Consider the following initial value problem for a spring-mass-dashpot system: 4x" + 16x' + kx = 0, x(0) = -1.5, x'(0) = 8
a) Find the value of the spring constant k that makes the spring critically damped.
b) If k=116, write the solution x(t) in the form Ce -pt cos( w1t_a1).

Someone answer this asap rn for ! a discount store’s prices are 25% lower than department store prices. the function c(x) = 0.75x can be used to determine the cost c, in dollars, of an item, where x is the department store price, in dollars. if the item has not sold in one month, the discount store takes an additional 20% off the discounted price and an additional $5 off the total purchase. the function d(y) = 0.80y - 5 can be used to find d, the cost, in dollars, of an item that has not been sold for a month, where y is the discount store price, in dollars. create a function d(c(x)) that represents the final price of an item when a costumer buys an item that has been in the discount store for a month. d(c(x)) =

Worth 30 points! in this diagram, both polygons are regular. what is the value, in degrees, of the sum of the measures of angles abc and abd?

In each diagram, line p is parallel to line f, and line t intersects lines p and f. based on the diagram, what is the value of x? ( provide explanation)