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Recent problems solved by 'stanbon'

stanbon answered: 57911 problems
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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Rational-functions/611133: f(x)=(-x-9x-20)/(x+4) 1 solutions Answer 384821 by stanbon(57984)   on 2012-05-15 08:40:41 (Show Source): You can put this solution on YOUR website! f(x)=(-x^2-9x-20)/(x+4) ------- Factor: f(x) = [-(x^2+9x+20)] / (x+4) ------- f(x) = [-(x+4)(x+5)] / (x+4) ========== At this point you might cancel the (x+4) factors, but you would lose the fact that f has a "hole" at x = -4. ================== Cheers, Stan H.

Rational-functions/611132: f(x)=(x^2-36)/(4x+24)...what are the discontinuities 1 solutions Answer 384819 by stanbon(57984)   on 2012-05-15 08:36:41 (Show Source): You can put this solution on YOUR website! f(x)=(x^2-36)/(4x+24)...what are the discontinuities ------------------ Factor: f(x) = [(x-6)(x+6)] / [4(x+6)] ------ f has a "hole" at x = -6. ---- Cheers, Stan H.

Mixture_Word_Problems/611045: If you get 5 Pineapples for $2.50, how many Pineapples you will get for $4.50 ? 1 solutions Answer 384754 by stanbon(57984)   on 2012-05-14 22:56:18 (Show Source): You can put this solution on YOUR website! If you get 5 Pineapples for $2.50, how many Pineapples you will get for $4.50 ? ----- x/450 = 5/250 ------ x = 450(5/250) ------ x = 9 pineapples ======================== Cheers, Stan H.

Triangles/611038: A tree 15 m high casts a shadow 8 m long. To the nearest degree, what is the angle of elevation of the sun? Also, how do I know which angle the elevation of the sun is? Is it the bottom or the top angle? *I am supposed to solve this using sin, cos, or tan. Thank you! 1 solutions Answer 384744 by stanbon(57984)   on 2012-05-14 22:36:29 (Show Source): You can put this solution on YOUR website! A tree 15 m high casts a shadow 8 m long. To the nearest degree, what is the angle of elevation of the sun? Also, how do I know which angle the elevation of the sun is? Is it the bottom or the top angle? ----------- Draw the picture: You have a right triangle with: height = 15 base = 8 --- Angle opposite the height is the angle of elevation. Call that angle "x": ----- Equation: tan(x) = 15/8 x = tan^-1[15/8] = 61.93 degrees ================================ Cheers, Stan H.

Probability-and-statistics/611034: Walton Pharmaceuticals experiments with a new allergy medication using a sample of 17 allergy sufferers. Six sufferers are randomly selected from the group for the first trial. What is the probability that the 5 youngest are chosen? 1 solutions Answer 384739 by stanbon(57984)   on 2012-05-14 22:19:54 (Show Source): You can put this solution on YOUR website! Walton Pharmaceuticals experiments with a new allergy medication using a sample of 17 allergy sufferers. Six sufferers are randomly selected from the group for the first trial. What is the probability that the 5 youngest are chosen? ---- # of groups of 6 that have the 5 youngest: 5C5*12C1 = 5*12 = 60 # of random groups of 6: 17C6 = 12376 ========================================== Cheers, Stan H.

Probability-and-statistics/611024: Find the number of possible outcomes: a number cube is rolled 3 times? My answer is 1:18 An 6- sided die is rolled 4 times. What is the probability of rolling a six on all 4 rolls? My answer 1:648 Tell if situation is permutation or combination. Solve. How many ways can an actor who try out for a play fill the 4 roles? My answer combination, and 210 ways Find the odds of the outcome if an 8-sided dice is rolled: a prime number. My answer. 1:2 There are 6 blue marbles, 7 black marbles, 4 orange marbles, and 3 green marbles in a bag. Once a marble is drawn, IT IS REPLACED. Find the probability of the outcome: a blue marble, an orange marble, and then a green marble. My answer 9/1000 I HOPE I DID THESE RIGHT. THANK YOU FOR YOUR HELP. 1 solutions Answer 384727 by stanbon(57984)   on 2012-05-14 21:45:25 (Show Source): You can put this solution on YOUR website! Find the number of possible outcomes: a number cube is rolled 3 times? Ans; 6*6*6 = 216 =============================== An 6- sided die is rolled 4 times. What is the probability of rolling a six on all 4 rolls? Ans: (1/6)^4 = 1/1296 ==================================== Tell if situation is permutation or combination. Solve. How many ways can an actor who tries out for a play fill the 4 roles? He can only fill one of the roles. Combination: 4C1 = 4 ==================================== Find the odds of the outcome if an 8-sided dice is rolled: a prime number. # of primes on an 8-sided die: 4 Ans: 4:8 or 1:2 ==================================== There are 6 blue marbles, 7 black marbles, 4 orange marbles, and 3 green marbles in a bag. Once a marble is drawn, IT IS REPLACED. Find the probability of the outcome: a blue marble, an orange marble, and then a green marble. Ans: (6/20)(4/20)(3/20) = 72/8000 = 9/1000 ================================================== Cheers, Stan H. ======================

Linear-systems/611022: Use the method of substitution to solve the system of linear equations. 2x-y=6 7x-3y=23 1 solutions Answer 384718 by stanbon(57984)   on 2012-05-14 21:34:24 (Show Source): You can put this solution on YOUR website! Use the method of substitution to solve the system of linear equations. 2x-y=6 7x-3y=23 ------ y = 2x-6 Substitute for "y" and solve for "x": 7x - 3(2x-6) = 23 7x -6x +18 = 23 x = 41 ---- Solve for "y": y = 2x-6 y = 2*41-6 y = 82-6 y = 76 ================== cheers, Stan H. ==================

Rate-of-work-word-problems/611021: Jill can paint a french in eight hours. Stefan can paint the same fence in ten hours. How long would it take them if they worked together? 1 solutions Answer 384717 by stanbon(57984)   on 2012-05-14 21:31:26 (Show Source): You can put this solution on YOUR website! Jill can paint a fench in eight hours. Stefan can paint the same fence in ten hours. How long would it take them if they worked together? -------- Jill rate: 1/8 job/hr Stef rate: 1/10 job/hr --- Together rate: 1/x job/hr ---- Equation: rate + rate = together rate 1/8 + 1/10 = 1/x 10x + 8x = 80 18x = 80 x = 4.44 hrs = 4 hr 27 minutes ================================ Cheers, Stan H. ================

Trigonometry-basics/611019: I'm currently doing a homework problem, (sec (theta) - cos (theta)) divided by sin (theta). I'm not sure how to simplify it. 1 solutions Answer 384714 by stanbon(57984)   on 2012-05-14 21:27:02 (Show Source): You can put this solution on YOUR website! (sec (theta) - cos (theta)) divided by sin (theta). ======= = [sec/sin] - [cos/sin] ----- = [1/cos*sin] - cot --- = [2/sin(2x)] - cot(x) ========= Note: There are many ways to "simplify" these trig expressions. The answer book can only show one of many possible answers. ==================== Cheers, Stan H.

test/611012: What is the unit rate for 300:12? 1 solutions Answer 384710 by stanbon(57984)   on 2012-05-14 21:18:37 (Show Source): You can put this solution on YOUR website! What is the unit rate for 300:12? ------ Ans (300/12):1 = 25:1 ========================== Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/611015: Sue earned $2 for each CD she sells and $2.50 for each DVD she sells. Sue earned $950 last week selling CDs and DVDs. Write an equation to represent the number of CDs (c) and DVDs (d) Sue sold last week given that she earned $950. 1 solutions Answer 384708 by stanbon(57984)   on 2012-05-14 21:15:00 (Show Source): You can put this solution on YOUR website! Sue earned $2 for each CD she sells and $2.50 for each DVD she sells. Sue earned $950 last week selling CDs and DVDs. Write an equation to represent the number of CDs (c) and DVDs (d) Sue sold last week given that she earned $950. ---------------------------- Equation: value + value = value 2C + 2.5D = 950 ----- Cheers, Stan H. ==============

Probability-and-statistics/611013: If a person is selected at random, compute the probability that his/her birthday does not fall in March and also does not fall on the 16th of any month. 1 solutions Answer 384705 by stanbon(57984)   on 2012-05-14 21:10:27 (Show Source): You can put this solution on YOUR website! If a person is selected at random, compute the probability that his/her birthday does not fall in March and also does not fall on the 16th of any month. ----- There are 31 days in March. There are 11 other days that are the 16 of a month. That makes 42 day on which the birthday CANNOT fall. That means the birthday can fall on 365-42 = 323 days ---- P(required condition) = 323/365 ===================================== Cheers, Stan H. =================

Rate-of-work-word-problems/611009: Hose A can fill a water tank in 14 hours, while Hose B can fill the same tank in 20 hours. How long will it take to fill the tank if both hoses are used? This needs to be written as a linear equation. What I have tried: X= Hose A which fills 1/14 of the tank in an hour Y= Hose B which fills 1/20 of the tank in an hour X+Y= (14+20)/20*14= 34/280= 17/140 This is as far as I got but my answer would be 17 hours which is incorrect. Thank you 1 solutions Answer 384703 by stanbon(57984)   on 2012-05-14 21:05:40 (Show Source): You can put this solution on YOUR website! Hose A can fill a water tank in 14 hours, while Hose B can fill the same tank in 20 hours. How long will it take to fill the tank if both hoses are used? This needs to be written as a linear equation. ------ A rate = 1/14 job/hr B rate = 1/20 job/hr Together rate = 1/x job/hr ------ Equation: rate + rate = together rate 1/14 + 1/20 = 1/x 20x + 14x = 14*20 34x = 280 x = 8.24 hrs. = 8 hrs 14 minutes ======================================= Cheers, Stan H. ===================

absolute-value/610592: What is the domain and range of -|x|-12 1 solutions Answer 384475 by stanbon(57984)   on 2012-05-13 19:46:22 (Show Source): You can put this solution on YOUR website! What is the domain and range of -|x|-12 --------- y = -|x|-12 ---- Domain: All Real Numbers ------ Range: -oo < y <= -12 ========================== Cheers, Stan H.

Trigonometry-basics/610583: state the amplitude, period, domain range and phase shift of the cycles a) y=sin(3x-180) when i graphed this function it turned into the base graph and then when i found the period i got 120 degrees and the phase shift was 60 derees so my graph doesnt match my answers :( 1 solutions Answer 384469 by stanbon(57984)   on 2012-05-13 19:41:50 (Show Source): You can put this solution on YOUR website! state the amplitude, period, domain range and phase shift of the cycles a) y=sin(3x-180) when i graphed this function it turned into the base graph and then when i found the period i got 120 degrees and the phase shift was 60 --------------------------------- Form: y = a*sin(bx-c)+d --- Your problem: a = 1 ; b = 3 ; c = 180 ; d = 0 ----- amplitude = |a| = |1| = 1 period = (360/b) = 360/3 = 120 phase shift = c/b = 180/3 = 60 ==================================== domain: All Real Numbers range: -1<= y <=1 ==================================== Cheers, Stan H.

Radicals/610582: Subtract. Simplify by collecting like terms if possible. 8 sqrt 48 minus 6 sqrt 3 1 solutions Answer 384468 by stanbon(57984)   on 2012-05-13 19:22:00 (Show Source): You can put this solution on YOUR website! Simplify by collecting like terms if possible. 8 sqrt 48 minus 6 sqrt 3 ------------------ 8*sqrt(16*3) - 6*sqrt(3) ------ = 8*sqrt(16)*sqrt(3) - 6*sqrt(3) ------ = 8*4*sqrt(3) - 6*sqrt(3) ------ = 32*sqrt(3) - 6*sqrt(3) ------ = 26*sqrt(3) ==================== Cheers, Stan H. ====================

Linear-systems/610579: how do i graph linear equations? grahing is so difficult for me and I hate to see it when I'm doing trigenometry or something like that. Please teach me. how do you solve this question: y=-2x+1 y=x-5 1 solutions Answer 384467 by stanbon(57984)   on 2012-05-13 19:18:29 (Show Source): You can put this solution on YOUR website! y=-2x+1 You need 2 points to determine the graph of a line. Let x = 0, then y = -2*0+1 ; so y = 1 Point (0,1) Let x = 2, then y = -2*2+1 = -4+1 = -3 Point (2,-3) --- Plot the 2 points and draw a line thru them to get: ========================================================== y=x-5 Let x = 0, then y = -5 Point (0,-5) ----------------- Let x = 2, ten y = 2-5 = -3 Point (2,-3) ---- Plot the points and draw the graph thru them to get: ========================================= Cheers, Stan H. =======================

Polynomials-and-rational-expressions/610577: Complete the table and choose the solution for each given value of x y = –x2 + 2 When x = – 1 y = –(–1)2 + 1 = 2; (–1, 1) y = (–1)2 + 2 = 1; (–2, 1) y = –(–1)2 + 2 = 1; (–1, 1) y = (–1)2 + 2 = 1; (1, –1) 1 solutions Answer 384466 by stanbon(57984)   on 2012-05-13 19:10:47 (Show Source): You can put this solution on YOUR website! Complete the table and choose the solution for each given value of x y = –x^2 + 2 When x = – 1 y = –(–1)^2 + 2 = -1 + 2 = 1 ----- (–1, 1) ====================================== Cheers, Stan H. ================

Quadratic_Equations/610554: I could use some help on this problem. Which of these is the first step in solving x^2 + 6x + 1 = 0 by completing the square? a. (x + 6)^2 = -1 b. x^2 + 6x = -1 c. x^2 + 6x + 9 - 9 + 1 = 0 d. (x + 6)^2 + 1 = 1 I came up with A., but I'm not sure if that is correct. 1 solutions Answer 384465 by stanbon(57984)   on 2012-05-13 18:44:10 (Show Source): You can put this solution on YOUR website! Which of these is the first step in solving x^2 + 6x + 1 = 0 by completing the square? --------- x^2 + 6x + 1 = 0 ---- x^2+6x+(3^2) - (3^2) + 1 = 0 ------ (x+3)^2 - 9 + 1 = 0 ---- (x+1)^2 = 8 etc. ===================================== Cheers, Stan H. ================== a. (x + 6)^2 = -1 b. x^2 + 6x = -1 c. x^2 + 6x + 9 - 9 + 1 = 0 d. (x + 6)^2 + 1 = 1

Functions/610542: What is the domain of x for f(x)=6+√x-1 if f(x) is to be a real number 1 solutions Answer 384462 by stanbon(57984)   on 2012-05-13 18:19:05 (Show Source): You can put this solution on YOUR website! What is the domain of x for f(x)=6+√x-1 if f(x) is to be a real number ----- Domain: x >= 1 ======================= Cheers, Stan H.

Geometry_proofs/610552: Find the slope of a line parallel to a line that contains the points (9, -3) and (-3, 8). 1 solutions Answer 384461 by stanbon(57984)   on 2012-05-13 18:12:20 (Show Source): You can put this solution on YOUR website! Find the slope of a line parallel to a line that contains the points (9, -3) and (-3, 8). ------ slope = (8--3)/(-3-9) = 11/-12 = -11/12 ======================= Cheers, Stan H. =======================

Trigonometry-basics/610543: How do you prove that 1-cos2x=2sin^2x? I don't even know how to start this problem. Please help =) 1 solutions Answer 384459 by stanbon(57984)   on 2012-05-13 18:07:27 (Show Source): You can put this solution on YOUR website! prove that 1-cos2x=2sin^2x ----- 1 - cos(2x) = 2sin^2(x) --- 1 - (cos^2(x) - sin^2(x)) = 2sin^2(x) --- 1-cos^2(x) + sin^2(x) = 2sin^2(x) ---- sin^2(x) + sin^2(x) = 2sin^2(x) --- 2sin^2(x) = 2sin^2(x) ============================================== Cheers, Stan H. ================================

Linear-equations/610533: I have not the slightest clue as to what this math problem's name is, so that's why I just put it under Linear Equations, Graphs, and Slope. If g(x)= x^2-6x+3 Find g(-2) ________ x+4 1 solutions Answer 384457 by stanbon(57984)   on 2012-05-13 17:55:53 (Show Source): You can put this solution on YOUR website! If g(x)= (x^2-6x+3)/(x+4) Find g(-2) ========================= g(-2) = ((-2)^2-6*(-2)+2) / (-2+4) ---- = (4+12+2)/2 ------ = 18/2 --- = 9 =================== Cheers, Stan H.

Miscellaneous_Word_Problems/610525: A rectangle has the dimensions 1080/x^2-5x+6 by x-2/x. If the area is 20 units^2, find the value(s) for x. I got 1060/x(x-3) but I don't think that is right. Help would be greatly appreciated! 1 solutions Answer 384446 by stanbon(57984)   on 2012-05-13 17:06:59 (Show Source): You can put this solution on YOUR website! A rectangle has the dimensions 1080/x^2-5x+6 by x-2/x. If the area is 20 units^2, find the value(s) for x. --------------------------- [1080/x^2-5x+6] * [x-2/x] = 20 ------------------ [1080/(x=3)(x-2)] * [x-2/x] = 20 ---- [1080/(x-3)] * [1/x] = 20 Multiply thru by x(x-3) to get: 1080 = 20x(x-3) ----- 20x^2-60x-1080 = 0 ----- x^2 - 3x - 54 = 0 (x-9)(x+6) = 0 x = 9 or x = -6 ==================== Cheers, Stan H.

Rectangles/610526: The formula for the perimeter of a rectangle is P = 2W + 2L. What is the width of a rectangle if the perimeter is 100 feet and the length is 30 feet? 1 solutions Answer 384442 by stanbon(57984)   on 2012-05-13 16:50:38 (Show Source): You can put this solution on YOUR website! The formula for the perimeter of a rectangle is P = 2W + 2L. What is the width of a rectangle if the perimeter is 100 feet and the length is 30 feet? ------- 100 = 2W + 2*30 100 = 2W + 60 2W = 40 Width = 20 feet ===================== cheers, Stan H.

Travel_Word_Problems/610521: I am riding a bike from point A to point B. The distance is 6.6km, and it takes me 20 minites to reach point B. How fast am I going? 1 solutions Answer 384441 by stanbon(57984)   on 2012-05-13 16:46:00 (Show Source): You can put this solution on YOUR website! I am riding a bike from point A to point B. The distance is 6.6km, and it takes me 20 minites to reach point B. How fast am I going? ---------- rate = dist/time ---- rate = 6.6/20 km/min = 6.6/(1/5) km/hr = 33 km/hr ---------------------------- Cheers, Stan H.

Numbers_Word_Problems/610428: The product of two numbers is 180 and the difference between the two numbers is 10 less than the sum of the two numbers. What are the two numbers? 1 solutions Answer 384390 by stanbon(57984)   on 2012-05-13 11:40:55 (Show Source): You can put this solution on YOUR website! (1)an isoceles triangle is such that each of the base angle is twice the vertical angle.find the angle of the triangle (2)The angle of a triangle are x, 2x and 3x.find the angles of the triangle ----- Let the vertex angle has size = "x": Then each base angle is "2x". ---- Equation: x + 2x + 2x = 180 degrees 5x = 180 x = 36 degrees (vertex angle) 2x = 72 degrees (each of the base angles) ===================== Cheers, Stan H. =====================

Probability-and-statistics/610434: On a history test you are given a question with 8 answer choices and you have to circle the two correct answers. Find the probability of getting the question correct without reading any of the choices. 1 solutions Answer 384389 by stanbon(57984)   on 2012-05-13 11:36:27 (Show Source): You can put this solution on YOUR website! On a history test you are given a question with 8 answer choices and you have to circle the two correct answers. Find the probability of getting the question correct without reading any of the choices. ----- # of correct pairs of answers: 1 # of possible pairs of ansers: 8C2 = 28 --- P(correct) = 1/28 ==================== Cheers, Stan H. ====================

Probability-and-statistics/610379: Determine whether each of the distributions given below represents a probability distribution. Justify your answer. (A) x 1 2 3 4 P(x)3/5 12/25 3/25 0 (B) x 3 6 8 P(x)0.15 3/5 0.25 (C) x 20 35 40 50 P(x)0.45 0.25 1/4 0.05 each is lined above each other. example in (c) 20 is directly above 0.45, 35 is directly above 0.25, 40 is directly above 1/4 etc. 1 solutions Answer 384354 by stanbon(57984)   on 2012-05-13 08:19:30 (Show Source): You can put this solution on YOUR website! (A) x 1 2 3 4 P(x)3/5 12/25 3/25 0 No, because the sum of the P(x)'s is greater than one. ======================================== (B) x 3 6 8 P(x)0.15 3/5 0.25 Yes beause sum of P(x)'s = 1 and each P(x) is between 0 and 1 =========================================== (C) x 20 35 40 50 P(x)0.45 0.25 1/4 0.05 Yes for same reason as for "B" ================================ Cheers, Stan H.

Geometry_proofs/610390: A marble is drawn from a jar containing 5 red, 5 blue, 3 green and 2 yellow marbles. That marble is replaced and another marble is drawn. What is the probability that both marbles are green? 1 solutions Answer 384353 by stanbon(57984)   on 2012-05-13 08:10:35 (Show Source): You can put this solution on YOUR website! A marble is drawn from a jar containing 5 red, 5 blue, 3 green and 2 yellow marbles. That marble is replaced and another marble is drawn. What is the probability that both marbles are green? ---- Ans: (3/15)^2 = 1/25 ======================= Cheers, Stan H. ================================

Human-and-algebraic-language/610383: the height of a cylinder measures 4 cm more than its radius. find the height of the cylinder if its total area is 140pi? 1 solutions Answer 384351 by stanbon(57984)   on 2012-05-13 08:06:36 (Show Source): You can put this solution on YOUR website! the height of a cylinder measures 4 cm more than its radius. find the height of the cylinder if its total area is 140pi? --- Total surface area = 2(pi)r^2 + 2(pi)r*h Solve: 140 = 2(pi)r^2 + 2(pi)*r(r+4) 70 = (pi)r^2 + (pi)(r^2+4r) 70 = 2(pi)r^2 + 4(pi)r 35 = (pi)r^2 + 2(pi)r Rearrange: (pi)r^2 + 2(pi)r - 35 = 0 r = 2.484 cm h = 6.484 cm ==================== Cheers, Stan H. ===================================