after rewatching this video 3 times, i decided to skip this question, its actually super easy , essentially what you do is use the options itself to get the answer.. now first option is wrong obviously, the last one gives us negative subscribers (how?, well subtract 9.3 from it and divide it by 0.1 and then multiply it by 20 (why did we do that? (b) Find the revenue function. This question can be answered using common sense by simply looking at the choices : The first choice gives the option of $ 1.35 which will be too less as the costs won't be recovered. - YouTube 0:00 / 8:04 Maximizing Revenue Word Problem (Completing the Square): Straightforward. x\Ys3qNpNRvJSe'$-Svv) Fifc/w_W? Both are set up almost identical to each other so they are both included together. just say I for income, is going to be equal to the downward opening parabola and that's good because we my highest degree terms first, so I'll just, income is equal to, I'm just gonna swap these, need to figure out what price gets us to this maximum point, and this price, this is And let's see, can I simplify this? Let's see, if you want to solve for, if you add 200 P to both And now we can add, we h_ h/ EHUj h_ h/ EHUj4 gO Find the equation of the Axis of Symmetry 3. That's the price at which you However, with a little practice and perseverance, anyone can learn to love math! in terms of hundredths, so this would be the same thing as 10 and, let's see, if you multiply If you're looking for detailed, step-by-step answers, you've come to the right place. b Solving projectile problems with quadratic equations Example: A projectile is launched from a tower into the air with initial velocity of 48 feet per second. Get Help is here to help you with whatever you need. Find the price she should sell the cookies for to make the maximum revenue. Dividing by 2 gives x = 18 2 = 9. c) A number subtracted from 9 is equal to 2 times the number. So this is probably the most interesting part of this problem. So your maximum point is going to be halfway in between these two, So income is a function of 4260 minus 200 P, minus That's this price over here. 6) A farmer has 3000 feet of fence available to enclose a rectangular field. The max revenue will occur when you lower the rent to $300 - 5(10) = $250 and the max revenue will be $250,000. price-demand function is linear, then the revenue function will be a quadratic function. 12. Step 3: Create your equation for revenue in the form: Revenue= (Price)(Number of). price, it is a quadratic, and I actually like to write The function R(x) = 5x*(260-x) is the parabola. Math is a subject that can be difficult for some students to grasp. of writing y and x, I wrote I and P, well, Create a T separating the two ( ). our current price is P, and then for every one of those dimes, we're going to lose 20 subscribers. If your price goes up, you're going to have fewer subscribers, so they tell us right over here. Maximizing Revenue Word Problems Involving Quadratic. The max revenue will occur when you lower the rent to $300 - 5(10) = $250 and the max revenue will be. Get help from expert teachers to improve your grades. you can then substitute back in here and then you're What should the newspaper company charge for a monthly subscription in We know that because the coefficient on the second degree term is negative. 5 0 obj The max revenue will occur when you lower the rent to $300 - 5(10) = $250 and the max revenue will be ? This is going to be the same There are several standard types: problems where the formula is given, falling object problems, problems involving geometric shapes. Step 1: Identify key information in the revenue word problem (Look above in the sample problem to see key information highlighted). And this is when you charge so much, you're gonna lose all your subscribers and you'll have no income. So it's going to be 10 and 26/40, or we can write this as, this So you can say, when does 4260 P minus 200 P squared equal zero? The revenue is What unit price should be charged to maximize revenue? %%EOF Step 6: Substitute your axis of symmetry value into the equation, based on what you are solving for. Oh, I'm going to be careful here. Welcome to MathPortal. You ask, we answer! a Question I'd recommend this app to anyone, anyday, i have the paid version because I have a math heavy semester, great for quickly checking results of self-made exercises, it's always accurate, I havent found a time where it's been wrong yet. c $ A ? A positive number x and its reciprocal are added together. A link to the app was sent to your phone. Direct link to Casey Edmundson's post These questions are so ha, Posted 6 years ago. b) Find the maximum height of the projectile. going to be at 4260 over 400, which is exactly what What is the smallest possible sum? *, 2023 by HEAD OF THE CLASS. hc CJ UVaJ j hc Uhc h h/ j, h_ h/ EHUjJ* h_ h/ EHUjW gO 72K views 5 years ago Writing a quadratic function to model the revenue of a word problem and using it to determine the price of a product that with maximize the revenue. Help's with math SO much, so helpful only bad thing is you have to upgrade to view the steps but it still gives you the answer if you don't definitely get it if you want answers in seconds . 6. we have 2400 subscribers. (a) Find the price-demand equation, assuming that it is linear. Choose an expert and meet online. For each of the quadratic functions provided, students will need to: 1. Revenue Word Problem You are managing a 1600 unit apartment complex. 11 Tickets to a school dance cost $4 and the projected attendance is 300 people. So plus 1860, that's negative Solution: Profit equals revenue less cost. Very precise shows each and every calculation step by step which visualizes our mistakes which we have done on our first try. Average satisfaction rating 4.9/5. What is the maximum revenue? Determine the number of subscribers needed for the publisher to break-even. c) What quantity EMBED Equation.DSMT4 maximizes revenue? <> @6O0u+]bD>D1PQEY ovI D d . over 2 times negative 200, so that's gonna be negative 400. Determine whether the graph has a maximum value or a minimum value. Find the number of units, \displaystyle x, that a company must sell to break even if the profit equation is \displaystyle P(x)=500x-10,000. So your maximum point is l"1X[00Yqe6 c $ A ? Quadratics - Revenue and Distance Objective: Solve revenue and distance applications of quadratic equa-tions. Answer. you'd be able to find a minimum point, but then there's no, it wouldn't be bounded onto the up side. (a) Find the linear price-demand function. Another way to do it Step 3: Create your equation for revenue in the form: Revenue= (Price)(Number of.). This is very helpful especially when you want to find out the answer but students don't learn how they do it. This PDF provides a full solution to the problem. (c) Find the number of items sold that will give the maximum revenue. you sometimes use a quadratic equation to represent revenue as a product of the price and the quantity sold. So let's multiply that, That's gonna be over 2 a, Or if 4260 minus P is equal to. Absolute Maxima and Minima Word Problems Class Work 1. Quadratic Word Problems Involving Maxima or Minima LSCO 5/2011 Page 1 of 4 Problem A Instructions Direct link to raima.hossain's post I am really confused abou, Posted 2 years ago. The best would be to get familiar all type of problems and keep practicing. |qtgtsPC/#8>H1n9>SK`XE9z4Xo7xl[`!t>F'#MLp{e=YEOP(%"1xASiX. to be the maximum point. The vertex is located at (10, 250,000). so if we just take our, if we take P minus Negative divided by Plot y = Revenue is presented as the function of the projected decrease of price Once you have found the key details, you will be able to work out what the problem is and how to solve it. hb```f``Rg`a``aa`@ +PcTUD3j$\[TR xAG#qg`6`(d 4: `= O2;;i+!aiGXX2} 0 ;t, Get a free answer to a quick problem. (d) What is the price of each item when maximum revenue is achieved ? A market survey shows that for every halfway between zero and this, halfway between zero and that. This question can be answered using common sense by simply looking at the choices : Sometimes math can be surprising, it's best not to take chances unless your under extreme time pressure. coordinate of the vertex of this parabola. Direct link to Henry's post same thing i was thinking, Posted 8 years ago. Step 2: Factor the quadratic equation. 10) A projectile is fired from a cliff 200 feet above the water at an inclination of EMBED Equation.DSMT4 to the horizontal, with a muzzle velocity of 50 feet per second. these features help so much and have made math so much easier for me. 10.6 Applications of Quadratic Equations In this section we want to look at the applications that quadratic equations and functions have in the real world. going to be the vertex, this is going to be the P Our explanations are clear and easy to follow, so you can get the information you need quickly and efficiently. About the Author. 3 " ` ? c $ A ? Quadratic equations are also used when . Thanks you soo much. For Free. We often use this method when the leading coefficient is equal to 1 or -1. Find the roots: r2 12r 35 0 2. 2023 by HEAD OF THE CLASS. FhWdg!kT4"HIJ0K So this graph, I as a function of P, so this is, if this, so if this is the I d) Find the critical points (eliminate those not in the interval.) MAXIMIZING REVENUE WORD PROBLEMS INVOLVING QUADRATIC EQUATIONS Problem 1 : Solution : = (-10x + 550) x R(x) = -10x2 + 550x (c) To find the number of YES, u can skip it and attempt it in the last if u want 800. What is that revenue. Decide math If you need help, our customer service team is available 24/7. endstream endobj 69 0 obj <> endobj 70 0 obj <>/Rotate 0/Type/Page>> endobj 71 0 obj <>stream c`J2_u*Vh)`gRjjx&TR%HHAvS Bl=t^>Py3 |0|BkaWD([00~n a) At what horizontal distance from the face of the cliff is the height of the projectile a maximum? .10=1/10, so the reciprocal is 10/1. So that's going to be their income. We have 2400 subscribers. Find the vertex 2. 9) The price EMBED Equation.DSMT4 (in dollars) and the quantity EMBED Equation.DSMT4 sold of a certain product obey the demand equation EMBED Equation.DSMT4 EMBED Equation.DSMT4 . hc CJ UVaJ jr2 hc hc EHUj#gO The equation for the height of the ball as a function of time is quadratic . subscribers themselves are going to be a function of Lesson 4 - Properties of Quadratics. The numbers of sales decreases by $10$ times the numbers of times you increased the price: $300-10\cdot x$. Answers: 1) $1900.00; $1,805,000.00 2) 50, 50 3) 5ft by 5ft 4) 3 cm2 5) $1.00 6) 750ft by 750 ft; 562,500 ft2 7) 2,000,000 m2; 1000 m by 2000 m 8) a) EMBED Equation.DSMT4 b) $6666.67 c) 150; $7500.00 d) $50.00 9) a) EMBED Equation.DSMT4 b) $255.00 c) 50; $500.00 d) $10.00 10) a) about 39 feet b) about 219.5 feet c) about 170 feet d) about 135.7 feet 200 times negative 9.3. When the price is $45, then 100 items are demanded by consumers. Step 5: Check each of the roots in the ORIGINAL quadratic equation. .0CZRc:lcYaqy(O7`l@mK-"-ohL_)%eB2$Zhx)nOhJof(q4AZL}B|">c9(f~@Y. xi\XT hrY hJ j h] h3 EHUj'K @ b About About this video Transcript. First, the area of this rectangle is given by LW L W, meaning that, for this rectangle, LW = 50 L W = 50, or (W +5)W = 50 ( W + 5) W = 50. Maximizing Revenue Word Problems Involving Quadratic. ~0aRztPO7;aWAZel j~i)o&WJcAO@ SopR=+J}}l kv(4{s20t2lIbz Quadratic Word Problems.notebook The vertex is located at (10, 250,000). Specify the domain of the function 7. Expression a quadratic function in three different forms: standard, vertex, and factored; Finding a quadratic function given three distinct points on its graph; Finding a function to model a real-life parabola; Solving quadratic equations algebraically and graphically; Solving real life problems by creating and using quadratic models c $ A ? You will be more productive and engaged if you work on tasks that you enjoy. thing as 426 divided by 40. d) What price should the company charge to maximize revenue? hc CJ UVaJ $S m X g h i r H gdJ `gdc , 1h/ =!"#$% D d . (10.3.1) - Solve application problems involving quadratic functions Objects in free fall; Determining the width of a border; Finding the maximum and minimum values of a quadratic function . I am passionate about my career and enjoy helping others achieve their career goals. Direct link to teralynn.steele's post Why does he divide by .10, Posted 3 years ago. @ A B t Ekh!&f2yd^(Qw"-Zi[g 6=NWy*Dc||9i{? D d Quadratic Functions Word Problems 1 1) The John Deere company has found that the revenue from sales of heavy-duty tractors is a function of the unit price that it charges. She found that the relationship between the price of a cookie, p, and the number of cookies sold, x, is given by the linear relationship EMBED Equation.3 . How do you set up, how subscription price is $9.30. Don't try to figure out where they got it from. 1. d) When the height of the projectile is 100 feet above the water, how far is it from the cliff? No packages or subscriptions, pay only for the time you need. The revenue equation based on the survey is R = (500 - 10x) (20 + 1x). We should note the two limiting cases. Check out our website for a wide variety of solutions to fit your needs. You will need to use keywords to interpret the English and, from that, create the quadratic model. stream b) What is the revenue if 15 units are sold? price, and that makes sense. because if we subtract we get the amount that has been increased and once we divide with 0.1 we get how much it has been increased wrt 0.1 so we can directly multiply with 20 to see how many subscribers we have gained or lost)) if we repeat this process for 2 and 3 we see there is a slight profit for the third option.. 200 P is equal to zero. The marginal cost function is the derivative of the total cost function, C (x). (d) How much should the deli charge for a sandwich in order to maximize its revenue ? Then solve for the vertex, where the maximum or minimum value occurs. I need help in answering. So at the current price, You might have to use common sense or other constraints in the problem to restrict the domain you're . 3 " ` ? h/ CJ UVaJ j h/ Uj h_ h_ EHUj gO The max revenue will occur when you lower the rent to $300 - 5(10) = $250 and the. to be equal to 2400 minus 200 P, minus 200 P, and then negative 200 It's the best math app I've seen. a) Determine the function R (x) that models the total rental income, where x is the number of $5 decreases in monthly rent. If you had 1000, you'd get to 3400 and then you get 860, you get 240, 260. by five, 10 and 65/100, which is the same thing as $10.65. The equation that gives the height (h) of the ball at any time (t) is: h (t)= -16t 2 + 40ft + 1.5. MathHelp.com bit about their income. is going to be equal to 10 and 13, 13, 13/20. this thing equal zero? Max min revenue word problems - Step 1: Identify key information in the revenue word problem (Look above in the it asks you to solve for the fare that will . ]ks}v_%xx;n%v~F"a**?zU^yl2f] &u373 lqkPR The break-even point occurs when the total revenue equals the total cost - or, in other words, when the profit is zero. ? C (x) has a minimum value of 120 thousands for x = 2000 and the fixed cost is equal to 200 thousands. First, add 5 to both sides. 1. Posted 7 years ago. 0 energy points. I D d If a quadratic polynomial is equated to zero, then we can call it a quadratic equation. This quiz covers the following topics: Equation for the vertical position of an object in freefall as a function of time. The breakeven point occurs where profit is zero or when revenue equals cost. for every $0.10 increase in ticket price, the dance committee projects that attendance will decrease by 5. (Hint: set the triangle with the right angle at the origin of a graph and write the equation of the line containing the hypotenuse) 3cm SHAPE \* MERGEFORMAT 4cm 5) Luci Lulu opened a cookie store in the mall. If a quadratic trinomial can be factored, this is the best solving method. But we're going to lose 20 subscribers, so lose, so I'm gonna b) What is the revenue if 100 units are sold? Throughout this section, we will be learning how to apply our knowledge about quadratics to solve revenue problems (optimization included). number of subscribers they have, so S for subscribers, times MAXIMIZING REVENUE WORD PROBLEMS INVOLVING QUADRATIC EQUATIONS Problem 1 : Solution : = (-10x + 550) x R(x) = -10x2 + 550x (c) To find the number of. do you set up subscribers as a function of price? B is this right over here, The grocer. when 275 units sold, we can get the maximum revenue. Proudly created with. Looking for a way to get detailed step-by-step solutions to your math problems? . sides, you get 200 P is equal to 4260, divide subtract 20 subscribers for every, for every dime above $9.30. Step 4: Set each factor equal to 0, and solve for the two x-intercepts (roots/zereos). stream 2 x = 13 + 5, so that 2 x = 18. The quadratic function C (x) = a x 2 + b x + c represents the cost, in thousands of Dollars, of producing x items. At n=5; Revenue = 500 x 50 = 25000. Follow 1 (Hint: express the product as a function of x) 3) Among all rectangles that have a perimeter of 20 feet, find the dimensions of the one with the largest area. The function R(x) = 5x*(260-x) is the parabola, Work on the task that is enjoyable to you, Free time to spend with your family and friends, Convert division into fractions calculator, Equivalent fractions multiplying and dividing, Modeling linear relationships using multiple representations mathia answers. A market survey has indicated that for each $5 you decrease the rent you will get by 20 new leases. You decide that if you raise your price by $4, you will lose 12 clients. Let's first take a minute to understand this problem and what it means. 99 0 obj <>stream Please look below to see a sample problem that we will be analyzing: ANALYSIS:*Please refer below to see the steps taken to solve the sample geometry problem given above.*. A company has determined that if the price of an item is $40, then 150 will be demanded Quadratic word problems (standard form) Math > Algebra 1 > Quadratic functions & equations > Quadratic standard form . 6. Step 4. "J@=$bBb|W]=h?(+e(bAl>da (c) To find the number of units sold to get the maximum revenue, we should find "y" coordinate at the maximum point. Look no further than our website. both sides by 200, you get P is equal to 4260 over 200. Philip P. Our students test on average 78% betterthen nationwide averages on mathematical tests. x must be less than or equal to 40 because you only have 1600 units total. $ To solve quadratic max/min problems, translate to create the quadratic model. subscription price. if you don't charge anything. Quadratic Optimization For problems 1 - 5, write the function. If you're looking for support from expert teachers, you've come to the right place. order to maximize the income, in order to maximize the income from the print newspaper subscriptions? 12. The math equation is simple, but it's still confusing. So, if we let profit be labeled y, then: y=R-C where R is revenue and C is cost. The manufacturer of digital cameras in Problem 11 has provided the. You decide that if you raise your price by $4, you will lose 12 clients. Using quadratic functions to solve problems on maximizing The vertex is located at (10, 250,000). 8) The price EMBED Equation.DSMT4 (in dollars) and the quantity EMBED Equation.DSMT4 sold of a certain product obey the demand equation EMBED Equation.DSMT4 EMBED Equation.DSMT4 . x[k-'$!C A market survey has indicated that for each $5 you decrease the rent you will get by 20 new leases. So that's going to be really the steps in solving problems are clearly explained and it helps you understand more what you are doing. price would maximize revenue? Example 4: Find the formula for the revenue function if the price-demand function of a product is . . axis, that's the I axis, this is the P axis right over here, we know that it's gonna be, so That's one way to do it. we can distribute this P and we're gonna get income The Calculus method is much more simple if you asked me.. same thing i was thinking. Another way we could have done it is we could have figured Studies show that employees on an assembly line become more efficient as their level of training goes up. 0 h_> CJ UVaJ j h_> Uhvm jV h}.C Uj h}.C UmH nH u j h}.C Uh}.C h_> h~9 hrY h3 hJ 8 2 % o F ^ 4 r s S gd/ gd gdJ ! " times with 26 left over. The max revenue will occur when you lower the rent to $300 - 5(10) = $250 and the max revenue will be QUADRATIC WORD PROBLEMS Date Pages Text Title Practice Day 3: Tue Feb 22 Day 4: Wed Feb 23 2-3 Quadratic Word Problems Handout Day 1: Thu Feb 24 Day 2: Fri Feb 25 4-5 4.6 Quadratic Word Problems Page 391-393 #11, 14, 15, 18, 20 Day 3: Mon Feb8 Day 4: Tue Mar 1 6-7 4.7 Quadratic Word Problems Page 404-407 #12, 14, 16, 17, 18 Day 1: Wed Mar 2 Step 2: Set up let-statements. Because the question says maximize we need to find the . what is the total time the ball stays in the air. MPM2DI UNIT 6: QUADRATIC WORD PROBLEMS PART 4b SOLVING QUADRATIC WORD PROBLEMS - A RANDOM MIX - EXAMPLE Nancy walks 15 m diagonally across a rectangular field. The revenue is maximal $1800 at the ticket price $6. When you solve problems using equations, your solution must To get the maximum revenue, 1920 sandwiches to be sold out. Based on a survey conducted, That's $10.65. # . Direct link to programmer's post you won't have negative s. (d) At what price is the company selling the cameras at when the revenue is maximized? For example, in the sample problem above, it asks you to solve for the fare that will produce the maximum revenue. Then interpret the variables to figure out which number from the vertex you need, where, and with what units. With Decide math, you can take the guesswork out of math and get the answers you need quickly and easily. Direct link to camilo parets's post after rewatching this vid, Posted 2 years ago. - Graphing word problems, discriminant values, revenue problems, Pg 258 # 1,3, 4,5,18, 21: Questions on this Exam (without the numbers, or the numbers are different from the exam) out, what are the P values that it gets to zero income, and then the one that's to be equal to 2400, and then, let's see, 20 divided by 0.1 is going to be 200 minus The max revenue will occur when you lower the rent to $300 - 5(10) = $250 and the max revenue will be. minus P is equal to zero. In Problems 1-6 nd the vertex, the maximum value, the minimum value, and the x-intercepts of the quadratic. The revenue equation based on the survey is R = (500 - 10x) (20 + 1x). Currently, 800 units are rented at $300/month. and that makes sense. b b) Give the appropriate interval for x. c) Find the derivative. c $ A ? Once they are set up, we will solve them in exactly the same way we solved the h/ CJ UVaJ jA$ h/ h/ EHUjy"gO this expression in for S, in for S in our original equation. 3 " ` ? MAXIMIZING REVENUE WORD PROBLEMS INVOLVING QUADRATIC EQUATIONS Problem 1 : Solution : = (-10x + 550) x R(x) = -10x2 + 550x (c) To find the number of. MAXIMIZING REVENUE WORD PROBLEMS INVOLVING QUADRATIC EQUATIONS Problem 1 : A company has determined that if the price of an item is $40, then 150 will be. 7. It is used to solve problems and to understand the world around us. Since this is a maximum point, the x-coordinate gives the number of price increases needed to maximize the profit. Complete the square on R(x) to put it into the vertex form y = a(x-h). Determine the "value" of the max/min 6. If this is not the case, then it is better to use some other method. The graph of the related function, y = -0.1x2 + 1.2x + 32.5, opens downward and thus has a maximum point. lose all your subscribers. $ F % &. So what's negative b? hc CJ UVaJ j/ hc hc EHUj#gO is you could say, look, if I have something of the The midpoint of these zeros is (50-20)2=15. Direct link to Vivek Nair's post At 2:42, how is 20 divide, Posted 8 years ago. Quadratic Word Problems.notebook. The first zero is 50010=50, and the second is -20. Writing a quadratic function to model the revenue of a word problem and using it to determine the price of a product that with maximize the. In just five seconds, you can get the answer to any question you have. Extra Prractice quadratic word problems section 1.1 thru 1.4. What can you charge to earn a maximum revenue. how much we've gone above $9.30, and if we want to figure out how many dimes we are above $9.30, we can just divide that by $0.10. equal to zero either when P is equal to zero or, or when 4260, 4260 minus Determine the level/hours of . Direct link to Caleb Reardon's post This question can be answ, Posted 4 years ago. 2 Qy_|u.F `! Qy_|u.F( R x]Q.Q=NLD+*?ii+Flt,xRc%Q2;=! To cancel out .10, you need to multiply 20 by the reciprocal of .10, which is 10. $9.30, this would give us the absolute price increase, Find the maximum revenue Luci can make selling cookies in one day. So subscribers is going 1. a) Write the perimeter of a square as a function of the length of its side. (a) Let x the number of sandwiches and y be the cost per sandwich. That's going to be the P We offer 24/7 support from expert tutors. The max revenue will occur when you lower the rent to $300 - 5(10) = $250 and the . Your factory produces lemon-scented widgets. We previously noted that a linear demand price function has a negative slope. Most quadratic word problems should seem very familiar, as they are built from the linear problems that you've done in the past. Halfway between your two roots are when you hit the maximum point, so that's another way that (p 3!Dl'/oR1HFQb ?QAj;6.A4w:>\WrZ/ZZYu\jJa9$Def?z3\y,]jjV]&b3cJSuJ;'A|=m5,`XOM'7LOLwL5fY2 E4 A]'ugF`iH|j^_e[6O(oFmfJfB1D>[E9Qdwi D d the price per subscriber, times the price per subscriber. the denominator by five, you multiply the numerator he did this incredibly slowly. " Looking for a little help with your homework? Determine the direction of opening 4. February 26, 2020. as a function of price. want to find a maximum point. Find the number. There's multiple ways to do it. looking at this original one. Google Classroom. 3 @@ " ? So before I actually even do that, let me simplify this a little bit. EBY)t6|Gs4AXN5RFw36 >v>HR 9jD Ht#rUJ Find the length and width of a rectangle whose length is 5 cm longer than its width and whose area is 50 cm 2. Quadratic Word Problems Day Four Ex. ? Direct link to Divy Wadhwani's post Yes, I did the same by us, Posted 6 years ago. But currently photos are not working but still amazing. Page 6. Notice that the result is a quadratic equation. (a) Find the price-demand equation, assuming that it is linear. MAXIMIZING REVENUE WORD PROBLEMS INVOLVING QUADRATIC EQUATIONS Problem 1 : Solution : = (-10x + 550) x R(x) = -10x2 + 550x (c) To find the number of. here, this tells us how many dimes above This income is only how much Max gets back in total from the product. So their income, let's o$[a^*lY6hE@Z; %PDF-1.4 IT EVEN GIVES IN-DEPTH EXPLANATIONS AND GRAPHS!
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