Find the actual cost of the 2001st bagel.(Use decimal notation. Give your answer to three decimal places )The actual cost of the 2O0lst bagel is $...

The dollar cost of producing $x$ bagels is given by the function $C(x)=300+0.25 x-0.5(x / 1000)^{3}$. Determine the cost of producing 2000 bagels and estimate the cost of the 2001 st bagel. Compare your estimate with the actual cost of the 2001 st bagel.

So six bagels and ate doughnuts cost a total of $4.10 and in additional three bagels. And the three dominance also cost a total of 58 So how much does each cost so we can create a system off simultaneous equations? So the first one is, if we have got to six barrels and we add $8 we get for 10 and also three each cost a total of 1. 80 means three bagels plus three donuts costing 1 80. So we solved this. Firstly, I would want to multiply this by two so that we can use elimination. So two by three. B is six b glass. So this is the question number one. This was the question number two. So we create a question number 36 b, uh, two times three D 60 equals to two thousands. 1.8 is $3.60. So this is the equation three. So the next step is to subject equation three from one. So let me write it. Close up, right. One close for them. So I'm subjecting. I'm subjecting three from one. So six B minus six, be it eliminates. And eight minus 62 D, which is equal to 4. 10 million. 3. 60. It's equal toe, uh, 50 cents. Then we divide by two both sides to find the cost off. One donor, so we do not is costing about 25 cents that. So what about a bangle? Could you excuse? So we can just take this 25 cents and substituted maybe into one. So live it's b class eight. They will substitute deal with 0.25 Oh, this is equals to 14 and six b is equal to 4.18 by 0.25 is to so put it to the other side becomes negative, too. So six b is equal to 2.1, then we divide by six. So be then, is 35 cents and it's done.

We're going to buy a six bagels and doughnuts for a cost of $8.60. And then we're going to buy three more bagels and three more donuts or cost of $3. 75 cents. So the first thing you want todo if you want to create a system of equations we wanted to find our variables, we're gonna let be, Well, bagels and D equal doughnuts. Now we're gonna write a system of equations. We have six bagels and ate doughnuts. So six B plus eight de before a total of $8.60. Then we have three bagels and three doughnuts, and we pay a total of $3.75 for those bagels and doughnuts. So now we have a system of equations that we can solve elimination that itself, using elimination. Gonna multiply this entire equation by negative too. When I do that, this equation becomes negative. Six B minus six. De he waas Negative seven. This we're gonna move our top equation over six b less Z equals 8 60 Then we're gonna solve this system by adding together are two equations. When we do that, our be variable will eliminate, and it will leave us with to De Exel's one. Next, we're gonna divide by two and we end up with do you? She goes zero point five, but so that means our doughnuts are going to cost 55 cents each. Once we figure out the cost of our doughnuts, you can choose an equation to plug in to get the cost of our Ebel's. So I'm gonna choose the bottom equation, which is three b waas three d equals 3 75 and I'm going to replace the letter D with 55 cents. So three B plus three times with 55 equals 3 75 To solve this, we're gonna multiply three times 55 cents. So we end up with three b waas one 65 equals three 75. We're gonna sit track 1 65 from both sides and we end up with three b equals to 10. We're gonna divide by free on me. On that B equals 0.7 zero. So that means our bagels are going to cost 70 cents each. So we will answer question. Oh, each bagel crusts 70 cents and each don't know, plus 55 cents

Were given go stuff. Six bodysuits is three different $50. So the rate here is There are $2.50 for six Marty sorts. We need to reduce it to a unit costs. So that is in dollars per unit. So we need to reduce the rate. So there the denominator is one body suit. You can write the date as a fraction $32.5 to 6 40 suits do anyway. Six. Now we rounded rounded numerator toe three Leishman places we good $5.417 by bodysuit is a ghost.

The goal here is to write in solving equation to answer the question. It says that we ate 3/8 of three of the eight pizza slices and you paid $3.30 as your share of the cost. How much did the whole pizza cost so again are unknown is how much the whole pizza costs. I'm gonna let X equal the cost of pizza. And since you ate three of the eight slices, that means that you ate three aides of the pizza. So 3/8 of means times the cost of the pizza in your share was $3.30. That would be my equation. To solve this, I would multiply by the reciprocal, which is eight thirds, and I would get a cost of the pizza about $8 and 80 cents. I could even check this by finding if the pizza is $8.80. How much would one slice cost so I could divide by eight? And that would mean it would be a dollar 10 for one slice, Which makes sense because when you ate three, you paid 3 30 so three times a dollar 10 would be 3. 30 My equation again. It's here 3/8 x equals 3 30 the total cost of the pizza is $8.80.