Find the particular solution of the differential equation dydx=(x−5)e−2y dydx=(x−5)e−2y satisfying the initial condition y(5)=ln(5)y(5)=ln⁡(5).

Two rectangular prisms have the same volume. the area of the base of the blue prism is 418 4 1 8 square units. the area of the base of the red prism is one-half that of the blue prism. which statement is true?

Given the quadratic function f(x)=3x^2-24x+49 a. use “completing the squares” to convert the quadratic function into vertex form b. state the vertex c. find the x and y intercepts d. graph the function

Aflagpole broke in a storm. it was originally 8 1 81 feet tall. 2 8 28 feet are still sticking straight out of the ground, where it snapped, but the remaining piece has hinged over and touches the ground some distance away. how far away is the end of the pole from the base of the pole along the ground?