Consider the system of differential equations dxdt=−5ydydt=−5x. convert this system to a second order differential equation in y by differentiating the second equation with respect to t and substituting for x from the first equation. solve the equation you obtained for y as a function of t; hence find x as a function of t. if we also require x(0)=1 and y(0)=3, what are x and y? x(t)= equation editorequation editor y(t)= equation editorequation editor

Tom is making a punch that contains 80% cranberry juice and the rest ginger ale. the punch has 2 liters of ginger ale. part a: write an equation using one variable that can be used to find the total number of liters of cranberry juice and ginger ale in the punch. define the variable used in the equation and solve the equation. hint: 0.8x represents the number of liters of cranberry juice in the punch. (5 points) part b: how many liters of cranberry juice are present in the punch? show your work.

To describe a sequence of transformations that maps triangle abc onto triangle a"b"c", a student starts with a reflection over the x-axis.how should the student complete the sequence of transformations to map triangle abc onto triangle a"b"c"? plz

Awater holding tank measures 105 m long, 50 m wide, and 8 m deep. traces of mercury have been found in the tank, with a concen- tration of 60 mg/l. what is the total mass of mercury in the tank? answer in units of kg.