Two straight sections of freeway cross at a right angle. at the point of crossing, the east-west highway is at elevation 150 ft and has a constant +5.0% grade (upgrade in the east direction), and the north-south highway is at elevation 125 ft and has a constant -3.0% grade (downgrade in the north direction). design a 90-degree ramp that connects the northbound direction of travel to the eastbound direction of travel. design the ramp for the highest design speed (to the nearest 5 mi/h) with the constraint that the minimum allowable value of d is 8.0. assume that the pc of the horizontal curve is at station 15 + 00, and that the vertical curve pvis are at the pc and pt. give the stationing and elevations of the pvis, pvcs and pvts. you may find that drawing out the horizontal and vertical curves aids in your solution. make sure to define the pvi elevations.

Need showing work for this problem 56.25 ×25.80

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).

Write a description of each inequality. 1. -5a + 3 > 1 2. 27 - 2b < -6 (this < has a _ under it) 3. 1/2 (c + 1) > 5 (this > has a _ under it)