Use laplace transform to solve the initial value problem y'' -4y'+13y =0 ,y(0) = - 5 , y'(0) = -1 . show all the work especially how you solve the partial fraction with complex roots.

30 in the diagram line e and made parallel to each other and line p and q are transversal. use properties of special angles formed by parallel lines and their transversals to find the missing angle measures. m< 3=65 m< 15=120 m< 7= m< 4= m< 6= m< 1= m< 16= m< 18= m< 21= m< 10= m< 11= m< 12=

Sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle and label its height and width. y= 5x, y=7x^2then find the area s of the region.

Ariana starts with 100 milligrams of a radioactive substance. the amount of the substance decreases by 20% each week for a number of weeks, w. the expression 100(1−0.2)w finds the amount of radioactive substance remaining after w weeks. which statement about this expression is true? a) it is the difference between the initial amount and the percent decrease. b) it is the difference between the initial amount and the decay factor after w weeks. c) it is the initial amount raised to the decay factor after w weeks. d) it is the product of the initial amount and the decay factor after w weeks.