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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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 Quadratic-relations-and-conic-sections/174252: I solved x^2-4 = 0: x = +2, x = -2 What other parabolas have the same solutions? I know 4 - x^2 = 0 is another, but I can't figure how to find any others. thx 1 solutions Answer 129181 by stanbon(57967)   on 2008-12-21 14:56:47 (Show Source): You can put this solution on YOUR website!f(x) = a(x-2)(x+2) has the same solutions for any value of "a" except a = 0. ======================= Cheers, Stan H.
 Functions/174251: log378= 2.5775 ------------------- 5In(r) + 3In(t) - 4In(s) = lnr^5 + lnt^3 - lns^4 = ln[r^5*t^3/s^4] ---------------------------- In(x) +In(x-2) = In(x+2) + In(x-3) g(x) = xto the 2nd power + 3 and h(x) = x+ 3 ______ 2 Find (h o g)(x)1 solutions Answer 129180 by stanbon(57967)   on 2008-12-21 14:51:45 (Show Source): You can put this solution on YOUR website!log378= 2.5775 ------------------- 5In(r) + 3In(t) - 4In(s) = lnr^5 + lnt^3 - lns^4 = ln[r^5*t^3/s^4] ---------------------------- In(x) +In(x-2) = In(x+2) + In(x-3) = ln[x(x-2)] = ln[(x+2)(x-3)] x(x-2) = (x+2)(x-3) x^2 - 2x = x^2 -x -6 x = 6 -------------------------------- g(x) = x^2+3 and h(x) = (x+ 3)/2 Find (h o g)(x) = h[x^2+3] = [(x^2+3)+3]/2 = [x^2+6]/2 =============================== Cheers, Stan H.
 Complex_Numbers/174249: I have a complex fraction: This fraction is the numerator: x/x+1 The denominator is: 1/x(exponent 2)-1 MINUS 1/x-1 Im pretty sure you have to find the LCD, but I don't know where to go from here. Thank you for any help.1 solutions Answer 129177 by stanbon(57967)   on 2008-12-21 14:41:41 (Show Source): You can put this solution on YOUR website!This fraction is the numerator: x/x+1 The denominator is: 1/x(exponent 2)-1 MINUS 1/x-1 --------------------------- [x/(x+1)] / [1/(x^2-1) - 1/(x-1)] = [x/(x+1)] / [1 -(x+1)] / (x^2-1)] = [x/(x+1)] / [-x / (x^2-1)] Invert the denominator and multiply : = [x/(x+1)] / [(x^2-1) /-x ] Cancel where you can to get: = [1/1] / [(x-1)/(-1)] = (x-1)/(-1) = 1-x ============= Cheers, Stan H.
 Linear-systems/174230: A hockey puck leaves the blade of a hockey stick, bounces off a wall, and travels in a new direction. a) Write and equation that models the path of the ordered pairs of (-4,0) and (0,8). b) Write and equation that models the path of the ordered pairs of (0,8) and (-4,16). c) Does the path of the puck form a right angle? Explain.1 solutions Answer 129171 by stanbon(57967)   on 2008-12-21 13:31:59 (Show Source): You can put this solution on YOUR website!a) Write and equation that models the path of the ordered pairs of (-4,0) and (0,8). slope = (8-0)/(0--4) = 2 intercept: Since f(0) = 8,8 is the intercept Equation: y = 2x + 8 ----------------------------------------- b) Write and equation that models the path of the ordered pairs of (0,8) and (-4,16). slope = (16-8)/(-4-0) = 8/-4 = -2 intercept: since f(0) = 8, the intercept is . Equation: y = -2x+8 ----------------------------------------- c) Does the path of the puck form a right angle? Explain. No, because the product of the slopes is not -1. ==================================== Cheers, Stan H.
 Permutations/174238: n! _______ 2!(n-2)! I understand that 5! is 5*4*3*2*1 I do not understand how to figure n! I understand that 2! is 2*1 and (n-2)! is (n-2)*(n-1) which would make the problem n! ________________ 2*1(n-2)*(n-1) Atleast I think that's what the problem would be, but now what? What do I do with the n! ??? I'm so confused. PLEASE HELP!! Thank you in advance!1 solutions Answer 129170 by stanbon(57967)   on 2008-12-21 13:21:18 (Show Source): You can put this solution on YOUR website!n! _______ 2!(n-2)! -------------------- = [n(n-1)(n-2)!] / [2!*(n-2)!] Cancel the (n-2)! that is common to the numerator and the denominator to get: = [n(n-1)]/2 ================= Cheers, Stan H.
 Volume/174228: What would the volume of the region between two cylinders be if the largerst cylinder radius is 12 and the smaller radius is 9. Both of the cylinders have a height of 20 inches.1 solutions Answer 129157 by stanbon(57967)   on 2008-12-21 09:35:06 (Show Source): You can put this solution on YOUR website!What would the volume of the region between two cylinders be if the largerst cylinder radius is 12 and the smaller radius is 9. Both of the cylinders have a height of 20 inches. -------------- Volume of larger : (pi)*12^2*20 cu. in Volume of inner : (pi)*9^2*20 cu. in -------------------------------------- Volume between = (pi)*20[12^2-9^2) cu in = 1260pi cu in ==================== Cheers, Stan H.
 Numbers_Word_Problems/174226: Paul jogged half as many miles (mi) as Lucy and 7 less than Isaac. If the three ran a total of 23 miles, how far did each of them run?1 solutions Answer 129156 by stanbon(57967)   on 2008-12-21 09:30:22 (Show Source): You can put this solution on YOUR website!Paul jogged half as many miles (mi) as Lucy and 7 less than Isaac. If the three ran a total of 23 miles, how far did each of them run? ------------- Equations: p = (1/2) L p = I - 7 p + I + L = 23 ----------------- Rearrange: p + 0 - (1/2)L = 0 p - I + 0 = -7 p + I + L = 23 --------------------- Solve the system by any means you know to get: p = 4 miles I = 11 miles L = 8 miles ========================= Another way to find the solution: Equations: p = (1/2) L p = I - 7 p + I + L = 23 --------------- Rearrange to get: L = 2p I = p+7 Equations: p = (1/2) L p = I - 7 p + I + L = 23 ---- Substitute into p + I + L = 23 to get: p + p+7 + 2p = 23 4x + 7 = 23 4x = 16 p = 4 miles (paul) L= 2p = 8 miles (Lucy) I= p + 7 = 4+7 = 11 miles (Isaac) --------------------------------------- Cheers, Stan H.
 Miscellaneous_Word_Problems/174218: how do you solve x^2-9/x+2*x^2-4/x-31 solutions Answer 129155 by stanbon(57967)   on 2008-12-21 09:24:27 (Show Source): You can put this solution on YOUR website![x^2-9/x+2] * [x^2-4/x-3] Factor: [(x-3)(x+3)/(x+2)] * [(x-2)(x+2)/(x-3)] Cancel factors common to a numerator and a denominator to get: =[(x+3)/1] * [(x-2)/1] = (x-3)(x-2) =================== Cheers, Stan H.
 Graphs/174225: How would I graph the line with a slope of -5 passing through the point (-3, -5)Ty in advance, Judy 1 solutions Answer 129154 by stanbon(57967)   on 2008-12-21 09:19:31 (Show Source): You can put this solution on YOUR website! How would I graph the line with a slope of -5 passing through the point (-3, -5)Ty in advance, ------------- The slope always tells you what happens to y when x increases by one. ------------ So y decreases 5 when x increases by one. -------------- 1st: Plot the point (-3,-5) 2nd: Move your pencil from that point one to the right and then down 5 to the point (-2,-10). 3rd: Draw your graph as a line thru those two points. ============= ============= Cheers, Stan H.
 Linear-equations/174206: Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 60 mph and train B is traveling at 80 mph. Train A passes a station at 4:10am. If train B passes the same station at 4:22am. at what time will train B catch up to train A? 1 solutions Answer 129145 by stanbon(57967)   on 2008-12-20 22:31:35 (Show Source): You can put this solution on YOUR website!Trains A and B are traveling in the same direction on parallel tracks. ----------------------------- Train A is traveling at 60 mph and train B is traveling at 80 mph. ----------------------------- Train A passes a station at 4:10am. If train B passes the same station at 4:22am. ------------- At what time will train B catch up to train A? -------------------------------------- Train A DATA: rate = 60 mph ; distance = x miles ; time = x/60 hours -------------- Train B DATA: rate = 80mph ; distance = x miles ; time = x/80 hours -------------- EQUATION: A time - B time = (12/60) hour x/60 - x/80 = 1/5 hr x/12 - x/16 = 1 (16x - 12x) = 12*16 4x = 12*16 x = 3*16 = 48 miles ===================== Cheers, Stan H.
 Equations/174209: divide Solve write as a single log A radioactive isotope has a halflife of 600 years. If 50g is on hand now, how much will be available in 1000 years? 1 solutions Answer 129144 by stanbon(57967)   on 2008-12-20 22:13:28 (Show Source): You can put this solution on YOUR website!divide Use synthetic division: 3)....1....0....1....0....2....7 .......1....3....10...30...92..|..283 Quotient: x^4 + 3x^3 + 10x^2 + 30x + 92 Remainder: 283 ========================================== Solve xlog(4) = log(12) x = log(12)/log(4) = 1.7925 =========================================== write as a single log log(x^3) - log(y^(1/3)) + log(z^4) = log[x^3*z^4/y^(1/3)] ============================================ A radioactive isotope has a halflife of 600 years. If 50g is on hand now, how much will be available in 1000 years? --- A(t) = Ao (1/2)^(t/600) A(1000) = 50*(1/2)^(1000/600) A(1000) = 50*0.31498 A(1000) = 15.749 grams ================================== Cheers, Stan H.
 Linear-equations/174193: This question is from textbook algebra 1 On a coordinate plane, draw a vertical line that passes through (5,3). b.List six points that are not on your line.1 solutions Answer 129122 by stanbon(57967)   on 2008-12-20 18:29:44 (Show Source): You can put this solution on YOUR website!On a coordinate plane, draw a vertical line that passes through (5,3) b.List six points that are not on your line. --------- List any six points points x is NOT 5. ========================================= Cheers, Stan H.
 Linear-equations/174194: This question is from textbook algebra 1 On a coordinate plane, draw a vertical line that passes through (5,3). c.How do you tell weather a point is on your line by looking at its coordinates?1 solutions Answer 129120 by stanbon(57967)   on 2008-12-20 18:23:46 (Show Source): You can put this solution on YOUR website!x must be 5. Cheers, Stan H.
 Linear-systems/174195: Which equation represents the line that passes through (0,0) and is parallel to the line passing through (2,3) and (6,1)? a) y= 1/2x b) y= -1/2x c) y= -2x d) y= 2x1 solutions Answer 129119 by stanbon(57967)   on 2008-12-20 18:21:40 (Show Source): You can put this solution on YOUR website!Which equation represents the line that passes through (0,0) and is parallel to the line passing through (2,3) and (6,1)? ------------- Since f(0)= 0, the intercept is 0. ---------- Those points yield a slope of (1-3)/(6-2) = -2/4 = -1/2 -------------- Ans: b ============= Cheers, Stan H. a) y= 1/2x b) y= -1/2x c) y= -2x d) y= 2x
 Linear-systems/174196: What is the equation of the line that passes through the given point and is perpendicular to the given line? i got y= -2x-3 I wasn't really understanding the problem and that's why i just want you to check my work. Thankyou so much!1 solutions Answer 129118 by stanbon(57967)   on 2008-12-20 18:12:50 (Show Source): You can put this solution on YOUR website!You didn't post the line or the point. Cheers, Stan H.
 expressions/174197: 1. A student pilot was required to fly to an airport and then return. The average speed on the way to the airport was 115mph, and the average speed returning was 172.5mph. Find the distance between the two airport if the total flying time was 5 hrs. 2.2x/3-11/2=-3/21 solutions Answer 129117 by stanbon(57967)   on 2008-12-20 18:08:49 (Show Source): You can put this solution on YOUR website!1. A student pilot was required to fly to an airport and then return. The average speed on the way to the airport was 115mph, and the average speed returning was 172.5mph. Find the distance between the two airports if the total flying time was 5 hrs. ------------------------------ To DATA: rate = 115 mph ; distance = x miles ; time = d/r = x/115 hrs ---------------------------- From DATA: rate = 172.5 mph ; distance = x miles ; time = d/r = x/172.5 hrs ---------------------------- Equation: time + time = 5 hrs. x/115 + x/172.5 = 5 (172.5x + 115x) = 115*172.5*5 287.5x = 115*172.5*5 x = 345 miles (distance between the airports) =============================================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/174173: a theather sold 478 tickets for a play . thickets cost \$20 for adults and \$13 for senior citizens.,if the total sreceips were \$6970, how many senior citizen tickets were sold?1 solutions Answer 129104 by stanbon(57967)   on 2008-12-20 15:34:02 (Show Source): You can put this solution on YOUR website!a theather sold 478 tickets for a play . thickets cost \$20 for adults and \$13 for senior citizens.,if the total receipts were \$6970, how many senior citizen tickets were sold? ------------------------- Quantity Equation: a + s = 478 Value Equation: 20a + 13s = 6970 ------------------------- 20a + 20s = 9560 20a + 13s = 6970 ------------------------ Subtract 2nd from 1st to get: 7s = 2590 370 s = 370 (# of senior tickets sold) ===================================== Cheers, Stan H.
 expressions/174168: if 10x-8=-28, evaluate 8x+101 solutions Answer 129098 by stanbon(57967)   on 2008-12-20 15:11:00 (Show Source): You can put this solution on YOUR website!if 10x-8=-28, evaluate 8x+10 -------------- 10x-8 = -28 10x = -20 x = -2 ---------- 8x = -16 8x+10 = -16+10 8x+10 = -6 =============== Cheers, Stan H.
 Equations/174160: -4*2+(1-2^)^ I worked this out and got -14. Could you help me with this? I think it is wrong, but am not sure. I do not know if I can check it. Thanks, Judy1 solutions Answer 129089 by stanbon(57967)   on 2008-12-20 12:55:00 (Show Source): You can put this solution on YOUR website!-4*2+(1-2^)^ Something is missing at the end of your posting. Cheers, Stan H.
 Linear-equations/174162: simplify: 1. -5/6(18y) 2. 3y-7[y-4(y-5)] 1 solutions Answer 129088 by stanbon(57967)   on 2008-12-20 12:53:12 (Show Source): You can put this solution on YOUR website!simplify: 1. (-5/6)(18y) = -5(3y) =-15y ============== 2. 3y-7[y-4(y-5)] = 3y - 7[y -4y+20] = 3y - 7[-3y+20] = 3y +21y - 140 = 24y - 140 ================ Cheers, Stan H.
 Mixture_Word_Problems/174077: some students simplify 2x^2-32/x-4 as 2x-8/x-4 =2x-8. choose values of x to mshow this is not true. Then simplify it correctly.1 solutions Answer 129081 by stanbon(57967)   on 2008-12-20 09:12:28 (Show Source): You can put this solution on YOUR website!The wrong way: 2x^2-32/x-4 as 2x-8/x-4 =2x-8 Example: Let x = 2 You would get 2*4-32 /2-4 = 2*2-8 8-32/-2 = 4-8 -24/-2 = -4 12 = -4 Which is wrong. ============================== The Right way: (2x^2-32)/(x-4) ------ = [2(x^2-16)]/(x-4) = [2(x-4)(x+4)]/(x-4) = 2(x+4) ============== Example: Let x = 2 You get (2*4-32)/(2-4) = 2(2+4) (8-32)/-2 = 2(6) -24/-2 = 12 12 = 12 Which is correct. ===================== Cheers, Stan H.
 Angles/174153: One angle in triangle FMU is one hundred eighty degrees. The difference between the measures of the other two angles is one degrees. What is the measure of each angle in triangle FMU?1 solutions Answer 129080 by stanbon(57967)   on 2008-12-20 08:39:43 (Show Source): You can put this solution on YOUR website!You cannot have a 180 degree angle in a triangle. The sum of the angles is always 180 but no one angle can be 180. Cheers, Stan H.
 Polynomials-and-rational-expressions/174155: I also need your help with this one: 3m^3+27m Thanks in advance1 solutions Answer 129079 by stanbon(57967)   on 2008-12-20 08:37:54 (Show Source): You can put this solution on YOUR website!3m^3+27m Common Factor: 3m(m^2 + 9) ================= Cheers, Stan H.
 Polynomials-and-rational-expressions/174154: Hello, I need some healp. How would you factor this completely? 6x^2y^2+12xy^2+12y^21 solutions Answer 129078 by stanbon(57967)   on 2008-12-20 08:36:27 (Show Source): You can put this solution on YOUR website!factor this completely? 6x^2y^2+12xy^2+12y^2 Common Factor: 6y^2(x^2 + 2x + 2) ------------------------ Cheers, Stan H.
 Functions/174147: This question is from textbook can you please let one more time please thank you in advance Evaluate the functions for the values of x given as 1, 2, 4, 8, and 16. Describe the differences in the rate at which each function changes with increasing values of x. f(x) = 2x^3 + 7x^2 -x-11 solutions Answer 129072 by stanbon(57967)   on 2008-12-19 22:31:29 (Show Source): You can put this solution on YOUR website!Evaluate the functions for the values of x given as 1, 2, 4, 8, and 16. Describe the differences in the rate at which each function changes with increasing values of x. -------------- f(x) = 2x^3 + 7x^2 -x-1 --- f(1) = 2 + 7 - 1 - 1 = 7 ; plot point (1,7) ---- f(2) = 2(2^3) + 7*2^2 -2 - 1 = 2*8 + 7*4 -3 = 16 + 28 - 3 = 41 ; plot point (2,41) --- f(4) = 2(4^3) +7*4^2 - 4 - 1 = 2*64 + 7*16 - 5 = 235 ; plot point (4,235) ---- f(8) = 2(8^3) + 7(8^2) -8 - 1 = 1463 ; plot point (8,1463) ------ f(16) = 9967 ; plot point (16,9967) ------------------------------------ The function is increasing at a pregressively faster and faster pace as x increases from one to 16. ========================================= Cheers, Stan H.
 Mixture_Word_Problems/174143: When a ball is thrown, its height in feet h after t seconds is given by the equation h=vt-16t^2 where v is the initial upwards velocity in feet per second. If v=15 feet per second, find all values t of for which h=3 feet. Do not round any intermediate steps. Round your answer to 2 decimal places.1 solutions Answer 129070 by stanbon(57967)   on 2008-12-19 22:05:55 (Show Source): You can put this solution on YOUR website!When a ball is thrown, its height in feet h after t seconds is given by the equation h=vt-16t^2 where v is the initial upwards velocity in feet per second. If v=15 feet per second, find all values t of for which h=3 feet. ---------------- h(t) = vt-16t^2 3 = 15t - 16t^2 16t^2 - 15t + 3 = 0 ---- Use the Quadratic formula to solve for "t": t = [15 +- sqrt(225 - 4*16*3)]/32 t = [15 +- sqrt(33)]/32 t = [15 + sqrt(33)]/32 = 0.64827 seconds or t = [15 - sqrt(33)]/32 = 0.28923 seconds ================================ Cheers, Stan H.
 Surface-area/174083: Q1. The length of a rectangular swimming pool is 2x-1 meters, and the width is x + 2 meters. Write a polynomial A(x) that represents the area. Find A(5). Q2.Find a trinomal A(x) that represents the area of a parallelogram whose base is 3x + 2 meters and whose height is 2x + 3 meters. Find A(3). Q3.The perimeter of a rectangular backyard is 6x +6 yards. If the width is x yards, find a binomial that represents the length. Q4.P dollars is inveted at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial P(1 + r/2)to the 2nd power represents the value of the investment after 1 year. Rewrite this expression without parentheses. Evaluate the polynomial if P=\$200 and r=10%.1 solutions Answer 129057 by stanbon(57967)   on 2008-12-19 19:26:58 (Show Source): You can put this solution on YOUR website!Q1. The length of a rectangular swimming pool is 2x-1 meters, and the width is x + 2 meters. Write a polynomial A(x) that represents the area. Find A(5). -------- A(x) = (2x-1)(x+2) A(5) = (10-1)(5+2) = 9*7 = 63 --------------------------------- Q2.Find a trinomal A(x) that represents the area of a parallelogram whose base is 3x + 2 meters and whose height is 2x + 3 meters. Find A(3). A(x) = (3x+2)(2x+3) A(3) = (9+2)(6+3) = 11*9 = 99 --------------------------------- Q3.The perimeter of a rectangular backyard is 6x +6 yards. If the width is x yards, find a binomial that represents the length. Perimeter = 2(L+w) 6x+6 = 2(L + x) 3x+3 = L + x Length = 2x+3 --------------------------------- Q4. P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial P(1 + (r/2))to the 2nd power represents the value of the investment after 1 year. Rewrite this expression without parentheses. Evaluate the polynomial if P=\$200 and r=10%. --- P(1+(r/2))^2 = P(1 + r + (r/2)^2) --- 200(1 + 0.10 + (0.05)^2) = 200(1 + 0.10 + 0.0025) = 200(1.1025) = 220.50 =========================== Cheers, Stan H.
 Matrices-and-determiminant/174121: please give me the answers.. use a caret (^) to indicate the power. For example, 53 would be written as 5^3. 1. Write the equation of a polynomial that has zeros at –3 and 2. Write each polynomial function in standard form. Then classify it by degree and by the number of terms. 2. n = 4m2 – m + 7m4 n = 4m3 + 4m – 2; cubic trinomial n = 7m4 + 4m2 – m; quartic trinomial n = 4m4 + 8m2 – m ; quartic trinomial n = 3m3 + 2m – 5; cubic trinomial 3. f(t) = 4t + 3t3 + 2t – 7 f(t) = 3t3 + 6t – 7; cubic trinomial f(t) = 2t3 + 4t – 1; cubic trinomial f(t) = 5t3 + 2t – 7; cubic trinomial f(t) = 7t3 + 3t – 4; cubic trinomial 4. f(r) = 5r + 7 + 2r2 f(r) = 8r3 + 5r + 1; cubic trinomial f(r) = r2 + 5r + 7; quadratic trinomial f(r) = 2r3 + 5r + 7; cubic trinomial f(r) = 2r2 + 5r + 7; quadratic trinomial For each function, determine the zeros and their multiplicity. 5. y = (x + 2)2(x – 5)4 –2, multiplicity 2; 5, multiplicity 4 2, multiplicity 2; 5, multiplicity 3 –2, multiplicity 4; 5, multiplicity 2 2, multiplicity 2; 7, multiplicity 4 6. y = (3x + 2)3(x – 5)5 4, multiplicity 2; 5, multiplicity 2 3, multiplicity 4; 2, multiplicity 4 , multiplicity 3; 5, multiplicity 5 2, multiplicity 3; 5, multiplicity 5 7. y = x2(x + 4)3(x – 1) 2, multiplicity 2; –4, multiplicity 2; 1, multiplicity 1 0, multiplicity 2; –4, multiplicity 3; 1, multiplicity 1 3, multiplicity 4; –3, multiplicity 2; 2, multiplicity 3 0, multiplicity 2; –3, multiplicity 2; 2, multiplicity 3 8. (x3 + 3x2 – x – 3) ÷ (x – 1) 10. Use synthetic division to find P(–3) for P(x) = –2x4 – 3x3 – x + 4.1 solutions Answer 129052 by stanbon(57967)   on 2008-12-19 18:36:30 (Show Source): You can put this solution on YOUR website!1. Write the equation of a polynomial that has zeros at –3 and 2. Equation: f(x) = (x+3)(x-2) --------------------------------------- Write each polynomial function in standard form. Then classify it by degree and by the number of terms. 2. n = 4m2 – m + 7m4 n = 4m3 + 4m – 2; cubic trinomial n = 7m4 + 4m2 – m; quartic trinomial---Correct n = 4m4 + 8m2 – m ; quartic trinomial n = 3m3 + 2m – 5; cubic trinomial ----------------------------------------- 3. f(t) = 4t + 3t3 + 2t – 7 f(t) = 3t3 + 6t – 7; cubic trinomial-----Correct f(t) = 2t3 + 4t – 1; cubic trinomial f(t) = 5t3 + 2t – 7; cubic trinomial f(t) = 7t3 + 3t – 4; cubic trinomial ------------------------------------------ 4. f(r) = 5r + 7 + 2r2 f(r) = 8r3 + 5r + 1; cubic trinomial f(r) = r2 + 5r + 7; quadratic trinomial f(r) = 2r3 + 5r + 7; cubic trinomial f(r) = 2r2 + 5r + 7; quadratic trinomial----Correct ------------------------------------------ For each function, determine the zeros and their multiplicity. 5. y = (x + 2)^2(x – 5)^4 –2, multiplicity 2; 5, multiplicity 4----Correct 2, multiplicity 2; 5, multiplicity 3 –2, multiplicity 4; 5, multiplicity 2 2, multiplicity 2; 7, multiplicity 4 ------------------------------------------ 6. y = (3x + 2)^3(x – 5)^5 4, multiplicity 2; 5, multiplicity 2 3, multiplicity 4; 2, multiplicity 4 -2/3, multiplicity 3; 5, multiplicity 5----Correct 2, multiplicity 3; 5, multiplicity 5 ------------------------------------------- 7. y = x^2(x + 4)^3(x – 1) 2, multiplicity 2; –4, multiplicity 2; 1, multiplicity 1 0, multiplicity 2; –4, multiplicity 3; 1, multiplicity 1----Correct 3, multiplicity 4; –3, multiplicity 2; 2, multiplicity 3 0, multiplicity 2; –3, multiplicity 2; 2, multiplicity 3 ------------------------------------------- 8. (x^3 + 3x^2 – x – 3) ÷ (x – 1) 1)....1....3....-1....-3 .......1....4.....3....|..0 Quotient: x^2 + 4x + 3 Remainder: 0 -------------------------------------------- 10. Use synthetic division to find P(–3) for P(x) = –2x^4 – 3x^3 – x + 4 -3)....-2....-3....-1....4 .........-2....3.....-8..|..28 Quotient: -2x^2 + 3x -8 Remainder: 28 ==================== Cheers, Stan H.
 Square-cubic-other-roots/174139: 16^-3/21 solutions Answer 129047 by stanbon(57967)   on 2008-12-19 18:12:51 (Show Source): You can put this solution on YOUR website!16^-3/2 ------------- The negative means "invert". The 3 means "cube" The 2 means "take the square root" ------------- You may perform these directions in ANY order. -------------------- Take the square root to get: 4^-3 ----------- Next invert to get: (1/4)^3 ----------- Cube to get 1/64 ======================== Cheers, Stan H.
 Surface-area/174098: Hello, I have a question that im extremely stuck on. The question is as follows:- A circular pool has a radius r. It is surrounded by a path which is 2 metres wide. Work out a formula for the area of the path and give its area when r=2.5 metres. Please could you show the step by step guide on how i would work this out. Many thanks1 solutions Answer 128984 by stanbon(57967)   on 2008-12-19 07:51:09 (Show Source): You can put this solution on YOUR website!A circular pool has a radius r. It is surrounded by a path which is 2 metres wide. Work out a formula for the area of the path and give its area when r=2.5 metres. ---------------------- Procedure: Draw the picture including the path around the circular pool. Subtract the area of the pool from the area of the pool with its path. That gives you the area of the path. ------------------------- Area of the pool alone = pi*r^2 = pi*2.5^2 = 6.25pi sq meters ------------------------ Radius of the pool/path combination = r+2 meters Area of the pool/path combination = pi*(2.5+2)^2 = 20.25pi sq. meters. -------------------------- Formula: Area of path = Area of pool/path - Area of pool Area of path = [pi*(r+2)^2 - pi*r^2 ---------------------------------------------- Your Answer: Area of path = [20.25pi - 6.25pi] sq. meters Area of path = 14pi sq meters ================================== Cheers, Stan H.
 Quadratic-relations-and-conic-sections/174072: 2y=(x-5)squared+6 find: the center the vertex's- the foci points- directrix - and end point lactus-1 solutions Answer 128971 by stanbon(57967)   on 2008-12-18 22:32:39 (Show Source): You can put this solution on YOUR website!2y=(x-5)squared+6 ---- Rearrange: (x-5)^2 = 2(y-3) 4p = 2, so p = 1/2 It is a parabola opening upward. --------------------------- find: the center------: It is a parabola. No center. the vertex's----------: (5,3) the foci points-------: (5,3+2) = (5,5) directrix ------------: x = 5-2 = 3 and end point lactus--: ??? ================================== Cheers, Stan H.