Research Articles Base: Math Problems And Solutions

Evaluate the expression if the value of r = -22, s = 7, and the value of t = -8

Evaluate the expression if the value of r = -22, s = 7, and the value of t = -8 39. │-r│ + [ - │t + (-s)│]      = 22 + (-15)      = 7 40. -│s + (-t) │+ │r│     = – 15 + 22     = 7 41. – │t + (-r)│ + │s + r│     = – 14 + 15     = 1 42. │-s + (-r) │ + [ - │r + (-t)│]     = 15 +( -14)     = 1   Credit:ivythesis.typepad.com

Evaluate the expression if the value of r = -22, s = 7, and the value of t = -8

Evaluate the expression if the value of r = -22, s = 7, and the value of t = -8 39. │-r│ + [ - │t + (-s)│] = 22 + (-15) = 7 ...

Meteorology Applications

Meteorology Applications

Meteorology : The temperature at 8:00 AM was 19o C. By noon it risen 6o, but by 4:00 PM it had fallen 8o. What was the temperature at 4:...

Sports Applications

Sports Applications

Sports: On the four successive plays, the football team gained 7 yd, lost 11 yd, and lost 6 yd, and gained 15yd. What was the total yard...

Aviation Math Application

Aviation Math Application

Aviation: A powered airplane towed a glider into the air to an altitude of 1000 m and then let it go. The glider dropped 60 m into a the...

Sample Mathematics Problems and Solution

GP Unit 4   Name:             Section Number:        Instructions:   <ul style="margin-top: 0in; margin-bottom: 0in" type="disc"> <li class="MsoNormal">Identify the document by typing your full name and 	section number next to the yellow text. </li> <li class="MsoNormal">Rename the file. </li> <li class="MsoNormal">Type your answers next to the yellow text.  </li> <li class="MsoNormal">To show your work, you will need to include</li> </ul> o       the formula with substituted values. o       the final calculated answer with units.   Please submit your assignment.   1)      An open-top box is to be constructed from a 4 by 6 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a)      Find the function V that represents the volume of the box in terms of x. Answer:  V = 4×3 – 20×2 + 24x V = (L) (W) (x)                  but L = 6 – 2x                        W = 4 – 2x                        Then V = (6-2x) (4-2x) x                                     = 24x – 12×2 – 8×2 + 4×3                                     = 4×3 – 20×2 + 24x                                     a)      Graph this function.  FORMTEXT Show Graph here.                                                                                             b)      Using the graph, what is the value of x that will produce the maximum volume? Answer. x = 1   2)      The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters. a)      Write h as a function of r. Answer:  h = 121/ πr2 Show work in this space.                            V = πr2h                             121= πr2h              therefore     h = 121/ πr2   b)      What is the measurement of the height if the radius of the cylinder is 3 centimeters? Answer:  4.28 cm Show work in this space.                                  h = 121/ πr2                                  = 121/ π (32)                               h = 4.28 cm   c)      Graph this function. Show graph here.     		  				    		  		  		  		  		  		 		 		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		    3)      The formula for calculating the amount of money returned for deposit money into a bank account or CD (Certificate of Deposit) is given by the following: A is the amount of returned P is the principal amount deposited r is the annual interest rate (expressed as a decimal) n is the compound period t is the number of years Suppose you deposit ,000 for 3 years at a rate of 8%. a)      Calculate the return (A) if the bank compounds annually (n = 1). Answer:  $ 25,194.24 Show work in this space. Use ^ to indicate the power.                            A=  20,000[1+ (0.08/1)] ^ (1)(3)                                  = $ 25,194.24   b)      Calculate the return (A) if the bank compounds quarterly (n = 4). Answer:  , 364.83 Show work in this space .                             A = 20,000[1+ (0.08/4)]^ (4)(3)                                = ,364.83   c)      Calculate the return (A) if the bank compounds monthly (n = 12). Answer: ,404.74 Show work in this space.                                A = 20,000 [1+ (0.08/12)]^ (12)(3)                                  = ,404.74   d)      Calculate the return (A) if the bank compounds daily (n = 365). Answer:  ,424.31 Show work in this space.                              A = 20,000 [1+ (0.08/365)]^ (365)(3)                                  = ,424.31   e)      What observation can you make about the increase in your return as your compounding increases more frequently? Answer:  As the compounding increases more frequently, the amount of return also increases.   f)        If a bank compounds continuous, then the formula becomes simpler, that is where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. Answer:  ,425.02 Show work in this space                                                                            = 20,000 (2.7183)^ (0.08)(3)                                         = 25,425.02   g)      Now suppose, instead of knowing t, we know that the bank returned to us ,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t). Answer:  2.79 years Show work in this space                                                                  25,000 = 20,000e0.08t                                 25,000/20,000 = e0.08t                                                           1.25 = e0.08t                                                     ln 1.25 = ln e0.08t                                                            ln 1.25  = 0.08t                                           t = ln 1.25/ 0.08                                            t = 2.79 years h)      A commonly asked question is, “How long will it take to double my money?” At 8% interest rate and continuous compounding, what is the answer? Answer: 8.66 years ≈ 9 years  Show work in this space.                                 t @ A = 2P                                              using                                                      2P = Pe0.08t                                                        2 = e0.08t                                                       ln 2 = 0.08t                                                      t = (ln 2)/ 0.08                                                      t = 8.66 years ≈ 9 years 4)      For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, , let r = 8%, P = 1, and n = 1 and give the coordinates (t,A) for the points where t = 0, 1, 2, 3, 4. a)      Show coordinates in this space.  t = 0, 1, 2, 3, 4                        A =,000; ,600; ,328; ,194.24; ,209. 78     Show work in this space.                      using ; n = 1; r = 8%; P = 20,000                          @ t = 0                               A = 20,000 [1.08] ^0                                A= 20,000                           @t = 1                               A = 20,000[1.08] ^ 1                               A = 21,600                           @ t = 2                                A = 20,000 [1.08] ^ 2                                 A = 23,328                            @ t = 3                                  A = 20,000 [1.08] ^ 3                                   A = 25,194.24                            @ t = 4                                   A = 27,209.78   b)      Show graph here.   		  				    		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		  		    1)      Logarithms: a)      Using a calculator, find log 1000 where log means log to the base of 10. Answer: 3   b)      Most calculators have 2 different logs on them: log, which is base 10, and ln, which is base e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to the computer, 0 and 1. When a computer scientist needs a logarithm, he needs a log to base 2 which is not on any calculator. To find the log of a number to any base, we can use a conversion formula as shown here: Using this formula, find . Answer:  9.965784285 Show work in this space.   log2 1000 = log 1000                                                                            log 2 = 3/ 0.301 = 9.965784285   Credit:ivythesis.typepad.com

Sample Mathematics Problems and Solution

GP Unit 4 Name: Section Number: Instructions: Identify the document by typing your full name and section number n...

Math Answers

Answers to the Assignment Questions: 1.  e2x – 9ex + 14 = 0  If z = ex This can be written as: z2 – 9z + 14 = 0 Get the values of z: (z -2) (z-7) = 0 z = 2 and z = 7 Bringing back in terms of ex yields, ex = 2              and                  ex = 7 Get the natural log of both sides will be: ln(ex = 2)        and                  ln ex = 7 x = ln 2            and                  x = ln 7              2.  Solve the equation: log (x-1) + log (x+1) = 2 log (x – 1) (x + 1) = 2 log (x2 -1) = 2 log10 (x2 – 1) = 2 102 = x2 -1 x2 – 101 = 0 Using the quadratic formula the value of x can be computed: - b+ √b2 – 4ac / 2a √-4(-101) / 2(1) √404 / 2 x = √101 The negative (-√101)is not the solution since, there is no negative value for log. To check, substitute the value to the original equation. log (√101-1) + log (√101+1) = 2 2 = 2 True   3. Find the AB and BA when          1    2    1                        2      4       1 A =    3   4    0                  B = 0      3       1         0    1    -1                        0      0       4   This can yield to: For the  BA: This yield to:     4. Solving the equations: x + 2y = 15 x – 2y = – 5 The first step is to convert into matrix. [3   4  : 5] [2  -1  : 7] Change into identity matrix by getting zero in the Row 1, Column 2. So add (1 x row 2) to row 1. [2    0  : 10]  added (1 x row 2) to row 1 [1    -2 : -5] Next is want 1 in the top left corner. [1    0  :   5 ] Divided row 1 by 2 [1    -2 :   -5] Next is to have zero in the bottom left corner. [1     0 :  5]   [0    -2 :  -10]  added (-1 x row 1) to row 2 Finally, is zero to bottom left corner. [1     0 : 5] [0    1 :  5]  divided by -2 Then, it has the 2 x 2 matrix which can read as: x = 5 y = 5 5. The data can be tabulated as: Grades of the Students Frequency 0 – 0.5 2 0.6 – 1 2 1.1 – 1.5 2 1.6 – 2 9 2.1 – 2.5 7 2.6 – 3 5 3.1 – 3.5 7 3.6 – 4 6   The frequency histogram is given below: The frequency Polygon is given below:   6. The O,give for the data is given below: 7. The stem and leaf display is given below: 9 14 8 006 7 0235 6 468   a. The mean for the data is 66 + 70 + 68 + 75 + 80 + 86 + 64 + 73 + 80 + 94 + 72 + 91                                                                                     12 The mean = 919 / 12 = 76.58   b. The median is the middle of 64, 66, 68, 70, 72, 73, 75, 80, 80, 86, 91, and 94. The median is 73 + 75 / 2 The median = 74   c. Mode occurrence of data most often which is 80.   8. The expression can be written as:  (x1 y1) + (x2 y2) + (x3 y3) + (x4 y4) +(x5 y5)   9. a. The range of the grades is 94 – 64 = 30 b. The standard deviation can be computed as: Frequency x – mean(76.58) {x -  mean(76.58)}squared 66 10.58 111.9364 70 6.58 43.2964 68 8.58 73.6164 75 1.58 2.4964 80 -3.42 11.6964 86 -9.42 88.7364 64 12.58 158.2564 73 3.58 12.8164 80 -3.42 11.6964 94 -17.42 303.4564 72 4.58 20.9764 91 -14.42 207.9364   Sum 1046.917       Using the formula: s = √ ∑(x – xbar)2 / n -1 s = √1046.917 / 11 s = √95.17 s = 9.76   c. The variance has the formula of: s2 =  ∑(x – xbar)2 / n -1 s2 = 1046.917 / 11 s2 = 95.17 Credit:ivythesis.typepad.com

Math Answers

Answers to the Assignment Questions: 1. e2x – 9ex + 14 = 0 If z = ex This can be written as: z2 – 9z + 14 = 0 Get the values of z: ...