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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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 Linear-equations/93096: Word Problem Wild and Crazy Productions wants to purchase a new CD producing machine. Its cost is \$5000.00. If their labor and other unit costs are \$5.00 per CD and they can sell the CD for \$10.00 each, how many must they manufacture before they pay for their new machine?1 solutions Answer 67722 by stanbon(57387)   on 2007-08-17 10:44:03 (Show Source): You can put this solution on YOUR website!The profit on each CD is \$5.00 5000/5 = 1000 CD's Selling 1000 CD's will give them back their \$5000. Cheers, Stan H.
 Miscellaneous_Word_Problems/93094: In the Central Sierra Nevada of California, the percent of moisture that falls as snow rather than rain is approximated reasonably well by: P=86.3inH-680 where P is the percent of moisture as snow at an altitude of H feet. At what altitude is 50% of the moisture snow?1 solutions Answer 67721 by stanbon(57387)   on 2007-08-17 10:41:51 (Show Source): You can put this solution on YOUR website!P=86.3inH-680 where P is the percent of moisture as snow at an altitude of H feet. At what altitude is 50% of the moisture snow? ---------- 50 = 86.3H - 680 50+680 = 86.3H H = 8.45 feet ============== Comment: This doesn't sound right but that is what your formula implies. =============== Cheers, Stan H.
 Inequalities/93069: hi i have faced problems in GRE like this(this is only example to explian to you) there were seperate questions for pirme,even and odd the questions were like which of the following is not (prime,even,odd) 2*(x-2) (x-4)+y (x+4)*3 like these please can you tell me from where i can get these types of questions for study please help tell me any website thanks waiting for response zamansoomro@yahoo.com1 solutions Answer 67720 by stanbon(57387)   on 2007-08-17 10:30:06 (Show Source): You can put this solution on YOUR website!which of the following is not (prime,even,odd) 2*(x-2) (x-4)+y (x+4)*3 like these please can you tell me from where i can get these types of questions for study please --------------- You might use Google with search word "prime even odd numbers" . But the key to answering this type problem is to consider the result if the variable is even or odd. For example: Consider (x+4)*3 x is either even or odd If x is even, x+4 is even When you multiply by three the result is still even -------- If x is odd, x+4 is still odd When you multiply an odd by an odd you get an odd result ------------ Therefore (x+4)*3 could be even or it could be odd. -------------- Now, is it prime? If it could be even and not equal to 2 it is definitely not prime. ----------------- Conclusion: You cannot say it is always even; you cannot say it is always odd; you cannot say it is always prime. --------------------- Hope that helps and good luck on your GRE. Cheers, Stan H.
 Rate-of-work-word-problems/93073: If Marichu can finish typing a report in 1 hour and 30 minutes, what part of the report can she finish in 1 hour?1 solutions Answer 67718 by stanbon(57387)   on 2007-08-17 09:49:33 (Show Source): You can put this solution on YOUR website!If Marichu can finish typing a report in 1 hour and 30 minutes, what part of the report can she finish in 1 hour? --------------- Note: 1 hr and 30 minutes = 90 minutes ----------------- 1/1.5 = x/1 x = 1/(3/2) x = 2/3 of a report in 1 hour. ============ Cheers, Stan H.
 Travel_Word_Problems/93075: A sprinter who averaged 30ft/sec completed a race one second before another sprinter who averaged 28 ft/sec. what was the distance of the race?1 solutions Answer 67717 by stanbon(57387)   on 2007-08-17 09:45:59 (Show Source): You can put this solution on YOUR website!A sprinter who averaged 30ft/sec completed a race one second before another sprinter who averaged 28 ft/sec. what was the distance of the race? --------------- 1st sprinter DATA: Rate = 30 ft/sec ; Time = x seconds ; distance = rt = 30x ft. --------------- 2nd sprinter DATA: Rate = 28 ft/sec ; Time = x+1 seconds ; diatance = rt = 28(x+1) = 28x + 28 ft. ----------------- EQUATION: distance = distance 30x = 28x + 28 2x = 28 x = 14 seconds --------------- Distance of the race = 30x = 30*14 = 420 ft. ==================== Cheers, Stan H.
 Linear-systems/93079: A= 1/2h (a+b)find b1 solutions Answer 67716 by stanbon(57387)   on 2007-08-17 09:40:46 (Show Source): You can put this solution on YOUR website!A= (1/2)h (a+b)find b Multiply both sides by 2 to get: 2A = h(a+b) Divide both sides by h to get: (2A/h) = a+b Subtract a from both sides to get: b = (2A/h)-a ============= Cheers, Stan H.
 Triangles/93086: a tiangle has two interior angle of 1 degree each. How many degrees does its 3rd angle have? 1 solutions Answer 67715 by stanbon(57387)   on 2007-08-17 09:37:42 (Show Source): You can put this solution on YOUR website!180 - 2 = 178 degrees. Cheers, Stan H.
 Rational-functions/93087: This question is from textbook Please help me with this equation: It is a rational expression and the directions are: Perform the operation and simplify completely: (5) divided by (x-1) mmultiplied by (1-x) divided by 25(x-2) 1 solutions Answer 67714 by stanbon(57387)   on 2007-08-17 09:36:34 (Show Source): You can put this solution on YOUR website!Perform the operation and simplify completely: (5) divided by (x-1) mmultiplied by (1-x) divided by 25(x-2) -------------- [5/(x-1)] --------- Note: (1-x) = -(x-1) Make that change and you get: [5/(x-1)] * [-(x-1)/(25(x-2)] ------------- Cancel the 5 factor and cancel the (x-1) factor to get: = -1 / [5(x-2)] ================ Cheers, Stan H.
 Rational-functions/93088: This question is from textbook Please help me solve this problem: the direction are as follow: Find the domain of the function, use interval notation: f(x)= 3 divided by (x+4)1 solutions Answer 67713 by stanbon(57387)   on 2007-08-17 09:30:56 (Show Source): You can put this solution on YOUR website!Find the domain of the function, use interval notation: f(x)= 3/(x+4) ---------- The denominator cannot be zero so x cannot be -4 So the Domain is "all Real Numbers except x=-4". Interval Notation: (-inf,-4)U(-4,+inf) -------------- Cheers, Stan H.
 Functions/93062: I was doing all right with replacing f of x with g until I came across this question dealing with tables, any help would be appreciated. Thanks. Several values of the two functions f and g are listed in the following tables: x 4567 x 4567 f(x) 7654 g(x) 6745 Find (f(g)(6)) 1 solutions Answer 67711 by stanbon(57387)   on 2007-08-16 22:38:25 (Show Source): You can put this solution on YOUR website!Several values of the two functions f and g are listed in the following tables: x... 4567 x... 4567 f(x) 7654 g(x) 6745 -------------- Find (f(g)(6)) = f[g(6)] = f[4] = 7 ================== Cheers, Stan H.
 Inequalities/93053: I have the following word problem and I don't know where to biggin answering it. For 1980 through 1998, the population (in thousands) of Hawaii can be modeled by 13.2t+ 965 where t is the number of years since 1980. What was the population of Hawaii in 1998? What was the population increase from 1980 to 1998? I believe i am to make an equation such as: 13.2(14)+965 btu i don't know where to go from there.1 solutions Answer 67710 by stanbon(57387)   on 2007-08-16 22:34:18 (Show Source): You can put this solution on YOUR website!For 1980 through 1998, the population (in thousands) of Hawaii can be modeled by 13.2t+ 965 where t is the number of years since 1980. What was the population of Hawaii in 1998? What was the population increase from 1980 to 1998? ---------------- P(t) = 13.2t + 965 1998 is 8 years after 1980 so let t=8. P(8) = 13.2*8 + 965 P(8) = 1070.6 ------------- 1980 is 0 years after 1080 so let t=0. P(0) = 965 -------------- Increase from 1980 to 1998 = 1070.6-965 = 105.6 thousand ================ Cheers, Stan H.
 Polynomials-and-rational-expressions/93056: Find the following product (a - 9)(a^2 + 9a + 8) a)a^3 + 89a +72 b)a^3 + 18a^2 + 73a + 72 c)a^3 + 73a + 72 d)18a^2 + 73a - 721 solutions Answer 67709 by stanbon(57387)   on 2007-08-16 22:22:40 (Show Source): You can put this solution on YOUR website!(a - 9)(a^2 + 9a + 8) =a(a^2+9a+8)-9(a^2+9a+8) = a^3 + 9a^2 + 8a -9a^2 - 81a -72 = a^3 -73a -72 ========================= Cheers, Stan H.
 Travel_Word_Problems/93049: Two cars traveled in oppostie directions from the same starting point. The rate of one car was 10km /h faster than the rate of the other car. After 4 hours the cars were 46okm apart. Find each car's rate.1 solutions Answer 67708 by stanbon(57387)   on 2007-08-16 22:16:19 (Show Source): You can put this solution on YOUR website!Two cars traveled in opposite directions from the same starting point. The rate of one car was 10km /h faster than the rate of the other car. After 4 hours the cars were 46okm apart. Find each car's rate. ---------------------- 1st car DATA: Rate = x kph ; Time = 4 hrs ; distance =rt =4x km --------------- 2nd car DATA: Rate = x+10 kph ; Time = 4 hrs. ; distance = rt = 4(x+10)= 4x+40 km ----------------------- EQUATION: distance + distance = 460 km 4x + 4x+40 = 460 8x = 420 x = 52.5 kph (speed of the 1st car) x+10 = 62.5 kph ( speed of the 2nd car) ================================ Cheers, Stan H.
 Linear-equations/92991: Solve each system b the addition method. Indicate whether it is independent, inconsistent,or dependent. 1/3X-1/6Y=1/3 1/6X+1/4Y=01 solutions Answer 67702 by stanbon(57387)   on 2007-08-16 21:00:05 (Show Source): You can put this solution on YOUR website!Solve each system b the addition method. Indicate whether it is independent, inconsistent,or dependent. 1st: 1/3X-1/6Y=1/3 2nd: 1/6X+1/4Y= 0 ------------- Multiply thru 1st by 6; Multiply thru 2nd by 12 3rd: 2x - y = 2 4th: 2x + 3y = 0 ------------------ Subtract 3rd from 4th to get: 4y=-2 y = -1/2 --------------- Substitute into 2x+3y=0 to solve for x: 2x + 3*(-1/2) = 0 2x = 3/2 x = 3/4 ------------------ Final Answer: x=3/4 ; y= -1/2 ========================== Cheers, Stan H.
 Rational-functions/93021: This question is from textbook Algebra 2 name the additive inverse and multiplicative inverse of 6/71 solutions Answer 67700 by stanbon(57387)   on 2007-08-16 20:45:25 (Show Source): You can put this solution on YOUR website!name the additive inverse and multiplicative inverse of 6/7 ----------- additive inverse is -(6/7) ------------- multiplicative inverse is 7/6 --------------- Cheers, Stan H.
 Equations/93016: Please help solve z=4/3(pi)r^3 find (pi)1 solutions Answer 67698 by stanbon(57387)   on 2007-08-16 20:43:39 (Show Source): You can put this solution on YOUR website!z=(4/3)(pi)r^3, find (pi) Multiply both sides by (3/4) to get: (3/4)z = pi*r^3 Divide both sides by r^3 to get: pi = [3z/4r^3] ================= Cheers, Stan H.
 test/93017: If the average (arithmetic mean) of x and y is k, which of the following is the average of x, y, and z? (A) 2k + z/3 (B) 2k +z/2 (C) k+z/3 (D) k+z/2 (E) 2(k+z)/31 solutions Answer 67696 by stanbon(57387)   on 2007-08-16 20:36:41 (Show Source): You can put this solution on YOUR website!If the average (arithmetic mean) of x and y is k, which of the following is the average of x, y, and z? ------------- If "k" is the average of x and y then (x+y)/2 = k and x+y=2k ----------- Average of x,y,and z is (x+y+z)/3 = (2k+z)/3 ================= Cheers, Stan H.
 Money_Word_Problems/92885: A man is paid Php300 for each day he works and forfeits Php80 for each day he is idle. At the end of 20 days he nets Php4,500. How many days did he work?1 solutions Answer 67694 by stanbon(57387)   on 2007-08-16 19:54:55 (Show Source): You can put this solution on YOUR website!A man is paid Php300 for each day he works and forfeits Php80 for each day he is idle. At the end of 20 days he nets Php4,500. How many days did he work? ------------ Let # of days he worked be "x"; His pay is 300x ------------- Then "20-x" is # of days he did not work: His loss = 80(20-x)= 1600-80x ------------------------ EQUATION: Gain - Loss = 4500 300x -(1600-80x) = 4500 380x = 6100 x = 16.0526 days ( which doesn't make any sense) He worked 16.0526 days ========================== Cheers, Stan H.
 Polynomials-and-rational-expressions/92999: I am really bad at solving word problems. I am not sure how to make the equation and then solve it. Please help me. The volume of the box is represented by Find the polynomial that represents the area of the bottom of the box. The side of the box is 1 solutions Answer 67692 by stanbon(57387)   on 2007-08-16 19:46:28 (Show Source): You can put this solution on YOUR website!The volume of the box is represented by Find the polynomial that represents the area of the bottom of the box. -------------- Area is a square measure so x^2+5x+6 represents the area of the bottom of the box. --------- Cheers, Stan H.
 Distributive-associative-commutative-properties/93006: 2(b+4)+8b= my work is this correct 2 x b+2 x 4+8b =2b+8+8b =18b 1 solutions Answer 67691 by stanbon(57387)   on 2007-08-16 19:44:22 (Show Source): You can put this solution on YOUR website!2(b+4)+8b= my work is this correct 2 x b+2 x 4+8b =2b+8+8b =18b ------------ Almost. After 2b+8+8b you should have the following: =10b + 8 ------------- You cannot add these as they are not "like" terms. ----------- Comment: It's like adding apples and oranges. 2 apples + 8 oranges + 8 apples = 10apples + 8 oranges You cannot add the apples and the oranges because they are not "like" fruit. ================ Cheers, Stan H.
 Quadratic_Equations/93003: I AM HAVING PROBLEMS SOLVING THIS PROBLEM AND NEED SOME HELP SOLVE BY COMPLETING THE SQUARE X^2=5X+2 THANK YOU1 solutions Answer 67685 by stanbon(57387)   on 2007-08-16 19:02:45 (Show Source): You can put this solution on YOUR website!SOLVE BY COMPLETING THE SQUARE X^2=5X+2 ------------ x^2-5x+? = 2+? Complete the square to get: x^2-5x+[(1/2)*(-5)]^2 = 2 + [(1/2)*(-5)]^2 Simplify to get: x^2 - 5x + (25/4) = 2 + (25/4) Factor to get: (x-(5/2))^2 = 33/4 Take the square root of both sides to get: (x-(5/2)) = [sqrt(33)]/2 or (x-(5/2)) = [-sqrt(33)]/2 x = (5/2)+(sqrt(33)/2 or x = (5/2) - [sqrt(33)]/2 =================== Cheers, Stan H.
 Linear-equations/92997: Graph compound or absolute value inequality. / X - 3Y/> or = 9 absolute value of x - 3Y is greater than or equal to 9.1 solutions Answer 67684 by stanbon(57387)   on 2007-08-16 18:53:45 (Show Source): You can put this solution on YOUR website!/ X - 3Y/> or = 9 ------------- This means (x-3y)>=9 or x-3y<=-9 Then: 3y<=x-9...............or 3y>=x+9 y <= (1/3)x-3.........or y>=(1/3)x+3 ------------------ ---------- This is the graph of the EQUALITIES. Cheers, Stan H.
 Exponents/92920: Divide: 4x^2-2x-2/x-11 solutions Answer 67616 by stanbon(57387)   on 2007-08-16 06:57:16 (Show Source): You can put this solution on YOUR website!Divide: 4x^2-2x-2/x-1 --------- Factor where you can. [2(2x^2-x-1)]/(x-1) =[2(2x+1)(x-1)]/(x-1) Cancel factors common to numerator and denominator to get: =[2(2x+1)] ============== Cheers, Stan H.
 Linear_Algebra/92921: Given r(x)=7x-22 and t(x)=x^2+3, express the sum (r+t)(x)1 solutions Answer 67615 by stanbon(57387)   on 2007-08-16 06:53:57 (Show Source): You can put this solution on YOUR website!Given r(x)=7x-22 and t(x)=x^2+3, express the sum (r+t)(x) ------------------ (r+t)(x) = r(x)+t(x) = 7x-22 + x^2+3 = x^2+7x-19 ============= Cheers, Stan H.
 Functions/92922: What is the range for the function y=-2x^2+4x1 solutions Answer 67614 by stanbon(57387)   on 2007-08-16 06:50:31 (Show Source): You can put this solution on YOUR website!What is the range for the function y=-2x^2+4x ----------- It's a parabola opening downward so you have to find the vertex or use x=-b/2a to find the x-coordinate of the vertex and then the corresponding y-value. x = -b/2a = -4/(2*-2) = 1 f(1) = -2+4 = 2 So the range is " all Real Numbers less than of equal to 2". ------------------ =============== Cheers, Stan H.
 Quadratic_Equations/92889: I'm really glad you're here. Math is just not my thing, obviously, but I'm glad its yours. Here it is: 1. The approximate distance it takes to stop a car, based on the speed the car is traveling, is given in the following chart: Miles per Hour Stopping Distance (ft) 25 62 35 106 45 161 50 195 55 228 65 306 a. Find the quadratic function based on the stopping distance for 55 mph and 65 mph and the fact that at 0 mph the stopping distance is 0 feet. b. Use that equation to predict the stopping distance for 55 mph and 65 mph and compare them with the distances given in the chart. c. If the equation continues to be valid for higher speeds, how many feet would it take to stop a drag racer that reaches a speed of 230 mph? Thanks so much for your help! Let me know if you or someone else knows trig or calculus...that not my cup of tea either. 1 solutions Answer 67587 by stanbon(57387)   on 2007-08-15 20:51:14 (Show Source): You can put this solution on YOUR website!1. The approximate distance it takes to stop a car, based on the speed the car is traveling, is given in the following chart: Miles per Hour Stopping Distance (ft) 25 62 35 106 45 161 50 195 55 228 65 306 a. Find the quadratic function based on the stopping distance for 55 mph and 65 mph and the fact that at 0 mph the stopping distance is 0 feet. You have two points: (55,228) and (65,306) You are told the intercept is 0 EQUATION Form: y = ax^2+bx+c You have three points so you have three equations: 0 = 0^2a + 0b + c ;;;So c=0 228 =55^2a + 55b +0 306 =65^2a + 65b + 0 ------------ Now you have two equations with two unknowns so solve for a and for b: Comment: I'm going to use a calculator matrix method to speed this up: a = 0.0562237762 and b = 1.053146853 -------- So the EQUATION: f(x) = 0.056237762x^2+ 1.053146853x ------------------ b. Use that equation to predict the stopping distance for 55 mph and 65 mph and compare them with the distances given in the chart st.dis.= f(55) = 228.04 ft st.dis.= f(65) = 306.06 ft. ------------------------------- c. If the equation continues to be valid for higher speeds, how many feet would it take to stop a drag racer that reaches a speed of 230 mph? st.dis =f(230) = 3217.2 ft ---------------- Thanks so much for your help! Let me know if you or someone else knows trig or calculus...that not my cup of tea either. I suggest you post your problems. I'm sure amoung the 600 responders someone knows trig and/or calculus. =============== Cheers, Stan H.
 Distributive-associative-commutative-properties/92883: can you name the property illustrated by each 1.x + y = y + x 2.k + 0 = k 1 solutions Answer 67586 by stanbon(57387)   on 2007-08-15 20:22:16 (Show Source): You can put this solution on YOUR website!can you name the property illustrated by each 1.x + y = y + x The communtative property of addition. --------------------- 2.k + 0 = k The additive identity property. ----------------------- Cheers, Stan H.
 Points-lines-and-rays/92877: I am trying to show the conjecture is false by finding a counterexample. The square of the sum of two numbers is equal to the sum of the squares of the two numbers. That is, (a+b)^2= a^2+b^2. I have absolutely no clue of how to even begin to work this problem because I do not have a book, this is a workbook. 1 solutions Answer 67585 by stanbon(57387)   on 2007-08-15 20:20:23 (Show Source): You can put this solution on YOUR website!Is 2^2 + 3^2 equal to (2+3)^2 ? Yes, if 4+9 = 25 But it doesn't. ----------- That is called a "counterexample" Cheers, Stan H.
 Points-lines-and-rays/92882: I need to complete the conjecture based on the pattern that I see in this specific cases. Conjecture: For any number two numbers a and b, the product of (a+b) and (a-b) is always equal to _?_ (2+1)*(2-1)=3=2^2-1^2 (4+2)*(4-2)=12=4^2-2^2 (3+2)*(3-2)=5=3^2-2^2 (6+3)*(6-3)=27=6^2-3^2 I have no clue on how to do this one!! Please help!!!!!1 solutions Answer 67584 by stanbon(57387)   on 2007-08-15 20:16:26 (Show Source): You can put this solution on YOUR website!For any number two numbers a and b, the product of (a+b) and (a-b) is always equal to _?_ (2+1)*(2-1)=3=2^2-1^2 (4+2)*(4-2)=12=4^2-2^2 (3+2)*(3-2)=5=3^2-2^2 (6+3)*(6-3)=27=6^2-3^2 (a+b)*(a-b) = a^2-b^2 ------------ You could check this using FOIL. ======================== Cheers, Stan H.
 Trigonometry-basics/92878: This question is from textbook Algebra and Trigonometry Find all roots of the polynomial x cube-x squared+16x-16.1 solutions Answer 67582 by stanbon(57387)   on 2007-08-15 20:12:14 (Show Source): You can put this solution on YOUR website!Find all roots of the polynomial x cube-x squared+16x-16. x^3-x^2+16x-16 Since the coefficients add up to zero x=1 is a root and x-1 is a factor. Use synthetic division to find the other factors and roots. ------------------------ 1)....1....-1....16....-16 .......1.....0.....16..|..0 Remainder is zero because 1 is a root. Quotient is x^2+16 ------------------- Factoring x^2+16 you get (x+4i)(x-4i) ----------------------- All the roots are: x=1, x= 4i, x= -4i ================== Cheers, Stan H.
 Trigonometry-basics/92873: This question is from textbook Algebra and Trigonometry The period of a simple pendulum is directly proportional to the square root of its length. If a pendulum has a length of 6 feet and a period of 2 seconds, to what length should it be shortened to achieve a 1 second period?1 solutions Answer 67580 by stanbon(57387)   on 2007-08-15 20:06:45 (Show Source): You can put this solution on YOUR website!The period of a simple pendulum is directly proportional to the square root of its length. If a pendulum has a length of 6 feet and a period of 2 seconds, to what length should it be shortened to achieve a 1 second period? ------------- Period = k(length)^2 If P = 2 sec and length = 6, find "k". 2 = k (6)^2 k = 2/36 k = 1/18 EQUATION for this pendulum: Period = (1/18)(length)^2 -------------- If the period is 1 second find the length: 1 = (1/18)(length)^2 length^2 = 18 length = 3sqrt(2) ft. =========== Cheers, Stan H.