Rolle's Theorem Question

if f(a)=f(b) then it is constant function, so every point c in the interval (a,b) is zero.

I don't understand the terms constant function, is it supposed to be a horizontal line or it can be a parabola curve.

For example, when f(a)=f(b) and they both exist at the endpoint then it can be a parabola curve then it break the assumption that f(a)=f(b) then it is constant function, so every point c in the interval (a,b) is zero.

Please draw the picture to describe and explain

y'' + y' + y = Asin(ωt), y(0) = 0 , y'(0) = 0

License plates in a given state must consist of three letters followed by four digits.  The state's DMV has determined that there are eighteen three-letter words that cannot appear on license plates, and there are five four-digit numbers that cannot appear.   How many license plates are banned? Your answer may be given as an integer, or as a formula.  Either is acceptable.

1) Low-dose aspirin tablets contain 1¼ grains of aspirin in each tablet. How many tablets can be prepared from 1.1 avoirdupois pound of aspirin?

2) If a physician prescribed 3.600 grams of aspirin to be taken by a patient daily, about how many 5-grain tablets should the patient take each day?

3) A physician advises an adult patient to take a children's tablet (81 mg of aspirin per tablet) daily as a precaution against a heart attack. Instead, the patient decides to cut 5-gr aspirin tablets into dosage units. How many full doses (theoretically) could be obtained from each 5-gr tablet?

Question 3 options:

Use any method you like to determine a reduced QR factorization A = QR and a full QR factorization A= QR

Consider the ODE y''(x) = λy(x) for some real constant λ. Determine ALL values of λ for which there exists solutions satisfying the boundary conditions y(0) = y(10) = 0. For each such λ, give all possible solutions. Are they unique?

Determine whether the given relation is an equivalence relation on the set. Describe the partition arising from each equivalence relation. (c) (x1,y1)R(x2,y2) in R×R if x1∗y2 = x2∗y1.

(a) Add 13134 + 22134 by hand.

(b) Form the base-3 complement x of 12123 such that 12123 + x = 22223 = 100003-1: Then use it to compute 21113-12123.


please explain steps

The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown: Constraint Television Radio Online Audience per advertisement 110,000 18,000 30,000 Cost per advertisement $1,500 $250 $500 Maximum media usage 11 21 13 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized.

(a) If the promotional budget is limited to $23,000, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter “0”. Advertisement Alternatives No of commercial messages Television Radio Online What is the allocation of the budget among the three media? Advertisement Alternatives Budget ($) Television $ Radio $ Online $ What is the total audience reached?

(b) By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Round your answer to the nearest whole number. Increase in audience coverage of approximately

1. Find the appropriate measure of center. Discuss why the chosen measure is most appropriate. Why did you decide against other possible measures of center? 2. Find the appropriate measure of variation. The measure of variation chosen here should match the measure of center chosen in Part 1. 3. Find the graph(s) needed to appropriately describe the data. These may be done by hand and inserted into the Word document. You can also use Excel or a Web Applet to create a Histogram of the chosen data. Graphs can be copied and pasting onto the template. 4. Define the random variable (X) so that your chosen data set represents values of X. 5. Is your chosen random variable discrete or continuous? Explain how you know. 6. Would the Normal or Binomial distribution be a good fit for the underlying sample distribution of X? If one of them is a good fit, state how you would approximate the distribution parameters (Use the mean and standard deviation of the data chosen) 7. If you selected column D, calculate the probability that a flight will depart early or on-time. If you selected column E, calculate the probability that a flight will arrive early or on time using the empirical definition of probability. 8. If you selected column D, calculate the probability that a flight will depart late. If you selected column E, calculate the probability that a flight will arrive late using the empirical definition of probability. 9. For those that selected column D, assume now that the random variable X = Departure Time is exactly normally distributed with mean m= -2.5 and standard deviation s= 23. Compute the probability of a flight arriving late based on this new information. For those that selected column E, assume now that the random variable X = Arrival Time is exactly normally distributed with mean m= -2.5 and standard deviation s= 23. Does this contradict your answer from Part 8? Data: 0 -3 0 -7 8 -1 3 11 -6 -5 -8 -4 -13 -13 -11 -14 -16 -14 -18 -18 -23 -23 2 1 -4 -6 7 -8 -8 -4 -4 -5 -13 -9 -12 -7 -12 1 4 -19 -13 -19 3 12 13 2 0 0 4 -7 8 9 -1 -10 -6 -12 -14 -13 9 -15 -13 -14 20 -16 11 -14 18 -19 -3 -4 0 -3 2 6 6 -6 1 11 -7 -10 -13 9 -13 -18 -17 -11 -20 -18 8 0 -20 -3 1 -1 -4 -6 -5 -8 -10 -9 -6 8 -9 -12 -15 -14 -9 -17 -13 -17 2 -18 -18 -16 1 -4 0 -5 7 -7 -7 -5 0 5 -6 -12 1 6 -10 -15 -18 -16 -17 0 -21 -18 5 1 3 -2 -1 -2 -3 4 3 -11 9 -11 -11 0 -11 17 -10 -11 0 -19 -18 0 8 -23 3 -3 -4 -6 0 2 -1 -9 -9 4 1 -9 -12 0 0 -11 -14 -19 -17 -13 23 8 21 3 4 -2 1 6 7 -9 -3 1 -9 -5 -11 -6 -6 -10 -13 -9 -17 -6 -20 1 -21 -22 -2 0 -4 -3 3 -5 -6 -3 -5 -8 -12 -10 -7 -16 1 -14 -14 -16 -7 13 -17 -16 7 0 1 1 4 1 -8 -5 -9 0 -4 8 -7 -14 7 -8 5 4 8 21 3 11 2 -23 0 4 3 2 0 -1 -7 5 3 8 12 -12 -15 -11 -7 17 -15 -13 -17 -21 4 -19 -24 3 0 4 0 -2 -8 -5 6 5 1 -12 -14 7 8 -16 -11 -17 -20 10 4 -14 -22 -22 -3 -4 2 -4 -2 0 6 -6 2 -9 -3 -10 -13 7 -10 -12 -13 -16 -20 1 -14 -21 -17 3 -1 -1 0 -2 -7 -4 0 11 3 -11 -12 -11 -8 -13 -16 -16 7 2 -21 3 9 0 3 0 -5 -3 -3 -3 -3 -4 9 0 -8 -10 12 5 -16 -16 -13 -13 3 -19 0 -20 2 -3 -2 3 5 -1 -8 -3 -7 -11 -7 -10 12 -12 -8 17 -9 -18 -17 -14 1 -13 -21 -22 -2 -3 3 -3 -2 -7 -5 -10 -8 -6 -13 11 -11 -16 -9 -13 -12 -13 -16 -10 -20 -19 -22 -1 -4 2 4 -3 -8 4 -3 -7 -11 -13 2 -13 -12 -15 3 -17 -10 3 0 -19 -20 -20 0 0 -5 -4 -3 -5 -1 -8 -7 -2 13 11 -10 -12 -15 -14 -17 -18 6 12 6 -19 -20 0 -1 -5 -1 4 6 3 8 0 -11 -8 -14 -13 -11 3 -7 -11 10 -19 -20 -21 0 3 0 -4 0 2 -6 -7 -6 -7 8 -12 -2 -13 -7 9 -15 -14 -14 -17

Using Piccard's theorem, determine whether the IVP has a unique solution

(x-t)x'=x+t, x(-1)=2

Solve the given differential equation by undetermined coefficients.

y''' − 3y'' + 3y' − y = x − 8e^x

Discrete Mathematics

Find the number of subsets of S = {1, 2, 3, ... , 10} that contain both 5 and 6.

I know the answer is 2^8, however I have no idea how to go on to solve this problem.

Find all possible signatures induced by a nilpotent mapping on R5.

Two independent methods of forecasting based on judgment and experience have been prepared each month for the past 10 months. The forecasts and actual sales are as follows:

a. Compute the MSE and MAD for each forecast. (Round your answers to 2 decimal places.)

b. Compute MAPE for each forecast. (Round your intermediate calculations to 5 decimal places and final answers to 4 decimal places.)

c. Prepare a naive forecast for periods 2 through 11 using the given sales data. Compute each of the following; (1) MSE, (2) MAD, (3) tracking signal at month 10, and (4) 2s control limits. (Round your answers to 2 decimal places.)