ocean-tides-are-caused-by-gravitational-forces-exerted-by-the-moon-tides-are-also-influenced-by-the-

Question

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.

Louisa Benatovich · Accepted Answer

talking about tides in Canada and we&#x27;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&#x27;ve got the shoreline. Let&#x27;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&#x27;s this 30 plus eight. That&#x27;s 38 meters right here and we can figure out the minimum tied distance, which would be this whole 30 minus. The eight that&#x27;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&#x27;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&#x27;re not artists, will. Some of this might be I&#x27;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&#x27;t told we weren&#x27;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&#x27;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&#x27;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&#x27;m exposed the equation. Have you got this 0 30? That&#x27;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.

Heather Zimmers · Answer

this problem is about high tides, and we have this equation D of tea, which represents the depth of the water and tea representative, represents the number of hours since midnight, and we&#x27;re asked for how fast the tide is rising or falling at different times. And when you see the phrase how fast you want to think about rate of change and when you think about rate of change, that means derivative in calculus. And so we want to start by finding the derivative of the function so deep prime of tea, the derivative of 70 And then we move on to the other term and we can leave the five and take the derivative of co sign, which is negative sign. So we have negative sign of the entire inside. And then, according to the chain rule, we&#x27;re going to multiply by the derivative of the inside. And so we would be multiplying by 0.503 Okay, so now that we have that derivative, we could simplify it if we wanted to. But chances are we&#x27;re just going to be using a calculator from this point. So the calculators not going to mind if you don&#x27;t simplify it for part A. We want to find the speed of the tide changing how fast the tide is rising or falling at 3 a.m. And 3 a.m. is going to be three hours since midnight, so we&#x27;re going to use T equals three. We&#x27;re going to substitute that into the derivative, use a calculator and you get approximately 2.39 meters per hour for part B. Three more hours have gone by, and now it&#x27;s 6 a.m. So T equals six. We&#x27;re going to substitute six into the derivative, use a calculator. Make sure your calculators and radiance, by the way, and we get 60.9 to 6 meters per hour. And for part C, it&#x27;s now 9 a.m. So we&#x27;re going to use T equals nine. Substitute that into the derivative. Put it in your calculator on you get approximately negative 2.28 Now, why is it negative? If the derivative is negative, that means you&#x27;re quantity is decreasing. So that&#x27;s telling us that the tide is going down and then finally, for party, it&#x27;s noon, so T is 12 12 hours since midnight, and the rate of change AT T equals 12 is approximately negative. 1.21 Again, the tide must still be going down at this point in time.

Foster Wisusik · Answer

Okay. This question wants us to find the rate of change of the water level at different times. So if we&#x27;re dealing with a rate here, that means we need to find the derivative. So de prime of tea would be taking the derivative. The derivative of co sign is negative sign. So we keep the inside the same and then we have to multiply by the derivative of the inside. And the only thing attached to a T would be that 0.503 So now D prime of tea can be simplified as negative 2.515 as our coefficient in front. And now we have a sine function. So now that we have D of tea, we can store this in our calculator as a function. And then we can use this to just plug in different values and t So first at 3 a.m. That would mean three hours past, so plugging in three, we get 2.39 and the units for D. R meters per hour. Then if it&#x27;s 6 a.m. it means that six hours have passed and looking into our calculator again for that one where you get that. Why one of six is zero point 9 to 6 the meters per hour, then for C. If it&#x27;s nine am, nine hours have passed and that one works out to approximately negative two point to a meters per hour. And then finally, if it&#x27;s noon than 12 hours have passed and our calculator says the D prime of 12 is approximately negatives. One point to what meters per hour and those are answers.

Adnan Gill · Answer

so looking at the data given in the question, we can draw this craft so this would be a sign craft starting A T is equal to zero. The repeated off 12 and the maximum height reaches 21 lost his negative 21. So this would be the graph that we can draw for this question, given the information. So the aptitude is 21. The period it is 12 hours, and that means we can count the B, which is two pi divided. Find a period. So that&#x27;s a two pi divided by 12 which is equal to pi or six. So the equation finding that beacon right would be equal Why is equal to 21 sign high over six times T?

Shaza Hammoud · Answer

basic question is talking about the tights were they resemble on move in a simple harmonic motion and one with ours, period. The water starts at mean Sea devil on drivers to 1 12 21 feet above, drops to 20 feet below and then goes again to the museum, so we&#x27;ll have to find an equation. Describe the emotion on toe sketch the graph. So it&#x27;s mentioned that the period is 12 hours on DDE. Let&#x27;s try toe. Draw the graph as it stays just enough. Ah, enough sketch off the graph. It stays. That it starts at means it well. So let&#x27;s consider This is the mean sea level, which is the X axis. Starting from the means available, it rises to 21 feet above. Then it goes down toe 21 feet below the mean sea level. So as if this one is minus 21 on Dhere is 21. Then it returns toe demean syllable. So this is the graph of the function on dhe. It&#x27;s clearly that the function of the emotion the motion of the object resembles a sign. Careful. So this is tanker Andi. Maximum aptitude is 21 on during our operative is minus the amplitude minus 20 months. So on this is just one period, and here is the 12 hours as one period means it&#x27;s on tip. It is the time that takes for one cycle to be completed. So now let&#x27;s right the function. What is the displacement off the water? Or the height of the water equals well that if the function equals y equals a sign Oh, Meg, etc. And this is the original form off these function, since there is no presenter shift or vertical shift. So just a simple form off the simple harmonic motion. Now the amplitude. I mentioned it already that it is equal to 21. Now let me get can be obtained from the period and we know that Omega it&#x27;s just to buy over the period 12 and this is equals to play over sex. So now just substituting the values in the equation is a 21 sign by over six multiplied by t on This is just D final solution off this a question as well as the graft drive here

Jonathan Ibarra · Answer

were given that the waves at Earth surface water has a time period of 12 hours and 24 minutes. Only teeter argue for or against this proposition. 14. So to solve this problem, we&#x27;re gonna use the fact that a time period t is equal 21 over f, which is also equal do the wavelength divided by its velocity. So what we&#x27;re gonna have to do to solve for this wavelength and also solved for this velocity sent? These are the two unknowns that we need to find. That&#x27;s all for this time period. So now we&#x27;re gonna start by gang this velocity and by the problem, this velocity is going to be equal to the square root of G time, Steve. So plug in 9.8 Fergie and then plug in an 36.1 40. And so this will give us a velocity of 18.8 meters per second. Next we can say that length, though, is equal to a wavelength divided by four. And so we plug in junior 10 times 10 to the three meters for ill and said it equal to Lambda, divided by four. And now take this solve it for Lambda and we&#x27;ll get away fling. That&#x27;s equal 2 840 kilometers. So now we can say that a time period t is equal to Lambda divided by. So we just plug in Lambda and then we plug in B and this will be you cool to 4.47 times 10 to the four seconds which we can also say is equal to 12 hours and 24 minutes. So we can say that we agree with the time period that is given by the problem.

Problem 46 Hard Difficulty

Answer

22 meters
38 meters

Related Courses

Algebra

Related Topics

Discussion

Top Algebra Educators

Grace H.

Catherine R.

Maria G.

Kristen K.

Algebra Courses

Absolute Value - Example 1

Absolute Value - Example 2

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript

Holliday, Luchin, Cuevas, Carter Marks, Day, Casey, Hayek

Algebra

Grace H.

Catherine R.

Maria G.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

22 meters38 meters

Algebra

Grace H.

Catherine R.

Maria G.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

Holliday, Luchin, Cuevas, Carter Marks, Day, Casey, HayekAlgebra

Grace H.

Catherine R.

Maria G.

Kristen K.

22 meters
38 meters

Holliday, Luchin, Cuevas, Carter Marks, Day, Casey, Hayek

Algebra