Question: Suppose we are planning to make a taco from a round tortilla with diameter 8 inches by bending the tortilla so that it is shaped

Suppose we are planning to make a taco from a round tortilla with diameter 8 inches by bending the tortilla so that it is shaped as if it is partially wrapped around a circular cylinder. We will fill the tortilla to the edge (but no more) with meat, cheese, and other ingredients. Our problem is to decide how to curve the tortilla in order to maximize the volume of food it can hold.
(a) We start by placing a circular cylinder of radius along a diameter of the tortilla and folding the tortilla around the cylinder. Let represent the distance from the center of the tortilla to a point P on the diameter (see the figure). Show that the cross-sectional area of the filled taco in the plane through P perpendicular to the axis of the cylinder is and write an expression for the volume of the filled taco.
(b) Determine (approximately) the value of that maximizes the volume of the taco. (Use a graphical approach with your CAS.)

16 - x? A(x) = r/16 - x? -r sin P.

Step by Step Solution

★★★★★

3.32 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Place the round flat tortilla on an zycoordinate system as shown in the first figure An equation o... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

M-C-I (227).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

A shaft is to be designed so that it is supported by roller bearings. The basic geometry is shown in the figure. The allowable slope at the bearings is 0.001 mm/mm without bearing life penalty. For a...

A 200-mm-focal-length lens can be adjusted so that it is 200.0 mm to 206.0 mm from the film. For what range of object distances can it be adjusted?

A balloon is weighted so that it is barely able to float in water. If it is pushed beneath the surface, will it return to the surface, stay at the depth to which it is pushed, or sink? Explain.

plz solve step by step. TIME VALUE OF MONEY 1. What is the future value of $2,000 invested today if it earns 10% interest for one year? 2. What is the future value of $2,000 invested today if it...

dear expert hope u will be fine.. due to chorona virus every person facing some issues. i requested to please solve this all questions.. i know the chagg policy only ask one question bt dear expert i...

Please find right answers: 1. Which of the following research Design approaches is best described as a research design that involves participants in the research process with the aim of solving an...

Is an education at SIU worthwhile? The purpose of this exercise is to practice using present value. Suppose you are again seniors in high school, but that you know then what you know now about your...

Given that P1A B2 = .4 and P1A B2 = .8, find P1B2. 3.100 From a production batch with 16 items, 8 items are randomly selected for quality assurance. In how many different ways can the sample be...

Suppose a firms planning audit guidelines specify the following risk level ranges for AR, RMM and DR.The firms risk ranges, for any materiality amount, are: VERY LOW5% LOW MODERATE10% to 30% HIGH...

Suppose a firms planning audit guidelines specify the following risk level ranges for AR, RMM and DR. The firms risk ranges, for any materiality amount, are: VERY LOW 1% to 5% LOW 5% to 10% MODERATE...

Q#1. Find out the following Derivatives w.r. to x. (i)F(x) = (x+ 2)2(iii) F(x) = tan2(x2) (ii)F(x) = _(x+ 1)2(iv)F(x) = x2 cos2(2x) \ Q#2. a)Define Integration and its Rules. b) Find out the...

Consider again the relationship between the population and ozone level of U.S. cities that you analyzed in Exercise 47. In Exercise 47 a) Give a 90% confidence interval for the approximate increase...

1 4 years ago, a high - tech printer cost $ 1 , 2 0 0 when the index at that time was 1 0 8 . If the current index is 1 3 1 , which cost is closest to the estimated current cost of the printer? None...

Dehydration of natural gas is necessary to prevent the formation of gas hydrates, which can plug valves and other components of a gas pipeline, and also to reduce potential corrosion problems. Water...

Which solutions of the following equations will exhibit convergent behavior? Which are oscillatory? All of the above differential equations have one common factor in their characteristic equations....

A 120-kg mail bag hangs by a vertical rope 3.5 m long. A postal worker then displaces the bag to a position 2.0 m sideways from its original position, always keeping the rope taut. (a) What...

Home stake Mining Company is a 120-year-old international gold mining company with substantial gold mining operations and exploration in the United States, Canada, and Australia. At year-end, Home...

Each of the following formulas for determining shareholders? required rate of return can be right or wrong depending on the circumstances: For each formula construct a simple numerical example...

For each of the following purchases, say whether you would expect the degree of imperfect information to be relatively high or relatively low: a. Buying apples at a roadside stand b. Buying dinner at...

The relationship between the Celsius and Fahrenheit temperature scales is given by C = 5/9 (F - 32), where C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit. What...

As dry air moves upward, it expands and in so doing cools at a rate of about 1C for each 100-m rise, up to about 12 km. (a) If the ground temperature is 20C, write a formula for the temperature at...

If a ball is thrown upward from the top of a building 128 ft high with an initial velocity of 16 ft/s, then the height h above the ground t seconds later will be h = 128 + 16t - 16t 2 During what...

If Barbara Guarin is single and in the 25% tax bracket, calculate the tax associated with each of the following transactions. (Use the IRS regulations for capital gains in effect in 2008.) EXHIBIT...

You buy 50 shares of ABC stock at $30/share; stock currently pays $3/share in annual dividends. Price of the stock increases at 20%/year and dividends grow at 10%/year. If you participate in DRIP,...

Assume an economy in which there are three securities: Stock A with rA = 10% and A = 10%; Stock B with rB = 15% and B = 20%; and a riskless asset with rRF = 7%. Stocks A and B are perfectly negativly...