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Ocean tides are caused by gravitational forces exerted by the Moon. Tides are also influenced by the size, boundaries, and depths of ocean basins and inlets. The highest tides on Earth occur in the Bay of Fundy in Nova Scotia, Canada. During the middle of the tidal range, the ocean shore is 30 meters from a rock bluff. The tide causes the shoreline to advance 8 meters and retreat 8 meters throughout the day. Write and solve an equation describing the maximum and minimum distances from the rock bluff to the ocean during high and low tide.

22 meters38 meters

Algebra

Chapter 3

Systems of Equations and Inequalities

Section 5

Solving Systems of Equations in Three Variables

Graphs and Statistics

Missouri State University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

02:41

Some of the highest tides …

02:51

00:59

Tides The Bay of Fundy in …

03:43

03:25

The Bay of Fundy, Nova Sco…

07:32

03:54

07:15

03:04

Lunar tides raise the ocea…

00:39

Most people today know tha…

talking about tides in Canada and we've got a lovely bluff, just like a rock face about the moon exerting its four samba tides. So you got idoc face and then we've got the shoreline. Let's say the shoreline is here in the smack middle of the day or in the middle of the title sequence. It is 30 meters away from the blood. At one end of the title sequence, it adds another eight meters, so it retreats eight meters and then it advances eight meters from the center point that we were told was 30. So we can figure out when the maximum tide is because it's this 30 plus eight. That's 38 meters right here and we can figure out the minimum tied distance, which would be this whole 30 minus. The eight that's encroaching in it and 30 minus eight is 22 So this would be 22 over here. Theun were asked to write an equation that represents the Max and men distance that it is a way from Rock bluff. Well, this is where we can get creative. So if we stay that why is the distance from the bluff that's not how you spell distance. Some people can do math and not spell distance from bluff. And we say that X is the title range. Then we can make some sort of y equals MX plus B equation to tell individuals what this is what this is without drawing this picture. We're not artists, will. Some of this might be I'm not an artist. Okay, so I want to make up my own range for X are my own title range for X because we weren't told we weren't given any X values. So in my mind, I want to say negative one goes to zero zero could be my middle right and then one on the other side. So zero could be my middle. This 30 meters right here the middle of the title range, 30 meters and maybe the one ca NBI the maximum 38 and the negative one could be the minimum. Sure, 22. So now it's like saying that we have texts. We have 0 30 is one point 1 38 as another in a negative 1 22 was another point that mind you, you can use any value that you want for acts as long as they're kind of a symmetrical situation like we have here. But I thought it would be easier to do one and negative one. And now we can solve to put into the like, ALS. I'm exposed the equation. Have you got this 0 30? That's our Why intercept. So B equals 30. And then we need to figure out M, which is the slope. The slope equation is why? To minus y one over x two minus x one. So we just need to choose two points. Have about this point in this point. Yeah. When we plug in to our slope, this is the slope a slope equation. You get 38 you got up with a bigger one first, 38 minus 30 over one minus zero, which just gives us 8/1, which is eight. So our slope will be eight. So when we plug all of those in, why equals eight X plus 30 with one specific caveat that we have to make sure with a domain this of and this is a special reiterated negative one to one. You can also write it like this with close brackets. Negative one 10 you can write it negative 1 to 1. But we have to put this part for it to make sense. Otherwise, people will go beyond the maximum or beyond the minimum. So why equals eight X plus 30? We solve it when we plugged the one in why equals eight times negative one plus 30. That gives us our men of 22. And when we plug in, why E cools eight times one plus 30 we get the max 38 which is exactly what we figure it out in our drawing above. So there you have it magical.

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