1 = 1/y2 ; (x − 7)2 + y2 = 1
Using implicit differentiation,
(x − 7)2 + y2 = 1
+ 2y dy dx = 0
(dy/dx)2 =
Since (x − 7)2 = 1 − y2, we have that (dy/dx)2 + 1 = 1/y2 .

Marla bought a book for $12.95, a binder for $3.49, and a backpack for $44.99. the sales tax rate is 6%. find the amount of tax and the total she paid for these items

Reduce fractions expressing probability to lowest terms. in 3,000 repetitions of an experiment, a random event occurred in 500 cases. the expected probability of this event is?

Write the contrapositive of the conditional statement. determine whether the contrapositive is true or false. if it is false, find a counterexample. a converse statement is formed by exchanging the hypothesis and conclusion of the conditional. a) a non-converse statement is not formed by exchanging the hypothesis and conclusion of the conditional. true b) a statement not formed by exchanging the hypothesis and conclusion of the conditional is a converse statement. false; an inverse statement is not formed by exchanging the hypothesis and conclusion of the conditional. c) a non-converse statement is formed by exchanging the hypothesis and conclusion of the conditional. false; an inverse statement is formed by negating both the hypothesis and conclusion of the conditional. d) a statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement. true