Concept explainers
Relative acuity of the human eye The fovea centralis (or fovea) is responsible for the sharp central vision that humans use for reading and other detail-oriented eyesight. The relative acuity of a human eye, which measures the sharpness of vision, is modeled by the function
where θ (in degrees) is the angular deviation of the line of sight from the center of the fovea (see figure).
- a. Graph R, for −15 ≤ θ ≤ 15.
- b. For what value of θ is R maximized? What does this fact indicate about our eyesight?
- c. For what values of θ do we maintain at least 90% of our maximum relative acuity? (Source: The Journal of Experimental Biology, 203, Dec 2000)
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)
Additional Math Textbook Solutions
Calculus & Its Applications (14th Edition)
University Calculus: Early Transcendentals (4th Edition)
Glencoe Math Accelerated, Student Edition
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus and Its Applications (11th Edition)
- A = 3 B = 6 C = 9 D= 7 mod10(X) is a function that returns the modulus of X after dividing it to 10. abs(X) is a function that returns the absolute value of X. Examples: mod10(6) = 6, mod10(16)=6, mod10(0) = 0, mod10(15)=5, mod10(41)+12 = 13 abs(4-8) = 4, abs(8-4)=4, abs(2-9) = 7, abs(8-1) = 7, abs(4-4)=0, abs(2-9)+8 = 15 Calculate the following: K1 = mod10(A+B) + 1= ……. K2 = abs(C-D) + 3 = ……. K3 = abs(D-2) + 1 = ……. K4 = mod10(A+B+C+D) + 1 = ……. K1 = mod((A+B), 10) + 1; K2 = abs(C-D) + 3; K3 = abs((D-2)) + 1; K4 = mod((A+B+C+D),10)+1;arrow_forward(Heat transfer) The formula developed in Exercise 5 can be used to determine the cooling time, t, caused only by radiation, of each planet in the solar system. For convenience, this formula is repeated here (see Exercise 5 for a definition of each symbol): t=Nk2eAT3fin A=surfaceareaofasphere=4r2 N=numberofatoms=volumeofthespherevolumeofanatom Volume of a sphere sphere=43radius3 The volume of a single atom is approximately 11029m3 . Using this information and the current temperatures and radii listed in the following chart, determine the time it took each planet to cool to its current temperature, caused only by radiation.arrow_forward(Numerical) Heron’s formula for the area, A, of a triangle with sides of length a, b, and c is A=s(sa)(sb)(sc) where s=(a+b+c)2 Write, test, and execute a function that accepts the values of a, b, and c as parameters from a calling function, and then calculates the values of sand[s(sa)(sb)(sc)]. If this quantity is positive, the function calculates A. If the quantity is negative, a, b, and c do not form a triangle, and the function should set A=1. The value of A should be returned by the function.arrow_forward
- (Statics) A beam’s second moment of inertia, also known as its area moment of inertia, is used to determine its resistance to bending and deflection. For a rectangular beam (see Figure 6.6), the second moment of inertia is given by this formula: Ibh3/12 I is the second moment of inertia (m4). b is the base (m). h is the height (m). a. Using this formula, write a function called beamMoment() that accepts two double- precision numbers as parameters (one for the base and one for the height), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 4a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.arrow_forward(Statics) An annulus is a cylindrical rod with a hollow center, as shown in Figure 6.7. Its second moment of inertia is given by this formula: I4(r24r14) I is the second moment of inertia (m4). r2 is the outer radius (m). r1 is the inner radius (m). a. Using this formula, write a function called annulusMoment ( ) that accepts two double-precision numbers as parameters (one for the outer radius and one for the inner radius), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 5a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.arrow_forward(Mechanics) The deflection at any point along the centerline of a cantilevered beam, such as the one used for a balcony (see Figure 5.15), when a load is distributed evenly along the beam is given by this formula: d=wx224EI(x2+6l24lx) d is the deflection at location x (ft). xisthedistancefromthesecuredend( ft).wistheweightplacedattheendofthebeam( lbs/ft).listhebeamlength( ft). Eisthemodulesofelasticity( lbs/f t 2 ).Iisthesecondmomentofinertia( f t 4 ). For the beam shown in Figure 5.15, the second moment of inertia is determined as follows: l=bh312 b is the beam’s base. h is the beam’s height. Using these formulas, write, compile, and run a C++ program that determines and displays a table of the deflection for a cantilevered pine beam at half-foot increments along its length, using the following data: w=200lbs/ftl=3ftE=187.2106lb/ft2b=.2fth=.3ftarrow_forward
- In Matlab: Write a function that takes a month, day, and year as inputs and returns the number of days that have passed since January 1, 780, the year al-Khwarizmi, the "father of algebra", was born (include the 1/1/780 date as day 1). The function should include a subroutine to deal with all leap year calculations. The subroutine is a function that will take a year as an input and will return a 1 if that year is a leap year or a 0 if that year is not a leap year. As a check, the number of days between 1/1/780 and 6/21/2011 is 449,786. Shown below is your starter code with some pseudocode to get you started:arrow_forwardlanguage: Python Problem: Define a global variable, countcalls, and increment it inside a power(x, n) function, so that it counts the number of times the power function is called. Show that it produces the expected number of calls for power(2, 10) and power(5, 10) and power(5, 0), each separately.arrow_forwardInteresting, intersecting def squares_intersect(s1, s2): A square on the two-dimensional plane can be defined as a tuple (x, y, r) where (x, y) are the coordinates of its bottom left corner and r is the length of the side of the square. Given two squares as tuples (x1, y1, r1) and (x2, y2, r2), this function should determine whether these two squares intersect, that is, their areas have at least one point in common, even if that one point is merely the shared corner point when these two squares are placed kitty corner. This function should not contain any loops or list comprehensions of any kind, but should compute the result using only integer comparisons and conditional statements. This problem showcases an idea that comes up with some problems of this nature; it is actually far easier to determine that the two squares do not intersect, and negate that answer. Two squares do not intersect if one of them ends in the horizontal direction before the other one begins, or if the same…arrow_forward
- Creat a function called free_fall with single input vector t that return values for distancex, velocity v, and acceleration garrow_forward(Fibonacci) The Fibonacci series0, 1, 1, 2, 3, 5, 8, 13, 21, …begins with the terms 0 and 1 and has the property that each succeeding term is the sum of the twopreceding terms. a) Write a nonrecursive function fibonacci(n) that calculates the nth Fibonaccinumber. Use unsigned int for the function’s parameter and unsigned long long int for its returntype. b) Determine the largest Fibonacci number that can be printed on your system.arrow_forwardRestructure Newton's method (Case Study: Approximating Square Roots) by decomposing it into three cooperating functions: newton, limitReached, and improveEstimate. The newton function can use either the recursive strategy of Project 2 or the iterative strategy of the Approximating Square Roots Case Study. The task of testing for the limit is assigned to a function named limitReached, whereas the task of computing a new approximation is assigned to a function named improveEstimate. Each function expects the relevant arguments and returns an appropriate value. An example of the program input and output is shown below: Enter a positive number or enter/return to quit: 2 The program's estimate is 1.4142135623746899 Python's estimate is 1.4142135623730951 Enter a positive number or enter/returnarrow_forward
- C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology PtrCOMPREHENSIVE MICROSOFT OFFICE 365 EXCEComputer ScienceISBN:9780357392676Author:FREUND, StevenPublisher:CENGAGE L