EXAMPLE 1 Show that every member of the family of functions y = 1 + cet 1 − cet is a solution of the differential equation y' = 1 2 (y2 − 1). SOLUTION We use the Quotient Rule to differentiate the expression for y: y' = (1 − cet) − (1 + cet)(−cet) (1 − cet)2 = − c2e2t + cet + c2e2t (1 − cet)2 = (1 − cet)2 . The right side of the differential equation becomes 1 2 (y2 − 1) = 1 2 2 − 1 = 1 2 (1 + cet)2 − 2 (1 − cet)2 = 1 2 (1 − cet)2 = (1 − cet)2 . Therefore, for every value of c, the given function is a solution of the differential equation.

answer: i can’t tell you that

step-by-step explanation:

total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100   * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

                                                            = $25.99 - $6.49

                                                            =$19.5

total amount to be paid = $19.5

answer: the correct answer is -32

step-by-step explanation:

c

step-by-step explanation:

there is vertical asymptote at x = 2 and x = 0

vertical asymptote occurs at the points where the denominator is 0. so we can say that

x = 2 occurs when there is a factor (x-2) in the denominator, and

x = 0 occurs when there is a factor "x" in the denominator

thus, the denominator of the equation would have "x * (x-2)", this is option c only. that's the correct answer.