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A rental car company charges $50 day and 20 cents mile for its cars_(a) Write formula for the cost, €, in dollars renting Car aS function f,ol the number of m...

Question

A rental car company charges $50 day and 20 cents mile for its cars_(a) Write formula for the cost, €, in dollars renting Car aS function f,ol the number of miles driven; and the number of days; If € = f(mn,d) , find f(500,2) , and give complete sentence interpretation of your answer in the context of this problem.For Problem 2, consider metal bar that is meters long: Specifically; H = f(T,t) - sce" gives the temperature of the DAl, degrees Celsius point that is meters from the lelt end

A rental car company charges $50 day and 20 cents mile for its cars_ (a) Write formula for the cost, €, in dollars renting Car aS function f,ol the number of miles driven; and the number of days; If € = f(mn,d) , find f(500,2) , and give complete sentence interpretation of your answer in the context of this problem. For Problem 2, consider metal bar that is meters long: Specifically; H = f(T,t) - sce" gives the temperature of the DAl, degrees Celsius point that is meters from the lelt end of the bar after minutes of time have elapsed. Find f(2,1). Include units; and give complete sentence interpretation of your AMSWCI bar. terms of the metal For Farts (a) match the graph with one o the contour diagrains (I)-(III) . For credit, give explanations for your answers: Yol may assume the difference in z-valules between adjacent contours is constant in each diagram.



Answers

A rental company charges $\$ 40.00$ a day plus $\$ 0.35$ per mile to rent a moving truck. The total cost, $y,$ for a day's rental if $x$ miles are driven is described by $y=0.35 x+40 . A$ second company charges $\$ 36.00$ a day plus $\$ 0.45$ per mile, so the daily cost, $y,$ if $x$ miles are driven is described by $y=0.45 x+36 .$ The graphs of the two equations are shown in the same rectangular coordinate system. (GRAPH NOT COPY) a. What is the $x$ -coordinate of the intersection point of the graphs? Describe what this $x$ -coordinate means in practical terms. b. What is a reasonable cstimate for the $y$ -coordinate of the intersection point? c. Substitute the $x$ -coordinate of the intersection point into each of the equations and find the corresponding value for $y .$ Describe what this value represents in practical terms. How close is this value to your estimate from part (b)?

So we have the function in two variables. C equals 40 d plus 400.15 m, and what this function is representing is the cost C of renting a car for D days and traveling and Miles. Um So, for example, if we have the, um Value or the argument f of three comma 200 we could just input three and 200 as the values off D and M's, this becomes 40 times three plus 0.15 times 200 40 times three is 1 20 plus 0.15 times 200 is just 30 which equals $150. So what this is saying is if you rent a car for three days and you drive 200 miles, then it will cost you $150 More generally, if we have the function f of three com a. M, we can do the same thing. We can substitute three and for D, and we just have 15.15 m. This is the same thing as 1 20 plus 0.15 m equals cost. If we see this equation, here is just a linear function in one variable where 120 is the why intercept 1200.15 is a slope. M is the independent variable and C is the dependent variable. So if we make a coordinate plain, um, where we have, um, the X and Y axes or the M and C axes, then we can grab this linear function. So we'll call this, um m and the sea. So if m increases by 100 that's our scale on the M axis and on the sea access, um, it increases by 25 hums. That's 5100 1 50 So if we graph this, um, why intercept is 120? So that's around, um, here and the slope this 0.15 which means that if you increase em, if you increase the number of miles by one, the cost will increase by 15 cents, or because our scale of the M axis is 100. If you increase in by 100 the cost increases by 15. So if this is 1 20 if m is 100 than that becomes 1 35 um, just a little bit higher and is 200 then that becomes 1 50 Um, if M is 300 than that becomes, um, 1 65 And you keep going until you have this linear function, which is just 1 20 plus 0.15 a M equals C. And what this is just representing is the cost of renting the car. Um, if you know that your only renting it for three days similarly, you can have a function of, um, de instead of em where m is 100. So in that case, you have 40 d plus 0.15 times 100 is just 15. So if we graph that function, um, then you have, um Then you have, um, a another linear equation Where in this case, um, the independent variable is days and the dependent variable is still cost. Um, so we know we can say that days are increasing by scale of one. And, um, will say this is increasing by 20 dollars. So we know the Y intercept is 15. Um, so that is around rate here. And for every, um, day, we add, because of slope is 40 for every one day, the cost increases by 40 dollars. So when d is equal toe one, we have 40 plus 15 was gonna be 55. So it's around up here when d is too. We have 80 plus 15. Um, so we have to add another 40 to 55. That becomes 95. Um, around up there, when we have d equals three, we have to add another 40 to 95 that becomes 1 35 sets around up there and we get, um, a rough sketch of the line 40 D plus 15 equals C. And just like the last graph, this is just a linear equation where if we hold the miles constant as 100 miles and you increase the number of days by one on the cost increases by 40 because that is a slope.

So no. In this question, the question which we have to fall will be. Why is equal to 1 20 eggs plus 65. So So 1 20 is basically dollar 1 20 is for for day on 65 is additional for insurance. So now we will see the blood. So now, according to this plot, odd line will come from Tzeitel. This where the equation for this life is Why is equals to 1 20 x bless 65. No, it is asking what is if the why intercept in meaning So part ceases, it will be zero almost 65. There on the explanation is the base cost. Do the rent. Oh, the God is donor 65 and now another next part? No. For two days, the rent will be. Why is equals to 1 20 excess for days plus 65. So therefore, why is equals to dollar 305. Similarly we will find for five days. So for five days it will be. Why is equals to 1 20 into five multiplied with five plus 65. Therefore, why would be dollars 6 65 and for seven days Why is equals to 1 20 multiplied with seven plus 65. So therefore are why is equals to dollar 905. So now we will compare the we clear it. So if we can create with the equation which is why I use because toe 1 20 well replied with seven which is equals and plus 65 which is because too wise equals $2. 905. And it was given that weekly Do you is dollar 7 99 So therefore our weekly rate is less This is less so No, If there is a six person judge so what will be the total cost? So first we will calculate Why is it closed for four days? So why is it goes to 1 20 multiplied with four? It is because 65 plus 65 So why is equals to 5 45 And this will be a plus 6% charge on this So we have to calculate, define and value off Why so therefore why is equal to 5 45 plus 6% off 5 45 32.7 So therefore which is request toe dolar 5 77 0.70 No, uh, last but with cities. So the statement would be no in the car in every way can not being get Do so. Therefore X cannot be negative, so x can not will be. Thank you.

Okay. So for this question we have to form some decorations in two variable and then we have to solve them by any algebraic method. So we can use any method that is substitution method or elimination method for solving these two equations. So our first, the first part is a part of monthly hostal charges is fixed and remaining depends on the number of days. Okay so let's say the fixed charges our X. And let's say the mess fees party. The mess fees per day is why. Okay. It says that When a student it takes for the food for 20 days, Okay. She has to pay the fixed charges Plus the mass charges for 20 days and she pays $1,000. This is our first equation And in the second equation we are given that she stayed stays for 26 days. So the fixed charges would be X. And Masterpiece will be for 2060s and it is given to be 11 80 This is our equation too. We can see by equation that we can simply are solid by elimination method that is subtracting these two equations. So just simply subtracting the two equations, we get six way Equals to 1 18. That is why is equals to 30. So mass charges are ₹30 party. Similarly we can find X which comes out to be 400. So fixed charges are ₹400. Okay, Moving on to the 2nd part, Moving on to the 2nd part, It talks about a fraction. So let's say the fraction is X upon Y. The fraction is except one why the numerator is X. and the denominator is by. So the condition we are given is when we subtract one from the numerator, The fraction becomes one x 3. Okay, solving this, we get three and 2 x -1 is equal to buy. That is three, X -Y is equal to three. This is our equation. Fun four k's too. We are given that when we add 8 to the denominator The fraction becomes one x 4. That is three X -Y. A Saudi four x minus Y equals to eat. Okay so we can simply see that subtracting those these two equations we can eliminate by. So we we will just subtract these two equations. Three x minus Y equals 23 and four X minus y equals to eight. Subtracting these two equations we get the value of X to be five And the value of Y. two B 12. So the fraction would be five upon 20. Okay So moving on to the 3rd part, it talks about some questions. The total number of questions. Okay so the total number of questions will be would be incorrect questions Plus the correct questions. Okay so let's say the correct questions are X. And the incorrect questions. Ry Okay. We will so make the equations on the basis of that given marks. Okay So it says uh for the right answer, he gets three months, okay? So three months for the right answer and -1 for the Wrong answer and he gets 40 score. Okay? So this is our equation first For second equation, we are given that if four marks would have been given for the correct answer and two marks would have been deducted for the incorrect ones that he would have got 50 marks. Okay, we can see that we cannot easily eliminate Y or X along these two equations because the coefficient are completely different. Okay, So what we will do is we even just multiply equation first by two, so that the coefficient of y becomes sane. Okay, so the first equation becomes six, X minus two way equals to 80. Okay, And the second equation is same, that is four X minus two by equals to 50. Now we can easily subtracted, We will get to works equals through party, that is x equals to 15, So the correct answers will fulfill and the incorrect ones were five. So the total questions are expressed why that is 20. Okay, so Let's just move on the 4th part. For the 4th part we are given places a and be. And there is 100 m distance between these two. Okay, Two cars Start from one, start from a. And the second car starts from B. Okay, When they move in the same direction, the car meet after five hours. Okay? And when the two cars moving oppose the direction, then the car meeting one of it. Okay, so we will use that concept of relative velocity here. When the car moves in opposing direction, let's say the velocity of first car is X, and the velocity of second car is Y. We have to find the spirits of these two cars that is X and Y. So when these are moving in the same direction, the relative velocity got subtracted. So the related velocity got subtracted, and the time taken velocity into time taken gives the distance the distance is 100. Similarly for the second equation, the relative velocity will add up. Okay to find the relative velocity we will add up though Velocities of these two cards into one which is time and is equals 200, which is distance between these two. Okay, now these are these are equations run an equation to. Okay, so just solving them them up, solving these two equations, we get x minus Y equals to 20 and X plus Y equals 200. These two are very simple equations. We can eliminate X. Or Y. Or we can also use substitution method. We are just uh adding these two equations, Why would be eliminated and two X would become 120. So the value of X. That the spirit of car a. Will be 16 and the spirit of car be would come out to be what people for the last part. Last part is about finding the length and breadth of rectangle. Okay we know that area of a rectangle is length and to breath. Okay? Alice length and B is breath. Okay here we are given condition that the area that is length into bread is Subtracted by nine. That is it is decreased by nine square units. When Length is decreased by five units and when breath is increased by three units. Okay so solving these equations we get L. B -5 B Plus three L -15. That is three L minus five B equals 26 This is our equation one. Okay, similarly for the for the second equation we are given that Al is increased by three and B is increased by to the area is increased by 67. Solving these two equations, we get six. L. A plus nine B Equals to 1 83. Okay, you can clearly see that it's not easy to eliminate X or Y from these two equations. What we have to do is we have to bring six here to eliminate L. Okay so we will just multiply this equation one by two. Okay, She want applying first equation by two we get six L -10 B Equals Truck. Well and the equation one Equation towards six and That's nine B equals two. When I think treat now we can subtract these two equations. Now subtracting those two equations, we get 19 B equals to 1 77. That is B comes out to be nice. Okay, so the bread come out out to be nine And similarly solving the length would come out to be 70. Thank you.


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