Consider the system of differential equations dxdt=−4ydydt=−4x. 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)=4 and y(0)=5, what are x and y?

The label on the car's antifreeze container claims to protect the car between ? 40°c and 125°c. to convert celsius temperature to fahrenheit temperature, the formula is c = 5 over 9 (f ? 32). write and solve the inequality to determine the fahrenheit temperature range at which this antifreeze protects the car. ? 40 > 5 over 9 (f ? 32) > 125; ? 40 > f > 257 ? 40 < 5 over 9 (f ? 32) < 125; ? 40 < f < 257 ? 40 < 5 over 9 (f ? 32); ? 40 < f 5 over 9 (f ? 32) < 125; f < 257

If set d is not the empty set but is a subset of set e, then which of the following is true? d ∩ e = d d ∩ e = e d ∩ e = ∅

"which statement is necessarily true if bd is an altitude to the hypotenuse of right ? abc? a.) ? adb? ? bdc b.) ? adb~? bdc c.) abbc=acbd d.) ? bac? ? bdc"