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Hello in this video we're going to go over problems 133 from the North Carolina released common exam for math to find out more information about this common exam and other common exams you can go to this website right here and if you follow the links for released you can actually find the PDF that these problems come from let's get started the equation s equals to square root of 5x can be used to estimate the speed s of a car in miles per hour given the length and feet X of the tire marks that lives in the ground a car traveling 90 miles per hour came to a sudden stop according to the equation how long will the tire marks be for this car so in any word problem like this one the first step is to do what I just didn't read it, and then we're going to go through we're going to pick out key information so our equation any kind of equation is probably important sometimes they throw one in there that just to be random and then try to mix you up variables are usually important as well and what they represent so s is the speed of a car and X is the length of the tire marks sometimes the units of measure for each variable and other things are important as well because sometimes you have to convert, so the speed is going to be a miles per hour and the length is going to be in feet all right this particular car is traveling 90 miles per hour when it came to a stop, and we want to know how long with the tire marks B all right, so that's the stuff let's just put it all together now and see if we can figure out how to tell how long these tire marks would be well they are to tell us that the car was traveling 90 miles per hour, so my speed is 90 so to figure out the tire marks I have to plug it into my equation that relates speed to tire marks, so I'm plugging 94 s, so I get 90 is equal to 2 square roots of 5 X and this is what we call a radical equation it's a radical equation because X is in the radical is the part underneath the radical, so we got to get the radical by itself before we can get the X out it's kinda like the prison whew get rid of the guard before we can bust it out, so we want to divide both sides by two to get rid of two we get 45 is equal to the square root of 5x now I can get rid of the radical by raising both sides of the equation to the index for this one is two, so I'm going to square both sides alright so but square root squared cancels out I'm left with 5x on that side 45 squared is 2025 my last step divide both sides by 5, and I get X is equal to 405 feet which is C number to the heights of two different projectiles after they are launched our model by f of X and G of X the function f of X is defined as f of X is equal to negative 16 x squared plus 42 X plus 12 the table contains the values for the quadratic function G what is the approximate difference in the maximum height achieved by the two projectiles alright so in this one we've got two different projectiles that are modeled by f of X and G of X f of X is this equation right...
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