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Problcm "anDIboatjs S0milez Away from the MacLa ciling directly awa; Tom 15 mike per no)urDefine the neceasury Varables for this problem. srid P~ Ov Alla DHanc...

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Problcm "anDIboatjs S0milez Away from the MacLa ciling directly awa; Tom 15 mike per no)urDefine the neceasury Varables for this problem. srid P~ Ov Alla DHanc QD mits AnavAnic65 mils Prr haer (spte d )(b) WiiteCouAtiouthe dlistAICLWat FTom thie qatita after Hours15+How fat AW"y" will thc boat Io-60 Uolt4from thc marina ater 1G0minuto?When will the boat be 215 tiles away from the mnarina?

Problcm "anDI boatjs S0milez Away from the MacLa ciling directly awa; Tom 15 mike per no)ur Define the neceasury Varables for this problem. srid P~ Ov Alla DHanc QD mits Anav Anic 65 mils Prr haer (spte d ) (b) Wiite CouAtiou the dlistAICL Wat FTom thie qatita after Hours 15+ How fat AW"y" will thc boat Io-60 Uolt4 from thc marina ater 1G0minuto? When will the boat be 215 tiles away from the mnarina?



Answers

In Exercises $45-56,$ set up appropriate systems of two linear equations in two unknowns and then solve the systems by determinants. All numbers are accurate to at least two significant digits. A boat carrying illegal drugs leaves a port and travels at $42 \mathrm{mi} / \mathrm{h}$. A Coast Guard cutter leaves the port 24 min later and travels at $50 \mathrm{mi} / \mathrm{h}$ in pursuit of the boat. Find the times each has traveled when the cutter overtakes the boat with drugs. See Fig. 5.35

So here we have a problem about the sailboat voyage, and we know that the crew starts with £145 of food and they're planning to eat £15 of food per day. We want to write an equation for the situation. Sorry equation would be in the form y equals MX plus B. And in order to write an equation in that form, we need to know the slope M. And we need to know the why intercept be so taking a look at the information we were given. Ah, they're eating £15 of food per day. That's their rate. That's the rate of change of the food. And the rate of change is what we call the slope now. Because the amount of food is going down, we would use negative 15 so we'll substitute that in our equation for em. We still need to know the value of B. That would be the starting amount. That's the amount of food they have on Day Zero. And so we know they're starting with £145 of food. So that's R B. So here we have our equation. We also want to graft the equation. So I'm going to put the Y intercept 1 45 on the Y axis. And then I want my lying to slant down. Since it has a negative slope. So goes down 15 and over, one that shows a going down £15 of food every day. Notice that have a break in my graph because they didn't have the space to make my graph really tall. Finally, we want to know how many days their food will last if they're going to have £25 remaining. In other words, how many days can they be on their voyage if they want to have £25 of food remaining? Well, why stands for the pounds of food? So we're gonna put 25 in the equation for why, and we'll solve for X X stands for the number of days so we can subtract 1 45 from both sides of this equation. And then we can divide both sides of the equation by negative 15 and we'll get eight. So that tells us they could be on the voyage for eight days and have £25 of food remaining

In this question. We have this situation, um, toe both living from points p at the same time and travel in the direction shown. So are we need to find the velocity off both a relative to both be and then the time You also need to find the time taken. 4 a.m. b two b uh, 1005 100 ft apart. Okay, so, um, this is a relative velocity problem. Hey, sort off to find the answer. To find a relative velocity. First, we need to write down on the velocity factors the velocity of boats A and B in rectal form. Okay, So based on the given that Graham, uh, we A is 40 kinds. I could sign 60 degrees. I had plus sign 60 degrees jihad. And so this is, uh, 20. I had passed through ST Jihad. Pete second. Okay, then, BB, is it for two. 30 co sign 45 degrees. I had thus sign 45 degrees jihad. And so this is 15 to I had supplies. Jihad sheet second. So the velocity off a relative to be, by definition, is velocity off a minus velocity of B. So putting the numbers together So you have 20 minus 15 to I had class 20 routes three minus 15 to J had. And using your calculator, you get minus 1.21 ahead because 13.4 jihad, Eat four seconds. Okay. So to find a magnitude, you need to find the magnitude. So you take the X component, you square the x component, and you add with square of the white component. Then you take the square it off the some, and you get 13.5 ft per second. And then the direction is attention. The wind component divide by the ex components. You calculate this gets in 4.8 Greece. So this is how the direction looks like. Okay, so this is a velocity off a relative to be, and then this angle is, uh, 84.8 degrees. Okay, then the next thing is to find the time taken. So I'm going to let the time taken for a and B to be 1500 ft putt our wiki. Okay, so, um, we can use the money to a relative velocity. Times time be equal. Set it equal to, uh, 1500. Uh huh. So, um, okay, t would just be 1500. Divide by 13.5. The concrete is you get 111 seconds. All one point. It's five minutes. Okay, so just boxing the answers. So this is the relative, the main two of the relative velocity. Uh, right. The velocity of area to to be. And this is the direction. And then this is the time taken for them to be 1500 ft putt. Okay, And that's all.

Okay. So in this problem the givens R. Equals 23 and 95 B equals 891. C. Equals 3 17 1. So if we do so if we do the formula so 10 10/2 and then 12/2 minus 4/2 is 56 negative too. So that means that the midpoint of A B. Maybe it's gonna eat well. 5 6 and negative two. So to determine uh the media from C. That means what we're going to have to do is copy at the midpoint of A. B. So what we're gonna do is C. D. Is equal to sparrow of 5 -3 sq Prophesies Homeless Green Square Close 6 -17 Squared. Mhm. Was -2 -1 Squared. Okay. So now what we can do to simplify that to Squared plus negative 11 square Plus -3 scored? Okay, so that's gonna be route 134 and that's going to equal 11.6. And that's your answer.

Okay. The given information is in. This problem is that the yacht is traveling at 20 knots, which means 20 nautical MPH. We know the trip it makes is 428 nautical miles. And we know the bearing is south 1.4 degrees east, and in part, they were finding how long it takes the yacht to make the trip. So we know the trip is 428 nautical miles and we're going to multiply that by one hour, her 20 nautical miles based on our rate of 20 knots. So, essentially, we're dividing our distance by 20 and that gives us 21.4 hours. If you want to put that in hours and minutes, that would be 21 hours and 24 minutes for this trip. Okay, let's move on to part B. Go ahead and circle that answer. Okay. In part B, we're going to figure out how far East and South the yacht is after 12 hours. So if it's travelling for 12 hours at 20 nautical MPH, then it goes into a total of 250 nautical miles. Excuse me, 240 nautical miles. Okay, so let's draw a picture of the situation. So let's draw our little compass. And then we know we need a 1.4 degree angle. So obviously not to scale, but we'll just make it kind of like that. So this angle here is 1.4 degrees east of south, and the distance traveled is 240. And so we're figuring out how far south and east this point down here is from the original point. So let's complete a right triangle, and we can label the horizontal distance X and the vertical distance wide and we're solving for X and Y. So we know that if this angle here is 1.4 degrees, then so is this angle. Here we have alternate interior angles with parallel lines cut by a transfer sel so we can set up some equations, such as the sign of 1.4 degrees is equal to opposite overhead pot News X over to 40 and then we can go ahead and multiply both sides of that equation by 2 40 So X equals 240 times a sign of 1.4 degrees, and then we'll use a calculator to approximate that we get about 5.86 nautical miles. So that tells us how far East the yacht is of its starting point. And then we'll do something similar to find why. So we'll do the coast sign of 1.4 degrees, and that's going to be why over to 40. So why is equal to 240 times co sign of 1.4 degrees? And we'll use a calculator to approximate that, and we get about 239.93 nautical miles. And that's how far South the yacht is of its starting point. Okay, finally, for part C, we're going to go ahead and find the bearing if it was a plane traveling this route instead of a yacht, so we'll find a bearing of a plane and remember for a plane we started north and we go clockwise to get the bearing. So let's draw this again. We have our north south east west, and we have our traveling line with a 1.4 degree angle down there. And so for the planes bearing, we want this entire angle here. So that's almost a straight line is just 1.4 degrees shy of a straight line, so 180 degrees, minus 1.4 degrees is 178.6 degrees, and that would be the bearing of the plane.


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