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Finance
Make a plot of a circle with its center at (4.2, 2.7) and radius of 7.5.
A parametric equation is given by x = sin(t)cos(t), y = 1 .5cos(t) Plot the function for –π < t
Evaluate the following expressions without using MATLAB. Check the answers with MATLAB. (a) 12 – 4 < 5 × 3 (b) y = 8/4 > 6 × 3 – 42 > -3 (c) y = -3 < (8 - 12) + 2 × (5 > 1 8/6 -4) (d) (∽5 +
Fibonacci numbers are the numbers in a sequence in which the first two elements are 0 and 1, and the value of each subsequent element is the sum of the previous two elements: 0, 1, 1, 2, 3, 5, 8, 13,
The reciprocal Fibonacci constant Ψ is defined by the infinite sum:where Fn are the Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, ... . Each element in this sequence of numbers is the sum of the
Write a program in a script file that determines the real roots of a quadratic equation ax2 + bx + c = 0. Name the file quadroots. When the file runs, it asks the user to enter the values of the
The value of 1t can be estimated by:Write a program (using a loop) that determines the expression. Run the program with n = 100, n = 10000, and n = 1000000. Compare the result with pi. (Use format
The value of 1t can be estimated from the expression: 2/π = √2/2 . √2 + √2/2 . √2/ + √2 + √2/2, ….. Write a MATLAB program in a script file that determine 1t for any number of terms.
Write a program that generates a vector with 20 random elements between -10 and 10 and then finds the sum of the positive elements.
Write a program that (a) generates a vector with 20 random integer elements with integers between -10 and 10, (b) replaces all the negative integers with random integers between -10 and 10, (c)
Write a program that asks the user to input a vector of integers of arbitrary length. The program then counts the number of elements, the number of positive elements, and the number of negative
A vector is given by x = [4.5 5 -16.12 21.8 10.1 10 -16.11 5 14 -3 3 2]. Using conditional statements and loops, write a program that rearranges the elements of x in order from the smallest to the
The Pythagorean theorem states that a2 + b2 = c2. Write a MATLAB program in a script file that finds all the combinations of triples a, b, and c that are positive integers all smaller or equal to 50
Given: a = -2 , b = 3 , c = 5 . Evaluate the following expressions without using MATLAB. Check the answers with MATLAB. (a) y = a – b > a – c < b (b) y = -4 < a < 0 (c) y = a - c < = b > a +
A twin primes is a pair of prime numbers such that the difference between them is 2 (for example, 17 and 19). Write a computer program that finds all the twin primes between 10 and 500. The program
An isolated prime is a prime number p such that neither p - 2 nor p + 2 is prime. For example, 47 is an isolated prime since 45 and 49 are both not primes. Write a computer program that finds all the
A list of 30 exam scores is: 31, 70, 92, 5, 47, 88, 81, 73, 51, 76, 80, 90, 55, 23, 43,98,36,87,22,61, 19,69,26,82,89,99, 71,59,49,64 Write a computer program that determines how many grades are
The Taylor series expansion for cos(x) is:where x is in radians. Write a MATLAB program that determines cos (x) using the Taylor series expansion. The program asks the user to type a value for an
Write a MATLAB program in a script file that finds a positive integer n such that the sum of all the integers 1 + 2 + 3 + ... + n is a number between 100 and 1000 whose three digits are identical. As
The following are formulas for calculating the training heart rate (THR) for men and women: For men (Karvonen formula): THR = [ (220-AGE)-RHR] x INTEN + RHR For women: THR = [(206-0.88xAGE)-RHR] ×
Body Mass Index (BMJ) is a measure of obesity. In standard units, it is calculated by the formulaBMI = 703/W/H2where W is weight in pounds, and His height in inches. The obesity classification
Write a program in a script file that calculates the cost of shipping a package according to the following price schedule:The program asks the user to enter the type of service (Ground, Express, or
Write a program that determines the change given back to a customer in a self-service checkout machine of a supermarket for purchases of up to $50. The program generates a random number between 0.01
The concentration of a drug in the body CP can be modeled by the equation:Cp = DG/Vd (ka/ke – ka)(e–ket – e–ket)where DG is the dosage administered (mg), Vd is the volume of distribution (L),
Given: v = [4 -1 2 3 1 -2 5 0] and u = [5 -1 0 3 -3 2 1 5]. Evaluate the following expressions without using MATLAB. Check the answers with MATLAB.(a) ∽ ∽μ (b) v = = ∽μ(c) u = = abs(v)(d) v
One numerical method for calculating the cubic root of a number, 3√P is in iterations. The process starts by choosing a value x1 as a first estimate of the solution. Using this value, a second,
Write a program in a script file that converts a measure of pressure given in units of either Pa, psi, atm. or torr to the equivalent quantity in different units specified by the user. The program
In a one-dimensioni random walk, the position x of a walker is computed by: xj = xj + s where s is a random number. Write a program that calculates the number of steps required for the walker to
The Sierpinski triangle can be implemented in MAILAB by plotting points iteratively according to one of the following three rules that are selected randomly with equal probability.Rule 1: xn+1 =
Cam is a mechanical device that transforms rotary motion into linear motion. The shape of the disc is designed to produce a specified displacement profile. A displacement profile is a plot of the
The overall grade in a course is determined from the grades of 6 quizzes, 3 midterms, and a final exam, using the following scheme: Quizzes: Quizzes are graded on a scale from 0 to 10. The grade of
The handicap differential (HCD) for a round of golf is calculated from the formula:HCD = (Score- Course Rating)/Course Slope à 113The course rating and the slope are measures of how
Use the vectors v and u from Problem 3. Use relational operators to create a vector w that is made up of the elements of u that are smaller than or equal to the elements of v.
Evaluate the following expressions without using MATLAB. Check the answers with MATLAB. (a) -3&3 (b) ∽5-3 (c) -2&2>318/3 (d) -3
Use loops to create a 3 x 5 matrix in which the value of each element is its row number to the power of its column number divided by the sum of its row number and column number. For example, the
A symmetric (5 x 5) Pascal matrix is displayed on the right. Write a MATLAB program that creates an n x n symmetric Pascal matrix. Use the program to create 4 x 4 and 7 x 7 Pascal matrices
The average monthly precipitations (in) for Boston and Seattle during 2012 are given in the vectors below (data from the U.S. National Oceanic and Atmospheric Administration). BOS = [2.67 1.00 1.21
Write a program in a script file that finds the smallest even integer that is divisible by 13 and by 16 whose square root is greater than 120. Use a loop in the program. The loop should start from 1
Write a user-defined MATLAB function for the following math function: y(x) = (- 0.2x3 + 7x2)e-0.3x The input to the function is x and the output is y. Write the function such that x can be a vector
Write a user-defined function that calculates grade point average (GPA) on a scale of 0 to 4, where A = 4, A- = 3.7, B+ = 3.3, B = 3, B- = 2.7, C+ = 2.3, C = 2, C- = 1.7, D+ = 1.3 D = 1, and E = 0.
The factorial n! of a positive number (integer) is defined by n! = n·(n-1)·(n-2)·. ..· 3·2·1, where 0! = 1. Write a user-defined function that calculates the factorial n! of a number. For
Write a user-defined MATLAB function that determines the angle that forms by the intersection of two lines. For the function name and arguments, use th=anglines (A,B,C). The input arguments to the
Write a user-defined MATLAB function that determines the unit vector in the direction of the line that connects two points (A and B) in space. For the function name and arguments, use n = unitvec (A,
Write a user-defined MATLAB function that determines the cross product of two vectors. For the function name and arguments, use w = crosspro (u,v). The input arguments to the function are the two
The area of a triangle ABC can be calculated by: A= 1/2 AB x AC where AB is the vector from point A to point B and AC is the vector from point A to point C. Write a user-defined MATLAB function that
Write a user-defined MATLAB function that determines the circumference of a triangle when the coordinates of the vertices are given. For the function name and arguments, use [cr] = cirtriangle (A, B,
Write a user-defined function that plots a circle given the coordinates of the center and a point on the circle. For the function name and arguments, use circle PC (c, p). The input argument c is a
Write a user-defined MATLAB function that converts integers written in decimal form to binary form. Name the function b=Bina (d), where the input argument d is the integer to be converted and the
Write a user-defined function that plots a triangle and the circle that circumscribes the triangle, given the coordinates of its vertices. For the function name and arguments, use TriCirc (A, B, C).
Write a user-defined MATLAB function for the following math function: r(θ) = 4cos(4sinθ) The input to the function is θ (in radians) and the output is r. Write the function such that e can be a
Write a user-defined function that plots an ellipse with axes that are parallel to the x and y axes, given the coordinates of its center and the length of the axes. For the function name and
In polar coordinates a two-dimensional vector is given by its radius and angle (r, e). Write a user-defined MATLAB function that adds two vectors that are given in polar coordinates. For the function
Write a user-defined function that finds all the prime numbers between two numbers m and n. Name the function pr=prime (m, n), where the input arguments m and n are positive integers and the output
The geometric mean GM of a set of n positive numbers x1, x2, ... , xn is defined by:GM =(x1. X2 . ... . xn)1/nWrite a user-defined function that calculates the geometric mean of a set of numbers. For
Write a user-defined function that determines the polar coordinates of a point from the Cartesian coordinates in a two-dimensional plane. For the function name and arguments, use [th rad] =
Write a user-defined function that determines the mode of a set of data (the value in the set that occurs most often). For the function name and arguments, use m=mostfrq (x). The input to the
Write a user-defined function that sorts the elements of a vector from the largest to the smallest. For the function name and arguments, use y=downsort (x). The input to the function is a vector x of
Write a user-defined function that sorts the elements of a matrix. For the function name and arguments, use B = matrixsort (A), where A is any size (m x n) matrix and B is a matrix of the same size
Write a user-defined function that fmds the largest element of a matrix. For the function name and arguments, use [Em, rc] = matrixmax (A), where A is any size matrix. The output argument Em is the
Write a user-defined MATLAB function that calculates the determinant of a 3 × 3 matrix by using the formula:For the function name and arguments, use d3 = det3by3 (A), where the input argument A
The fuel consumption of an airplane is measured in gal/mi (gallon per mile) or in L/km (liter per kilometers). Write a MATLAB user-defined function that converts fuel efficiency consumption from
A two-dimensional state of stress at a point in a loaded material in the direction defmed by the x-y coordinate system is defined by three components of stress σxx σyy, and τxy. The
The dew point temperature Td and the relative humidity RH can be calculated (approximately) from the dry-bulb T and wet-bulb Tw temperatures by (www.wikipedia.org):where the temperatures are in
In a lottery the player has to select several numbers out of a list. Write a user-defined function that generates a list of n integers that are uniformly distributed between the numbers a and b. All
The Taylor's series expansion for cosx about x = 0 is given by:where x is in radians. Write a user-defined function that determines cosx using Taylor's series expansion. For function name and
Write a user-defined function that determines the coordinate yc of the centroid of the U-shaped cross-sectional area shown in the figure. For the function name and arguments, use yc = centroidU (w,
The area moment of inertia Ixo of a rectangle about the axis x0 passing through its centroid is Ixo = 1/12 bh3. The moment of inertia about an axis x that is parallel to x0 is given by Ix = Ixo +
In a low-pass RL filter (a filter that passes signals with low frequencies), the ratio of the magnitudes of the voltages is given by:where ω is the frequency of the input signal.Write a
A circuit that filters out a certain frequency is shown in the figure. In this filter, the ratio of the magnitudes of the voltages is given by:where ω is the frequency of the input signal.Write a
The first derivative df(x)/dx of a function f(x) at a point x = x0 can be approximated with the two-point central difference formula: df(x)/dx = f(x0 + h)-f(x0 - h)/2h where h is a small number
The new coordinates (X,, Y,) of a point in the x-y plane that is rotated about the z axis at an angle e (positive is clockwise) are given by Xr, = X0cosθ- Y0sinθ Yr, = X0sinθ + Y0cosθ where (X0,
Tables of materials properties list density, in units of kg/m3, when the international system of units (SI) is used and list specific weight, in units of lb/in3, when the U.S. customary system of
In lottery the player has to guess correctly r numbers that are drawn out of n numbers. The probability, P, of guessing m numbers out of the r numbers can be calculated by the expression: p =
Write a user-defined MATLAB function that converts speed given in units of knots (one knot is one nautical mile per hour) to speed in units of feet per second. For the function name and arguments,
The body surface area (BSA) in m2 of a person (used for determining dosage of medications) can be calculated by the formula (DuBois formula): BSA = 0.007184w0.425H0.75 in which w is the mass in kg
The fuel tank shown in the figure in shaped as a frustum of cone with r = 20 in., and H = 2r.Write a user-defined function (for the function name and arguments, use V = Volfuel (y)) that gives the
The surface area S of a ring in shape of a torus with an inner radius r and a diameter d is given by: S = π2(2r + d)d The ring is to be plated with a thin layer of coating. The weight of the coating
The windchill temperature Twc is the perceived air temperature felt by the body on exposed skin due to the flow of air. For temperatures below 50°F and wind speed higher than 3 mph, it is calculated
Plot the polynomial y = 0.lx5 - 0.2x4 -x3 + 5x2 - 41.5x + 235 in the domain -6 < x < 6 . First create a vector for x, next use the polyval function to calculate y, and then use the plot function.
An aluminum fuel tank has a cylindrical middle section and a semi-spherical ends. The outside diameter is 10 in., and the length of the cylindrical section is 24 in. The wall-thickness of the
A 20 ft-long rod is cut into 12 pieces, which are welded together to form the frame of a rectangular box. The length of the box's base is 15 in. longer than its width.(a) Create a polynomial
A rectangular piece of cardboard, 40 in. long by in. wide is used for making a rectangular box (open top) by cutting out squares of x by x from the corners and folding up the sides.(a) Create a
Write a user-defined function that adds or subtracts two polynomials of any order. Name the function p=polyadd (pl, p2, operation). The first two input arguments pl and p2 are the vectors of the
Write a user-defined function that multiplies two polynomials. Name the function p=polymul t (pl1, p2). The two input arguments pl and p2 are vectors of the coefficients of the two polynomials. The
Write a user-defined function that calculates the maximum (or minimum) of a quadratic equation of the form: f(x) = ax2 + bx + c Name the function [x, y, w] = maxormin (a, b, c). The input arguments
A cone with base radius r and vertex in contact with the surface of a sphere is constructed inside a sphere, as shown in the figure. The radius of the sphere is R = 9 in.(a) Create a polynomial
Consider the parabola y = 1.5(x - 3)2 + 1 and the point P(3, 5.5) .(a) Create a polynomial expression for the distance d from point P to an arbitrary point Q on the parabola.(b) Make a plot of d
The following data is given:(a) Use linear least-squares regression to determine the coefficients m and b in the function y = mx + b that best fits the data.(b) Make a plot that shows the function
The boiling temperature of water TB at various altitudes his given in the following table. Determine a linear equation in the form TB = mh + b that best fits the data. Use the equation for
Plot the polynomial y = 0.008x4 - 1.8x2 -5.4x + 54 in the domain -14 < x < 16. First create a vector for x, next use the polyval function to calculate y, and then use the plot function.
The U.S. population in selected years between 1815 and 1965 is listed in the table below. Determine a quadratic equation in the form P = a2t2 + at1 + a0, where t is the number of years after 1800 and
The number of bacteria NB measured at different times t is given in the following table. Determine an exponential function in the form NB = Neat that best fits the data. Use the equation to estimate
Growth data of a sunflower plant is given in the following table:The data can be modeled with a function in the form H = C/(1 + Ae-Bt) (logistic equation), where H is the height, C is a maximum value
Use the growth data from Problem 22 for the following: (a) Curve-fit the data with a third-order polynomial. Use the polynomial to estimate the height in week 6. (b) Fit the data with linear and
The following points are given:(a) Fit the data with a first-order polynomial. Make a plot of the points and the polynomial.(b) Fit the data with a second-order polynomial. Make a plot of the points
The standard air density, D (average of measurements made), at different heights, h, from sea level up to a height of 33 km is given below.(a) Make the following four plots of the data points
Write a user-defined function that fits data points to a power function of the form y = bxm. Name the function [b, m] = powerfit (x,y), where the input arguments x and y are vectors with the
Viscosity is a property of gases and fluids that characterizes their resistance to flow. For most materials viscosity is highly sensitive to temperature. For gases, the variation of viscosity with
Measurements of the fuel efficiency of a car FE at various speeds v are shown in the table.(a) Curve-fit the data with a second-order polynomial. Use the polynomial to estimate the fuel efficiency at
The relationship between two variables P and t is known to be:p = mt/b + tThe following data points are givenDetermine the constants m and b by curve-fitting the equation to the data points. Make a
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