2. A diner is open from 6 a.m. to 6 p.m. and the average number of customers in the diner at any timecan be modelled by the function C(h) = -30 cos (π/6) h+34, where h is the number of hoursafter the 6 a.m. opening time. The average amount of money, in dollars, that each customer in thediner will spend can be modelled by the function D(h) = −3 sin(π/6)h +7.a) Write the function that represents the diner's average revenue from the customers.b) What is the average revenue from the customers in the diner at 2 p.m.?

Answered: Image /qna-images/answer/bd931e6d-35ed-4308-b2d5-fed9f291aa37.jpg

Answered: 2. A diner is open from 6 a.m. to 6…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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18. What 3-digit number has the number 5 as its digit in the tens place and the digit in the hundreds place twice as big as the digit in the ones place?
During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)
The biologist has a second culture to examine. She knows that the population of the culture doubles every 15 minutes. After 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. 2. (a) What was the size of the initial population? Predict the size of the culture at t=3 hours. What was the size of the population at 40 minutes? Explain and justify your answers. (b) Create a graph of the population as a function of time. Find an equation that can be used to predict the size of the population at any time t. (c) Examine the rate at which the bacteria culture is growing. How fast growing after 1 hour? After 1.5 hours? After 2 hours? Use a time interval of h = 0.01 hours to estimate these rates. Interpret these rates in terms of the context of the problem situation. How do these three rates compare? (d) the culture
The function f(s) = 400 + 0.0066667s2 – 0.0000001s4 approximates the length of the cable between the two vertical towers of a suspension bridge, where s is the sag in the cable. Estimate the length of the cable of the bridge in the next column if the sag is 28.3 feet. (Round your answer to the nearest foot.) ft 400 ft
Suppose s(t) is the total number of miles of railroad in the US built by the end of year t. Give an expression for cach of the following, using the function 8. (You don't need to find a formula.) (a) The number of miles of railroad built by the end of 1885. (b) The number of miles of railroad built during 1884. (c) The average number of miles of railroad built per year during the 1890s.
A clock is hung on a wall so that the center is 20 cm below the ceiling. The minute hand is 10 cm long, and the hour hand is 6 cm long. Find a function m(t)that gives the distance the tip of the minute hand is from the ceiling as a function of minutes past midnight. The function should have the form m(t)=A(Bt-C)+D.
Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $7900 per month. Materials and labor for each helmet of this model are $55, and the company sells this helmet to dealers for $85 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.) (a) For this helmet, write the function for monthly total costs C(x). C(x) = (b) Write the function for total revenue R(x). R(x) = (c) Write the function for profit P(x). P(x) = (d) Find C(200). C(200) = Interpret C(200). O When this many helmets are produced the cost is $200. O This is the cost (in dollars) of producing 200 helmets. O For every additional helmet produced the cost increases by this much. O For each $1 increase in cost this many more helmets can be produced. Find R(200). R(200) =

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