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Questions and Answers of
Finance
Shakee Venture wants to purchase 1,000 shares of an Internet technology stock for $15 a share. She figures that she needs $15,000 plus $90 brokerage commission to purchase or sell the stock. She
You deposit the following at the end of each year into a growth mutual fund that earns 11 percent per year.YearDeposit1$4,00023,50032,50042,00051,700$13,700a. How much should the fund be worth at the
Starting in 2012, Ira Roth places $5,000 in a Roth IRA at the beginning of each year for the next 40 years. Ira believes the account will earn 10 percent a year compounded yearly. How much will he
N. Ebriate, a college student at a party university, decides to forego beer drinking and invest the $100 he saves at the end of each month in a mutual fund that is currently earning 11 percent
Your city is expanding. There have been several problems with street flooding, which is affecting your business. You decided to attend a city council meeting, during which there is a discussion of
Grandpa Russ thinks he needs a fixed income for the next 10 years. He currently has $10,000 in CDs which are maturing at the end of this month. The CDs can be renewed for one year at 4½ percent.
Sarah Mix is a single, 30-year-old business owner who has $500 a month to invest. This money is in excess of the contribution to her company pension plan. Sarah hears that many of her friends are
Sarah Mix decides to invest in three funds, with $200 going into a small capital growth fund, $150 going into a large capital growth fund, and $150 into an international fund. She tracked the price
Larry Kraft owns a restaurant that is open 7 days a week. He has 25 full-time employees, but he has fairly high employee turnover. He believes that he can stabilize his workforce if he has a pension
Larry Kraft plans to open six more restaurants during the next five years. He believes that he will then have 125 employees. a. What recommendations would you make for Larry at this time? b. Could
Larry has expanded his business. When he met with his accountant at the end of the year, he learned that his total assets are in excess of $1 million. His accountant asked Larry if he had a will, and
You purchase a tax-free municipal bond paying an annual rate of 6 percent. Find the before-tax rate if you are in thea. 15 percent tax bracketb. 28 percent tax bracketc. 36 percent tax bracket
Calculate:(a) 22 + 5.12/50-6.32(b) 44/7 + 82/5 – 99/3.92The following problems can be solved by writing commands in the Command Window, or by writing a program in a script file and then executing
A sphere has a radius of 24 cm. A rectangular prism has sides of a, a/2, and a/ 4.(a) Determine a of a prism that has the same volume as the sphere.(b) Determine a of a prism that has the same
The arc length of a segment of a parabola ABC of an ellipse with semi-minor axes a and b is given approximately by:LABC = 1/2b2 + 16a2 + b2/8a In(4a + b2 + 16a2)/b.(a)
Two trigonometric identities are given by: (a) sin 5x = 5sinx- 20sin3x+ 16sin5x (b) sin2xcos2x = 1 - cos4x/8 For each part, verify that the identity is correct by calculating the values of the left
Two trigonometric identities are given by: (a) tan 3x = 3tanx – tan3x/1 – 3tan2x (b) cos 4x = 8(cos4x - cos2x) + 1 For each part, verify that the identity is correct by calculating the values of
Define two variables: alpha = π/6, and beta= 3π/8. Using these variables, show that the following trigonometric identity is correct by calculating the values of the left and right sides of the
Given: ∫x sin axdx = sin ax/a2 – x cos ax/a. Use MATLAB to calculate the following definite integral: ∫π/33x/2 x sin(0.6x)dx.
In the triangle shown a = 5. 3 in., y = 42°, and b = 6 in. Defme a, y, and b as variables, and then:(a) Calculate the length b by using the Law of Cosines. (Law of Cosines: c2 = a2 + b2 -
In the triangle shown a = 5 in., b = 7 in., and y = 25°. Define a, b, and y as variables, and then:(a) Calculate the length of c by substituting the variables in the Law of Cosines. (Law of
In the ice cream cone shown, L = 4 in. and e = 35°. The cone is filled with ice cream such that the portion above the cone is a hemisphere. Determine the volume of the ice cream.
For the triangle shown, a = 48 mm, b = 34 mm, and y = 83o. Define a, b, and y as variables, and then:(a) Calculate c by substituting the variables in the Law of Cosines. (Law of Cosines: c2 = a2 +
Calculate: (a) √412- 5.22/e5- 100.53 (b) 3√132 + ln(500)/8 The following problems can be solved by writing commands in the Command Window, or by writing a program in a script file and then
The parametric equations of a line in space are: x = x0 +at, y = y0 + bt, and z = z0 + ct. The distance d from a point A (xA, yA, zA) to the line can be calculated by:d = dA0sin [acos((xA - x0)a +
The circumference of an ellipse can be approximated by:C = Ï[3(a + b) - ./(3a + b) (a + 3b)]Calculate the circumference of an ellipse with a = 16 in. and b = 11 in.
315 people have to be transported using buses that have 37 seats. By typing one line (command) in the Command Window, calculate how many seats will remain empty if enough buses will be ordered to
739 apples are to be packed and shipped such that 54 are placed in a box. By typing one line (command) in the Command Window, calculate how many apples will remain unpacked if only full boxes can be
Assign the number 316,501.673 to a variable, and then calculate the following by typing one command: (a) Round the number to the nearest hundredth. (b) Round the number to the nearest thousand.
The voltage difference V ab between points a and b in the Wheatstone bridge circuit is:Vab = V(RIR3 R2R4]/(RI + R2)(R3 + R4)Calculate the voltage difference when V = 14 volts, R1 = 120.6
The resonant frequency f(in Hz) for the circuit shown is given by:f = l/2Ï1/LC (R/L)2Calculate the resonant frequency when L = 0.15henrys, R = 14 ohms, and C = 2.6
The number of combinations Cn, r of taking r objects out of n objects is given by: Cn,r = n!/r!(n-r)! (a) Determine how many combinations are possible in a lottery game for selecting 6 numbers that
The formula for changing the base of a logarithm is: logaN = logbN/logba (a) Use MATLAB's function log (x) to calculate log4 0.085. (b) Use MATLAB's function logl0 (x) to calculate log61500.
The equivalent resistance, Req, of four resistors, R1, R2, R3, and R4, that are connected in parallel is given by:Req = 1/1/R1 + 1/R2 + 1/R3 + 1/R4Calculate Req if R1 = 1200¦, R2 = 2200,
Calculate:(a) 14.83-6.32/(√13 + 5)2(b) 45(288/9.3 – 4.62) – 1065e–1.5The following problems can be solved by writing commands in the Command Window, or by writing a program in a script file
The voltage Vc t seconds after closing the switch in the circuit shown is:Vc = Vo(l- e-t/(RC))Given Vc = 36 V, R = 2500 ¦, and C = 1600 μF, calculate the current 8 seconds
Radioactive decay of carbon-14 is used for estimating the age of organic material. The decay is modeled with the exponential function f(t) = f(0)ekt, where t is time, f(0) is the amount of material
The greatest common divisor is the largest positive integer that divides the numbers without a remainder. For example, the GCD of8 and 12 is 4. Use the MATLAB Help Window to find a MATLAB built-in
The Moment Magnitude Scale (MMS), denoted Mw, which measures the total energy released by an earthquake, is given by: Mw = 2/3log10M0 - 10.7 where M0 is the magnitude of the seismic moment in dyne-em
According to special relativity, a rod of length L moving at velocity v will shorten by an amount c, given by:where c is the speed of light (about 300 x 106 m/s). Calculate how much a rod 2 m long
The value B of a principal P that is deposited in a saving account with a fixed annual interest rate r after n years can be calculated by the formula: B = P1 + r/m)nm where m is the number of times
Newton's law of cooling gives the temperature T(t) of an object at time tin terms of T0, its temperature at t = 0, and Ts, the temperature of the surroundings. 33 T(t) = T3 + (T0 - T3)e-kt A police
The stress intensity factor K predicts the stress state (stress intensity) near a crack tip. F or a plate with a crack and loading shown in the figure, K is given by:Determine K for the case where
The spread of a computer virus through a computer network can be modeled by: N(t) = 20e0.I5t where N(t) is the number of computers infected and t time in minutes. (a) Determine how long it takes for
Use the Help Window to find a display format that displays the output as a ratio of integers. For example, the number 3.125 will be displayed as 25/8. Change the display to this format and execute
Calculate: (a) 24.5 + 64/3.52 + 8.3 . 12.53/√76.4 - 28/15 (b) (5.92 – 2.42)/3 + (log1012890/e0.3)2 The following problems can be solved by writing commands in the Command Window, or by writing a
Stirling's approximation for large factorials is given by: n! = 2πn(n/e)n Use the formula for calculating 20!. Compare the result with the true value obtained with MATLAB's built-in function
Calculate: (a) cos(7π/9) + tan(7/15 π) sin(15°) (b) sin280° – (cos14°sin 80°)2/3√0.18 The following problems can be solved by writing commands in the Command Window, or by writing a program
Define the variable x as x = 6. 7, then evaluate: (a) 0.01x5-1.4x3 + 80x + 16.7 (b) √x3 + ex – 51/x
Define the variable t as t = 3.2, then evaluate: (a) 56t-9 .81 t2/2 (b) 14e-O.ltsin(2πt)
Define the variables x and y as x = 5.1 and y = 4.2, then evaluate: (a) 3/4 xy – 7x/y2 + √xy (b) (xy)2- x + y/(x-y)l2 + √ x + y/2x - y
Defme the variables a, b, c, and d as: a = 12, b = 5.6, c = 3a/b2, and d = (a–b)c/c, then evaluate: (a) a/b + d–c/ d+c -(d-b)2 (b) d–c/ea-2b + ln(c–d + b/a)
Create a row vector that has the following elements: 8, 10/4, 12 × 1.4, 51, tan85°, √26, and 0.15.
Create a column vector with 9 equally spaced elements in which the first element is -34 and the last element is -7. (A column vector can be created by the transpose of a row vector.)
Using the colon symbol, create a row vector (assign it to a variable named Fives) with five elements that are all 5.
Using the linspace command, create a row vector (assign it to a variable named Nines) with nine elements that are all 9.
Use a single command to create a row vector (assign it to a variable named a) with 6 elements such that the last element is 4.7 and the rest of the elements are 0s. Do not type the vector elements
Use a single command to create a row vector (assign it to a variable named b) with 8 elements such that the last three element are 3.8 and the rest of the elements are 0s. Do not type the vector
Use a single command to create a row vector (assign it to a variable named b) with 11 elements such that b = 0 2 4 6 8 10 12 9 6 3 0 Do not type the vector explicitly.
Create two row vectors: a = 2 : 3 : 17 and b = 3 : 4 : 15. Then, by only using the name of the vectors (a and b), create a row vector c that is made from the elements of a followed by the elements of
Create two column vectors: a= [2 : 3 : 17]' and b = [3 : 4 : 15]'. Then, by only using the name of the vectors (a and b), create a column vector c that is made from the elements of a followed by the
Create a vector (name it vtA) that has 10 elements of which the first is 8, the increment is 7, and the last element is 71. Then, assign elements of vtA to a new vector (call it vtB) such that vtB
Create a vector (name it vet C) that has 12 elements of which the first is 5, the increment is 4 and the last element is 49. Then, by assigning elements of vctC to new vectors, create the following
Create a row vector that has the following elements: √15 x 103, 25/14 – 62, ln 35/0.43, sin65º/cos80º, 129, and cos2(π/20).
Create a vector (name it vctD) that has 9 elements of which the first is 0, the increment is 3 and the last element is 27. Then create a vector (name it vctDop) that consist of the elements of vctD
Create the following matrix by using vector notation for creating vectors with constant spacing and/or the linspace command. Do not type individual elements explicitly.
Create the following matrix by using vector notation for creating vectors with the linspace command. Do not type individual elements explicitly.
Create the following matrix by typing one command. Do not type individual elements explicitly.
Create the following matrix by typing one command. Do not type individual elements explicitly.
Create the following matrix by typing one command. Do not type individual elements explicitly.
Create the following matrix by typing one command. Do not type individual elements explicitly.
Create three row vectors:a = [3 -1 5 11 -4 2]b = [7 -9 2 13 1 -2]c = [-2 4 -7 8 0 9](a) Use the three vectors in a MATLAB command to create a 3 × 6 matrix in which the rows are the vectors a, b, c,
Create three row vectors:a = [3 -1 5 11 -4 2]b = [7 -9 2 13 1 -2]c = [-2 4 -7 8 0 9](a) Use the three vectors in a MATLAB command to create a 3 × 4 matrix such that the first, second, and third rows
Create two row vectors: a = [3 9 -0.5 3 6. 1 5. -0.8 4] b = [12 -0.8 6 2 5 3 -7.4] (a) Use the two vectors in a MATLAB command to create a 3 × 4 matrix such that the first row consists of elements 3
Create a column vector that has the following elements: 25.5, (l4tan58o)/(2.12 + 11)' 6!, 2.74, 0.0375, and π/5.
By hand (pencil and paper) write what will be displayed if the following commands are executed by MATLAB. Check your answers by executing the commands with MATLAB. (Parts (b), (c), (d), and (e) use
The following vector is defined in MATLAB: v = [6 11 -4 5 8 1 -0.2 -7 19 5] By hand (pencil and paper) write what will be displayed if the following commands are executed by MATLAB. Check your
The following vector is defined in MATLAB:v = [6 11 -4 5 8 1 -0.2 -7 19 5]By hand (pencil and paper) write what will be displayed if the following commands are executed by MATLAB. Check your answers
Create the following matrix A.By writing one command and using the colon to address range of elements (do not type individual elements explicitly), use the matrix A to:(a) Create a six-element row
Create the following vector A.A = [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18]Then using the MATLAB's built-in reshape function create the following matrix B from the vector A:By writing one
Create the following vector C.c = [1.5 2 2.5 3 3.5 4 4.5 5 9.6 9.1 8.6 8.1 7.6 7.1 6.6 6.1]Then use MATLAB's built-in reshape function and the transpose operation to create the following matrix D
Create the following matrix E:(a) Create a 2 × 3 matrix F from the second and third rows, and the third through the fifth columns of matrix E.(b) Create a 4 × 4 matrix G from all rows and the
Create the following matrix H:(a) Create a 2 × 5 matrix G such that its first row includes the first three elements and the last two elements of the first row of H, and the second row of G
The following matrix is defined in MATLAB:By hand (pencil and paper) write what will be displayed if the following commands are executed by MATLAB. Check your answers by executing the commands with
The following matrix is defined in MATLAB:By hand (pencil and paper) write what will be displayed if the following commands are executed by MATLAB. Check your answers by executing the commands with
Create a column vector that has the following elements: 32/3.22, sin235°, 6.1, ln292, 0.00552, In229, and 133.
By hand (pencil and paper) write what will be displayed if the following commands are executed by MATLAB. Check your answers by executing the commands with MATLAB. V = 1:2 : 23 M = reshape (v, 3,
Using the zeros, ones, and eye commands, create the following arrays by typing one command:(a)(b)(c)
Using the zeros, ones, and eye commands create the following arrays by typing one command:(a)(b)(c)
Use the eye, ones, and zeros commands to create the following arrays:Using the variables A, B, and C, writes a command that creates the following matrix D:
Create a 2 Ã 3 matrix A in which all the elements are 1. Then reassign A to itself (several times) such that A will become
Define the variables x = 0.85, y = 12.5, and then use them to create a column vector that has the following elements: y, yx, In (y/x), x × y, and x + y.
Define the variables a = 3.5, b = -6.4, and then use them to create a row vector that has the following elements: a, a2, a/b, a · b, and √a.
Create a row vector in which the first element is 1 and the last element is 43, with an increment of 6 between the elements (1, 7, 13, . . . , 43).
Create a row vector with 11 equally spaced elements in which the first element is 96 and the last element is 2.
Create a column vector in which the first element is 26, the elements decrease with increments of -3.6, and the last element is -10. (A column vector can be created by the transpose of a row vector.)
For the function y = x2- e0·5x + x, calculate the value of y for the following values of x using element-by-element operations: -3, -2, -1, 0, 1, 2, 3.
The following two vectors are defined in MATLAB: v = [15, 8, -6] u = [3, -2, 6] By hand (pencil and paper) write what will be displayed if the following commands are executed by MATLAB. Check your
Two vectors are given: u = 5i - 6j + 9k and v = 11i + 7j - 4k Use MATLAB to calculate the dot product u · v of the vectors in three ways: (a) Write an expression using element-by-element calculation
Define the vector v = [2 3 4 5 6]. Then use the vector in a mathematical expression to create the following vectors:(a) a = [4 6 8 10 12](b) b = [8 27 64 125 216](c) c = [22 33 44 55 66](d) d = [1
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