ONLINE- MAT1033 - CRN10316 - Spring 2020 (1)Homework: Section 8.1 Homework Score: 0 of pt 108.1.47The sides of the box shown are labeled with the dimensions in feet...

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. Architecture A parabolic arch has a span of 120 feet and a maximum height of 25 feet. Choose suitable rectangular coordinate axes and find the equation of the parabola. Then calculate the height of the arch at points 10 feet, 20 feet, and 40 feet from the center.

Hi, guys. Welcome back to today's video today. We're gonna take a look at Paula. No meals and long division and how we can apply in our day to day lives with this simple world problem we have here. So today's word problem is we have a rectangular prism with the volume of 10 x Q plus 30 X squared minus eight X minus 24. And they tell us that the length is to the width is expo story. But we need a solve for the height, okay? And just so that we remind ourselves the volume of rectangular prism is always length terms with times height. Okay, now that we have that, let's plug and chug some numbers to see where we get. Okay, so we have 10 x cube plus 30 x squared in this e X minus 24 and then we're gonna multiply, too. We're gonna also multiply an X plus three, and we're gonna have our height. The first thing I'm gonna do is I'm gonna divide this too by both sides. So then we get five x cubed plus 15 x squared minus for X minus 12 equals X plus three times height Okay, Now we want to get this h variable by itself. So I'm gonna divide explosives. Three. Okay. Fied X plus three. It's ages gonna equal that. So I'm gonna take all this. We're gonna add another page here. So we had five X cube plus 15 x squared, minus four x minus 12. All divided by X plus three. Okay, so I think the best way to go about this is we can try Synthetic division. Okay, so I'm gonna pull these coefficients over in our little box right here, so I'm gonna go by the highest coefficient first. So that's five. Then we have 15 for X squared. We have negative for. And then we have negative 12 as our constant, and we need to bring this plus three over here. So in order to do that, we have to always multiplied by a negative one. So three times negative one is gonna get us negative. Three. We're gonna bring this five down. We're gonna multiply this three with this five, and we're gonna get negative 15 okay? And then we're gonna get 15 top plus 15 which is gonna get a zero. So we're going to negative three. Time zero. We're just going to get us zero. We're gonna add this negative four with zero, and we're gonna end up with negative for and then we're gonna do negative three times. Negative four. Bring it up. We're gonna get positive. 12. Okay, so negative 12 plus 12 is gonna get a zero. So how do we write this all out as their fracked factor? Remember this. What? H equals ages gonna equal. We have to look at our biggest exponents in our biggest polynomial. And it is X Cube. We're gonna do one less of the expert, which is gonna get us X squared. So five X squared plus zero X minus four. And since zero is gonna be a remainder, we don't even have to write it. So let's just clean this up a little bit. We're gonna get five X squared minus four as her answer, and we can box that. And that is a height. We

To right, um, in expression for the surface area of this box that's an open top or covering the base that's X by X or X squared. And to that, we've got a side that is, ah, height of 10 in a width of X. So it has an area of 10 X, and we're gonna have four of those sides. Eso that's X squared plus 40 x in factor form. That would be X Times X plus 40.

This question asked us to find the value of X to the nearest 10th of a foot. What we know by looking at this is that we can multiply the mono meals of ex post one times X plus two distribute. In other words, this is also known as the foiling method we can now see. R B is three, which means our sea is be divided by two squared, which is nine divided by four, which means we now have exposed three over to squirt on the left hand side. And then we have 1 61/4 on the right hand side, which means we have acts plus three over to a 6.3, which means our acts is 4.8 and then this is the nearest 10th of a foot. So we could just write this his feet. The reason why I mean I got to the negative solution is because you can't

In this question we able to solve the quadratic equation. X square minus nine. X plus 10 equals two minus eight. And we have to check our answer. Okay so first of all we will simplifying it. We will add eight both of the side and it will be X squared minus nine. X plus 18 equals to zero. Okay. And now we will do the factor of this political equation and it can be written as X minus six. Multiplied by x minus three equals to zero. Okay these are the factors. And now using zero product property we will equate each of them equals to zero. So X -6 equals to zero and X -3 close to zero. So it will give us X equals to six. For the value of one. X one is six and X two is three. Okay there are two value that of X. These will be your answers and now we will check whether our answers character or not. So I'm checking here. Okay so first I'm checking for X equals to six. I'm putting the X equals to six and the quality equation and it will be X squared minus nine. X plus 10 equals two minus eight. So it will be 60 Squire minus nine, multiplied by six plus 10 equals two minus eight. Okay? And it will be 36 -54 plus 10 calls to -8. Okay? And now it will be minus 18 plus 10 equals two minus eight. Actually it is a question here, question mark here. Okay and here minus eight equals two minus eight. So we can say this is the correct answer and second answer that is X equals +23 So X squared minus nine, X plus 10 equals two minus eight. So it will be excess square. That is three square minus nine, multiplied by three plus 10 equals two minus eight. So here nine minus 27 plus 10 equals two minus eight. And when we saw it will be left inside minus eight and right inside minus eight. So we can say all this answer is also correct. Thank you.