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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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>Next

 Trigonometry-basics/722988: Use the trigonometric substitution to write the algebraic equation as a trigonometric equation of θ, where −π/2 < θ < π/2. (4 = sqrt (64 − x^2)) , x = 8 sin θ 4=? Find sin θ and cos θ. sin θ= ? cos θ=?1 solutions Answer 442971 by stanbon(57219)   on 2013-03-06 21:55:49 (Show Source): You can put this solution on YOUR website!Use the trigonometric substitution to write the algebraic equation as a trigonometric equation of θ, where −π/2 < θ < π/2. (4 = sqrt (64 − x^2)) , x = 8 sin θ 16 = 64-x^2 x^2 = 32 x = 4sqrt(2) or x = -4sqrt(2) ----- Substitute for "x": 8sin(theta) = 4sqrt(2) or 8sin(theta) = -4sqrt(2) --------------------- sin(theta) = sqrt(2)/2; and cos(theta) = sqrt(2/2) in QI or sin(theta) = -sqrt(2)/2 and cos(theta) = sqrt(2)/2) in QIV ====================== Find sin θ and cos θ. sin θ= ? cos θ=? ====== Cheers, Stan H.
 test/722990: Johnny says that if a family has two children, then. the only possibilities are two boys, two girls, or one boy and one girl. Because there are only three possibilities, Johnny claims the probability of having two boys is 1/3. Is Johnny correct? Why or why not?1 solutions Answer 442970 by stanbon(57219)   on 2013-03-06 21:47:47 (Show Source): You can put this solution on YOUR website!Johnny says that if a family has two children, then. the only possibilities are two boys, two girls, or one boy and one girl. Because there are only three possibilities, Johnny claims the probability of having two boys is 1/3. Is Johnny correct? Why or why not? ---- No. The possible arrangements are: bb ; bg ; gb ; gg --- Each has probability 1/4 ============================= Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/722989: A small business buys a computer for \$4900. After 4 years the value of the computer is expected to be \$200. For accounting purposes the business uses straight-line depreciation (this means that if V is the value of the computer at time t, then a linear equation is used to relate V and t) to assess the value of the computer at a given time. (a) Find a linear equation that models the value V of the computer t years since its purchase.1 solutions Answer 442969 by stanbon(57219)   on 2013-03-06 21:45:46 (Show Source): You can put this solution on YOUR website!A small business buys a computer for \$4900. After 4 years the value of the computer is expected to be \$200. For accounting purposes the business uses straight-line depreciation (this means that if V is the value of the computer at time t, then a linear equation is used to relate V and t) to assess the value of the computer at a given time. (a) Find a linear equation that models the value V of the computer t years since its purchase. --- You have two points relating time and value: (0,4000) and (4,200) --- slope = (200-4000)/4 = -3800/4 = -950 intercept = f(0) = 4000 ----- Equation: value(x) = -950x + 4000 where x is the number of years. ---------- Cheers, Stan H. =================
 test/722980: log[10](x)+log[10](3x+55)=2 How do you solve this?1 solutions Answer 442966 by stanbon(57219)   on 2013-03-06 21:40:40 (Show Source): You can put this solution on YOUR website!log[10](x)+log[10](3x+55)=2 ----- log[x(3x+55)] = 2 ---- 3x^2+55x = 10^2 --- 3x^2 + 55x -100 = 0 ---- x = [-55 +- sqrt(55^2-4*3*-100)]/6 ---- x = 5/3 or x = -20 --- Usable solution: x = 5/3 ================== Cheers, Stan H. ==================
 Average/722981: gerald had scores of 80,92,89,and 95 on four exams in his algebra class. what score will he need on his fifth exam to have an overall average of 901 solutions Answer 442965 by stanbon(57219)   on 2013-03-06 21:33:37 (Show Source): You can put this solution on YOUR website!gerald had scores of 80,92,89,and 95 on four exams in his algebra class. what score will he need on his fifth exam to have an overall average of 90 ---- Let the 5th exam score be "x": (80+92+89+95+x)/5 = 90 --- 356+x = 450 x = 94 =========== Cheers, Stan H. =============
 Probability-and-statistics/722361: Swift Auto Service has taken advantage of some of the results you provided (HW #4) and has improved their process. Their oil & lube “service time per car” still follows a normal distribution, but now with a mean of 30 minutes per car, and a standard deviation of 4.0 minutes. b) if you select a random sample of 16 oil & lube jobs, what is the probability the sample mean “service time” from that group will be shorter than 28 minutes ? 1 solutions Answer 442806 by stanbon(57219)   on 2013-03-06 07:31:51 (Show Source): You can put this solution on YOUR website!follows a normal distribution, but now with a mean of 30 minutes per car, and a standard deviation of 4.0 minutes. b) if you select a random sample of 16 oil & lube jobs, what is the probability the sample mean “service time” from that group will be shorter than 28 minutes ? ----- x-bar = 28 min -------------------- z(28) = (28-30)/[4/sqrt(16)) = -2 ---- P(x-bar < 28) = P(z < -2) = 0.0228 ============== Cheers, Stan H. ==============
 Probability-and-statistics/722362: Swift Auto Service has taken advantage of some of the results you provided (HW #4) and has improved their process. Their oil & lube “service time per car” still follows a normal distribution, but now with a mean of 30 minutes per car, and a standard deviation of 4.0 minutes. c) how large would your random sample need to be, so that your sample mean “service time” would be 99% likely to be within 1 minute of the true population mean service time ?1 solutions Answer 442805 by stanbon(57219)   on 2013-03-06 07:27:29 (Show Source): You can put this solution on YOUR website!Swift Auto Service has taken advantage of some of the results you provided (HW #4) and has improved their process. Their oil & lube “service time per car” still follows a normal distribution, but now with a mean of 30 minutes per car, and a standard deviation of 4.0 minutes. c) how large would your random sample need to be, so that your sample mean “service time” would be 99% likely to be within 1 minute of the true population mean service time ? ----- Since E = z*s/sqrt(n), n = [z*s/E]^2 = [2.5758*4/1]^2 = 106 when rounded down ----- Cheers, Stan H.
 Probability-and-statistics/722367: if a 5 questions have 4 answers what is the possibility of choices ?1 solutions Answer 442804 by stanbon(57219)   on 2013-03-06 07:23:03 (Show Source): You can put this solution on YOUR website!if a 5 questions have 4 answers what is the possibility of choices ? ----- Each one of the 5 quesstions has 4 possible answers. Ans: 4^5 = 1024 choices ============== Cheers, Stan H.
 Probability-and-statistics/722435: 1. Joe has been given a 10 multiple-choice question in his Geography class. Each question has 5 answers, of which only one is correct. Since Joe has not studied for the quiz, he plans in guessing all of the answers. What is the probability that he answers at least one question correctly?1 solutions Answer 442803 by stanbon(57219)   on 2013-03-06 07:21:16 (Show Source): You can put this solution on YOUR website!1. Joe has been given a 10 multiple-choice question in his Geography class. Each question has 5 answers, of which only one is correct. Since Joe has not studied for the quiz, he plans in guessing all of the answers. What is the probability that he answers at least one question correctly? ----- Binomial Problem with n = 10 ; p(correct) = 1/5 ; p(wrong) = 4/5 ------------------- P(at least one correct) = 1 - P(none correct) = 1 - (4/5)^10 = 0.8926 --------------- Cheers, Stan H. ==============
 Probability-and-statistics/722567: This question is on normal distribution, I need some help understanding how to solve these problems. I am taking a NCPace course through the military and do not have an actual instructor to ask for help. Determine the answers to the following questions which relate to a sample of students who took a physics test. Their scores were normally distributed with a mean of 70 and a standard deviation of 10. What percentage of students made 90 on the test? Using the rules of normal distribution my answer would be 1.18%. I just don't know if I am going about solving this the correct way. Thank you in advance. Respectfully, STG2(SW/EXW)Purvis, Sarah M. , USN1 solutions Answer 442802 by stanbon(57219)   on 2013-03-06 07:18:22 (Show Source): You can put this solution on YOUR website!scores were normally distributed with a mean of 70 and a standard deviation of 10. What percentage of students made 90 on the test? Using the rules of normal distribution my answer would be 1.18%. I just don't know if I am going about solving this the correct way. ------ Find the z-score of 90. z(90) = (90-70)/10 = 2 ---- Then P(x > 90) = P(z > 2) Using a TI-84 calculator I get: P(z > 2) = normalcdf(2,100) = 0.0228 or 2.28% ------------------ Let me know if you need further help. Cheers, Stan H.
 Travel_Word_Problems/722374: A passenger train leaves the train depot four hours after the cargo train traveling in the same direction leaves the same depot the cargo train is traveling 10 mph slower than the passenger train given that the passenger train the freight train passes the freight train in two hours find the speed of each train1 solutions Answer 442735 by stanbon(57219)   on 2013-03-05 20:25:50 (Show Source): You can put this solution on YOUR website!A passenger train leaves the train depot four hours after the cargo train traveling in the same direction leaves the same depot ----------------------------------------------------------- the cargo train is traveling 10 mph slower than the passenger train ----------------------------------------------------------- given that the passenger train the freight train passes the freight train in two hours find the speed of each train --------------------- Passenger train DATA time = 2 hrs ; rate = r + 10 mph ; distance = 2r + 20 miles ----------------- Cargo train DATA: time = 6 hrs ; rate = r mph ; distance = 6r miles -------- Equation: distance = distance 6r = 2r+20 4r = 20 r = 5 mph (cargo train rate) r+10 = 15 mph (passenger train rate) ============= Cheers, Stan H.
 Linear-equations/722376: I can't figure out how to do this problem. The sum of three times a number and 7 more than the number is the same as the difference between-11 and twice the number. What is the number?1 solutions Answer 442729 by stanbon(57219)   on 2013-03-05 19:31:03 (Show Source): You can put this solution on YOUR website!The sum of three times a number and 7 more than the number is the same as the difference between-11 and twice the number. What is the number? ---- 3x + (3x+7) = -11-2x ------- 10x+7 = -11-2x 12x = -18 x = -3/2 ============== Cheers, Stan H. ==============
 Miscellaneous_Word_Problems/722363: Payrolls for the 3 highest paid baseball teams (the Yankees, Red Sox, and Angels) for 2006 totaled 418 million. If the team payroll for the Yankees is 75 million dollars higher than the Red Sox and the Red sox is 17 million dollars higher than the Angels, then what was the 2006 payroll for each team? My work: Yankees= 75+R (R stands for Red Sox) Red Sox= 17+A (A stands for Angels) Angels= X X+17+X+75+X=418 X=108.666666667 or 108.67 Angels= 108.67 Red Sox= 125.67 Yankees= 200.67 When added together it comes out to: 435.01 I am close to the 418, I just can't figure out where i messed up. I assume in my equation. Thanks1 solutions Answer 442728 by stanbon(57219)   on 2013-03-05 19:24:37 (Show Source): You can put this solution on YOUR website! Payrolls for the 3 highest paid baseball teams (the Yankees, Red Sox, and Angels) for 2006 totaled 418 million. If the team payroll for the Yankees is 75 million dollars higher than the Red Sox and the Red sox is 17 million dollars higher than the Angels, then what was the 2006 payroll for each team? My work: Yankees= 75+R = 75+17+A = 92+A (R stands for Red Sox) Red Sox= 17+A (A stands for Angels) Angels= X ------ Equation: A + 17+A + 92+A = 418 3A + 109 = 418 3A = 309 A = 103 ---------- etc. Cheers, Stan H.
 Triangles/722346: The segment connecting point A(1,2) to point B(4,2) is one side of a 30º-60º-90º triangle, , but you do not know which side. It could be the shorter leg, the longer leg or the hypotenuse. How many 30º-60º-90º triangles can be drawn under these conditions? For each triangle, state: • the coordinates of point C. • the lengths of the 3 sides. I have all the lengths of all sides of every triangle and the coordinate C for every triangle except four. I have all 12 possible triangles, but when AB is the hypotenuse, I cannot find the coordinate of C. Please help me find a way or a formula to solve for coordinate C when I have all side lengths and two other points? Thank you very much!1 solutions Answer 442725 by stanbon(57219)   on 2013-03-05 19:08:42 (Show Source): You can put this solution on YOUR website!The length from A to B is 3 --- If AB is the hypoteuse, the side opposite the 30 degree angle is (1/2)(3 = 3/2 ------------------------------ The side opposite the 60 degree angle is [sqrt(3)/2]*3 = (3/2)sqrt(3) ==================================================== Cheers, Stan H.
 Polynomials-and-rational-expressions/722349: Please factor this polynomial so that it is in the FOIL solution: 15c+351 solutions Answer 442724 by stanbon(57219)   on 2013-03-05 18:57:30 (Show Source): You can put this solution on YOUR website!Please factor this polynomial so that it is in the FOIL solution: 15c+35 ---- Note: FOIL relates to the multiplying of two binomial of the factoring of a quadratic. It does not apply to your problem. ---- 15c+35 = 5(3c+7) ================= Cheers, Stan H. =================
 Average/722351: if john makes a 77% on his test and ansewered 34 questions correct, how many questions were on the test1 solutions Answer 442723 by stanbon(57219)   on 2013-03-05 18:54:03 (Show Source): You can put this solution on YOUR website!if john makes a 77% on his test and ansewered 34 questions correct, how many questions were on the test ---- Let "x" be the number of questions. --- Equation: 0.77x = 34 ---- x = 34/0.77 --- x = 44 when rounded down =========================== Cheers, Stan H.
 Percentage-and-ratio-word-problems/722345: I have some small candies i want to sell in packages of 15 candies for \$0.25 per package. how much would I charge for 60 candies?1 solutions Answer 442722 by stanbon(57219)   on 2013-03-05 18:50:53 (Show Source): You can put this solution on YOUR website!I have some small candies i want to sell in packages of 15 candies for \$0.25 per package. how much would I charge for 60 candies? ------------------- Use a proportion: cost/number = cost/number c/60 = 25/15 ---- c = 60(25/15) = 100 --- Cost for 15 is \$1.00 ------------------------- Cheers, Stan H. =============
 Mixture_Word_Problems/722341: How many liters of 70% acid solution must be mixed with 10% acid solution to get 480 L of a 60% acid solution1 solutions Answer 442721 by stanbon(57219)   on 2013-03-05 18:40:41 (Show Source): You can put this solution on YOUR website! How many liters of 70% acid solution must be mixed with 10% acid solution to get 480 L of a 60% acid solution ------ Using 2 variables: Quantity Eq::: x + y = 480 L Acid Eq::::: 70x+10y = 60*480 -------------------------------- Modify for elimination: 70x + 70y = 70*480 70x + 10y = 60*480 ------------------- Subtract and solve for "y": 60y = 10*480 ----- y = 80 L (amt. of 10% solution needed) ---- x = 400 L (amt. of 70% solution needed) ========================================== Cheers, Stan H. =========
 Quadratic_Equations/722335: Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. f(x)=x^2+2x-91 solutions Answer 442719 by stanbon(57219)   on 2013-03-05 18:29:53 (Show Source): You can put this solution on YOUR website!Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. f(x)=x^2+2x-9 ---- Since the coefficient of x^2 is positive the function opens up, so it has a minimum point. ---- Minimum occurs when x = -b/(2a) = -2/2 = -1 ---- f(-1) = (-1)^2 + 2*-1 - 9 = 1 +2-1 = 2 --- Minimum point (-1,2) ======================= Cheers, Stan H. =======================
 Angles/722327: hey my son has a math problem and im not sure how to solve and he does not have his book to look up. he is in 7th grade pre algebra and it shows an angle on a grid we will say if you can please help us thanks for your time1 solutions Answer 442716 by stanbon(57219)   on 2013-03-05 18:19:21 (Show Source): You can put this solution on YOUR website!I'll give it a try if you can send a clear explanation of the problem. Cheers, Stan H.
 logarithm/721370: 4logm-logn1 solutions Answer 442696 by stanbon(57219)   on 2013-03-05 16:11:46 (Show Source): You can put this solution on YOUR website!4logm-logn ---- = log(m^4)-log(n) --- = log[m^4/n] ------------------ Cheers, Stan H. ==================
 logarithm/721371: The value of a new car depreciates at a rate of 34% each year from the year it is driven off the lot of the dealership. If the value of the car was \$33,000 the year it was bought, how long will it be until the car is worth only \$4,000. Write an exponential model for the value of the car, V(t), in dollars, as a function of time, t, years since the car was purchased. b) Determine the year in which the value of the car isworth only \$2000. Set up the equation to be solved then solve this using logarithm. You can check your solution graphically. Round to two decimals1 solutions Answer 442695 by stanbon(57219)   on 2013-03-05 16:10:01 (Show Source): You can put this solution on YOUR website!The value of a new car depreciates at a rate of 34% each year from the year it is driven off the lot of the dealership. a) If the value of the car was \$33,000 the year it was bought, How long will it be until the car is worth only \$4,000. ---------- Write an exponential model for the value of the car, V(t), in dollars, as a function of time, t, years since the car was purchased. V(t) = 33,000(0.66)^t Solve for "t": 33,000(0.66)^t = 4000 0.66^t = 4/33 Take the log: t = log(4/33)/log(0.66) t = 5.08 years ------------------------- b) Determine the year in which the value of the car is worth only \$2000. Set up the equation to be solved then solve this using logarithm. You can check your solution graphically. Round to two decimals 33,000(0.66)^t = 2000 0.66^t = 2/33 t = log(2/33)/log(0.66) t = 6.737 ------------- Cheers, Stan H. =============
 logarithm/722248: log base 4 of 5 + log base 4 of x = log 4 of 601 solutions Answer 442692 by stanbon(57219)   on 2013-03-05 15:48:42 (Show Source): You can put this solution on YOUR website!log base 4 of 5 + log base 4 of x = log 4 of 60 ------- log4(5) + log4(x) = log4(60) ---- log4(5x) = log4(60) ------ 5x = 60 x = 12 ------------- Cheers, Stan H. =============
 Travel_Word_Problems/722249: Car A starts at an initial position at 19 m and travels to a final position at 72 m . Car B starts at an initial position at 38m and travels to a final position at 120 m . Which car traveled the shortest distance?1 solutions Answer 442691 by stanbon(57219)   on 2013-03-05 15:46:38 (Show Source): You can put this solution on YOUR website!Car A starts at an initial position at 19 m and travels to a final position at 72 m . ------------------------------- Car B starts at an initial position at 38m and travels to a final position at 120 m . ------------------------------- Which car traveled the shortest distance? ---------- A distance: 72-19 = 53 m B distance: 120-38 = 82 m ------------------------------ Cheers, Stan H. ================
 Polynomials-and-rational-expressions/722247: simplify the expression (4^-5(64)^3)^21 solutions Answer 442689 by stanbon(57219)   on 2013-03-05 15:42:40 (Show Source): You can put this solution on YOUR website! (4^-5(64)^3)^2 --------------------------- = ((1/4)^5 (2^6)^3)^2 --------- = ((1/2^10)(2^18))^2 ---- = (2^8)^2 ---- = 2^16 ----- = 65536 =============== Cheers, Stan H. ===============
 Finance/722013: Find the balance in the accoubt: \$2,400 principal earning 2%, compounded quarterly, after 7 years1 solutions Answer 442586 by stanbon(57219)   on 2013-03-04 22:03:55 (Show Source): You can put this solution on YOUR website! Find the balance in the account: \$2,400 principal earning 2%, compounded quarterly, after 7 years ------ A(t) = P(1+(r/n))^(nt) ------ A(7) = 2400(1+(0.02/4))^(4*7) ------ A(7) = 2400*1.1499 ---- A(7) = \$2759.69 ================= Cheers, Stan H.
 Inequalities/721800: My question is a word problem so ill just type it: Word Problem: "The height of a triangle is (2x+3)inches, and the corresponding base is 5 inches. If the area of the triangle is less than 55 square inches, create and solve the inequality to find the value of x. what is the maximum height of the triangle?" A= 1/2b*h so would it be 5(2x+3)over 2? would I destribute the 5 to the 2x+3? & wouldnt that at the same time find the max height? if i resolved the equation?1 solutions Answer 442514 by stanbon(57219)   on 2013-03-04 16:25:04 (Show Source): You can put this solution on YOUR website!"The height of a triangle is (2x+3)inches, and the corresponding base is 5 inches. If the area of the triangle is less than 55 square inches, create and solve the inequality to find the value of x. what is the maximum height of the triangle?" ---- Area = (1/2)(base)(height) ------ 55 > (1/2)*5*(2x+3) ----- 22 > 2x+3 2x < 19 x < 9.5 inches ---- Max height < 2x+3 = 22 ---- Max height is not an exact number. Cheers, Stan H.
 Complex_Numbers/721801: Simplify: (5)/(3-i) stuck, need help. 1 solutions Answer 442512 by stanbon(57219)   on 2013-03-04 16:20:18 (Show Source): You can put this solution on YOUR website!answered
 Trigonometry-basics/721787: Hello tutor, how do I solve the following trig function using the Factor Formula method, where theta is between -90degrees and +90 degrees: 2cos(θ+30)cos(θ-30) = 1 Many thanks 1 solutions Answer 442508 by stanbon(57219)   on 2013-03-04 16:04:30 (Show Source): You can put this solution on YOUR website!how do I solve the following trig function using the Factor Formula method, where theta is between -90degrees and +90 degrees: 2cos(θ+30)cos(θ-30) = 1 ---- Formula: 2cos(A)cos(B) = cos(A+B)+cos(A-B) ----- Your problem: cos[theta+30+theta-30] + cos[(theta+30)-(theta-30)] = 1 ----- cos[2theta] + cos(60)= 1 --- cos(2theta) + (1/2) = 1 ----- cos(2theta) = 1/2 ----- 2theta = 60 degrees or 2theta = -60 --- theta = 30 degrees or theta = -30 ==================================== Cheers, Stan H. ===============
 Inequalities/721786: 4x + 3y = 12 for y1 solutions Answer 442502 by stanbon(57219)   on 2013-03-04 15:45:11 (Show Source): You can put this solution on YOUR website!4x + 3y = 12 for y ---- 3y = -4x + 12 ----- y = (-4/3)x + 4 ====================== Cheers, Stan H. ======================
 Polynomials-and-rational-expressions/721783: what would be the lowest terms for x to the 3rd - 8 over x - 41 solutions Answer 442501 by stanbon(57219)   on 2013-03-04 15:42:22 (Show Source): You can put this solution on YOUR website!what would be the lowest terms for x to the 3rd - 8 over x - 4 -------- (x^3-8)/(x-4) is a quadratic plus some remainder. ---- Using synthetic division I get: 4)....1....0....0....-8 .......1....1....1...|..-7 Quotient: x^2 + x + 1 Remainder: -7 ===================== Cheers, Stan H.