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# Recent problems solved by 'Alan3354'

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 Rate-of-work-word-problems/591084: Hi, Thanks Sonia1 solutions Answer 375487 by Alan3354(30955)   on 2012-03-24 18:54:41 (Show Source): You can put this solution on YOUR website!15 labourers can lay 85 metres of cable in 10 days. How long will it take a) 12 labourers to ly 85 metres of cable? b) 8 labourers to lay 100 metres of cable? ---------------- 15 labourers can lay 85 metres of cable in 10 days. 85 metres = 15*10 man-days = 150 man-days -------- a) 12 labourers to ly 85 metres of cable? 150 man-days/12 men = 12.5 days ---------- b) 8 labourers to lay 100 metres of cable? ----- = (100/85)*(12/8) = 1200/340 days =~ 35.29 days
 Inequalities/591086: Which inequality represents at least 6 dogs? 1 solutions Answer 375486 by Alan3354(30955)   on 2012-03-24 18:45:04 (Show Source): You can put this solution on YOUR website!Which inequality represents at least 6 dogs? ------------- "at least 6" is 6 for more --------------- v >= 6
 Geometry_Word_Problems/591088: Find the volume of this tube. You can think of it as a hollow cylinder. The tube consists of a smaller tube inside of a larger tube. The smaller tube has a radius of 5, and the larger tube has an overall radius of 10. the height for them both is 15. a.1125 π in.3 b.375 π in.3 c.1500 π in.3 d.1875 π in.31 solutions Answer 375485 by Alan3354(30955)   on 2012-03-24 18:43:52 (Show Source): You can put this solution on YOUR website!Find the volume of this tube. You can think of it as a hollow cylinder. The tube consists of a smaller tube inside of a larger tube. The smaller tube has a radius of 5, and the larger tube has an overall radius of 10. the height for them both is 15. a.1125 π in.3 b.375 π in.3 c.1500 π in.3 d.1875 π in.3 ------------------- cubic inches Vol = pi*15*75 = 1125*pi cubic inches.
 Graphs/591056: Hi! I'm so frustrated with this question I was assigned. I would appreciate your help. Mrs. McKage encloses her rectangular garden, whose width is 57 feet, with 292 of chain link fencing. What is the length of her garden? I don't know how to get the equation I only have some info. 57 feet 292 of chain link fencing ? Thanks1 solutions Answer 375481 by Alan3354(30955)   on 2012-03-24 18:16:05 (Show Source): You can put this solution on YOUR website!Mrs. McKage encloses her rectangular garden, whose width is 57 feet, with 292 of chain link fencing. What is the length of her garden? I don't know how to get the equation I only have some info. 57 feet 292 of chain link fencing ? -------------------- Perimeter = 2W + 2L 292 = 2W + 2L 146 = W + L 146 = 57 + L L = 89 feet
 logarithm/591068: What is 3 1/3 - 11 solutions Answer 375480 by Alan3354(30955)   on 2012-03-24 18:14:08 (Show Source): You can put this solution on YOUR website!What is 3 1/3 - 1 2 1/3
 Trigonometry-basics/591078: How can I prove this identity? (1-cos^2theta)(1+cos^2theta)=2sin^2theta-sin^4theta? I tried to do it, and this is what I've come up with so far, and am not sure if I am doing it correctly. Working with the left side, I have the following: sin^2theta(1+cos^2theta) = sin^2theta+(sin^2theta*cos^2theta) And then it stops. 1 solutions Answer 375479 by Alan3354(30955)   on 2012-03-24 18:13:06 (Show Source): You can put this solution on YOUR website!How can I prove this identity? (1-cos^2theta)(1+cos^2theta)=2sin^2theta-sin^4theta? I tried to do it, and this is what I've come up with so far, and am not sure if I am doing it correctly. Working with the left side, I have the following: sin^2theta(1+cos^2theta) = sin^2theta+(sin^2theta*cos^2theta) --------------- (1-cos^2theta)(1+cos^2theta)=2sin^2theta-sin^4theta? sin^2(t)*(1+cos^2theta)=2sin^2theta - sin^4theta? (1+cos^2theta) = 2 - sin^2theta? 1+cos^2theta + sin^(t) = 2 cos^2(t) + sin^(t) = 1 I'm convinced.
 Age_Word_Problems/591077: If a plane can travel 500 miles per hour with the wind 400 miles per hour against the wind, find the speed of the plane without a wind and the speed of the wind? What is the speed of the plane in still air?1 solutions Answer 375478 by Alan3354(30955)   on 2012-03-24 18:08:27 (Show Source): You can put this solution on YOUR website!If a plane can travel 500 miles per hour with the wind 400 miles per hour against the wind, find the speed of the plane without a wind and the speed of the wind? What is the speed of the plane in still air? --------------- The "speed of the plane without a wind" is called the airspeed, and it's the average of the 2 groundspeeds. ------------- The windspeed is the difference between airspeed and groundspeed.
 Geometry_Word_Problems/591072: What is the effect of on volume of tripling the dimensions of this cylinder? The radius is 2 and the height is 7. a.The volume is multiplied by 6. b.The volume is multiplied by 21. c.The volume is multiplied by 9. d.The volume is multiplied by 9.1 solutions Answer 375476 by Alan3354(30955)   on 2012-03-24 18:06:48 (Show Source): You can put this solution on YOUR website!What is the effect of on volume of tripling the dimensions of this cylinder? The radius is 2 and the height is 7. -------------- If both the radius and the height are tripled, the volume is multiplied by 27. ------------- The radius is 2 and the height is 7. That is not relevant. It's x27 for any dimensions.
 Geometry_Word_Problems/591066: What is the effect on volume of multiplying the right rectangle's dimensions by 1/4? It is a rectangular prism and has a length of 12, a width of 4, and a height of 8. a. The volume is multiplied by 4. b. The volume is multiplied by 1/8. c. The volume is multiplied by 1/4. d. The volume is multiplied by 1/64.1 solutions Answer 375469 by Alan3354(30955)   on 2012-03-24 17:13:50 (Show Source): You can put this solution on YOUR website!What is the effect on volume of multiplying the right rectangle's dimensions by 1/4? ------------ Vol --> (1/4)L*(1/4)*W*(1/4*H = 1/64
 Geometry_Word_Problems/591059: Suppose the ratio of the volumes of two balls is 8 to 1. What is the ratio of their radii?1 solutions Answer 375468 by Alan3354(30955)   on 2012-03-24 17:12:38 (Show Source): You can put this solution on YOUR website!Suppose the ratio of the volumes of two balls is 8 to 1. What is the ratio of their radii? ---------- 2 to 1
 Geometry_Word_Problems/591063: Find the volume of the cylinder rounded to the nearest tenth. The height is 10 feet and the cylinder has a diameter of 12 feet. 1 solutions Answer 375467 by Alan3354(30955)   on 2012-03-24 17:08:48 (Show Source): You can put this solution on YOUR website!Find the volume of the cylinder rounded to the nearest tenth. The height is 10 feet and the cylinder has a diameter of 12 feet. -------- r = d/2 = 6 ft
 Pythagorean-theorem/591058: sideA=20 sideB=12 so what is the hypotinuse1 solutions Answer 375466 by Alan3354(30955)   on 2012-03-24 17:04:38 (Show Source): You can put this solution on YOUR website!sideA=20 sideB=12 so what is the hypotinuse [sic] -----------------------
 Linear-systems/591044: Please help me solve this system and graph 6u+v=32, 6u=v+401 solutions Answer 375459 by Alan3354(30955)   on 2012-03-24 16:03:12 (Show Source): You can put this solution on YOUR website!Please help me solve this system and graph 6u+v=32, 6u=v+40 -------------- 6u+v=32 6u=v+40 -------------- 6u+v=32 6u-v=40 ------- Add =================== Both eqns are linear, straight lines. You need 2 points to plot a straight line. Pick 2 values for 1 variable and find the other. Plot the 2 points. Draw a line thru them. ======================== Do the same for the other eqn. Notice that the intersection is the solution to the system.
 Functions/591021: Please help me and show work. 1. F(x)=3/x^2+2x-35 2. f(x)= x-1/x^2-1 1 solutions Answer 375458 by Alan3354(30955)   on 2012-03-24 16:00:27 (Show Source): You can put this solution on YOUR website!Please help me and show work. 1. F(x)=3/x^2+2x-35 What's the denomoninator? x^2? x^2 + 2? All 3 terms? 2. f(x)= x-1/x^2-1 Same question. ============== And, help you do what?
 Trigonometry-basics/591041: Name an angle on the interval [0,2pi] that is coterminal with an angle whose measure is -19pi/51 solutions Answer 375457 by Alan3354(30955)   on 2012-03-24 15:49:21 (Show Source): You can put this solution on YOUR website!Name an angle on the interval [0,2pi] that is coterminal with an angle whose measure is -19pi/5 ---------------- Add 2pi repeatedly until you get a positive value --- -19pi/5 + 10pi/5 = -9pi/5 ----- -9pi/5 + 10pi/5 = pi/5 ------ = pi/5
 Travel_Word_Problems/591040: A plane flew 1740 km in 6 hours with tail wind. On return trip, going into the wind, the plane flew 570 km in 3 hours. What is the planes speed if there was no wind.1 solutions Answer 375456 by Alan3354(30955)   on 2012-03-24 15:46:15 (Show Source): You can put this solution on YOUR website!A plane flew 1740 km in 6 hours with tail wind. On return trip, going into the wind, the plane flew 570 km in 3 hours. What is the planes speed if there was no wind. ---------------- 1740 km/6 hr = 290 km/hr 570 km/3 hr = 190 km/hr ------------- The plane's airspeed is the average = 240 km/hr ----------------- The term is airspeed, and planes don't use kilometers. They use nautical miles and knots.
 Money_Word_Problems/590908: You recieve a penny on January 1st, two cents the next day, four cents the next and so on,doubling every day. How long will it take to be a millionaire? Suppose you started with a nickle and doubled, how long before you were worth a million dollars?1 solutions Answer 375455 by Alan3354(30955)   on 2012-03-24 15:42:24 (Show Source): You can put this solution on YOUR website!You recieve a penny on January 1st, two cents the next day, four cents the next and so on,doubling every day. How long will it take to be a millionaire? --- The total each day is cents. \$1,000,000 = 100,000,000 cents. d*log(2) = log(99999999} d = log(99999999)/log(2) d =~ 26.575 days --> 26 days ------------------- Suppose you started with a nickle and doubled, how long before you were worth a million dollars? \$1,000,000 = 100,000,000 cents = 20,000,000 nickels Amt = d*log(2) = log(19999999} d = log(19999999)/log(2) d =~ 24.25 days --> 25 days ---------------- Not much difference. If you multiply by 5 each day, it was reduce the time more drastically.
 Rectangles/591033: if a rectangle has a perimeter 36 and area 65, how would I write the equation that you need to solve to find the width.1 solutions Answer 375453 by Alan3354(30955)   on 2012-03-24 15:19:30 (Show Source): You can put this solution on YOUR website!if a rectangle has a perimeter 36 and area 65, how would I write the equation that you need to solve to find the width. ------------- P = 2L + 2W Area = L*W
 Trigonometry-basics/590941: cscx=-5/3 pi1 solutions Answer 375451 by Alan3354(30955)   on 2012-03-24 14:44:45 (Show Source): You can put this solution on YOUR website!cscx=-5/3 pi --------------- sin(x) = 1/csc = -3/5 x is in Q3 or Q4 --------------- cos = 4/5 in Q4 or - 4/5 in Q3 ------------- tan = sin/cos --------------- Use the half-angle formulas on Wikipedia. It's all plug-in formulas.
 real-numbers/591022: Please help me and show work Find all real solution 1. square rootx+8 + squarerootx-9 =17 2.x^2/7=21 solutions Answer 375445 by Alan3354(30955)   on 2012-03-24 14:37:13 (Show Source): You can put this solution on YOUR website!Find all real solution 1. square rootx+8 + squarerootx-9 =17 Square both sides x-9 = 64 x = 73 -------------- 2.x^2/7=2 x^2 = 14 x = sqrt(14) x = -sqrt(14)
 Word_Problems_With_Coins/590978: a parking meter contains \$27.05 in dimes and quarters. There are 146 coins in the meter. How many of each type are in the meter?1 solutions Answer 375441 by Alan3354(30955)   on 2012-03-24 14:32:55 (Show Source): You can put this solution on YOUR website!a parking meter contains \$27.05 in dimes and quarters. There are 146 coins in the meter. How many of each type are in the meter? ---------------- d + q = 146 10d + 25q = 2705 Can you finish it? -------------------- Or, If it's 146 dimes, it's worth 1460 cents. Each dime replaced by a quarter adds 15 cents. 2705 - 1460 = 1245 1245/15 = q
 Equations/591019: It's algebra M over 15 + 62 = 23 What is m? 1 solutions Answer 375438 by Alan3354(30955)   on 2012-03-24 14:28:17 (Show Source): You can put this solution on YOUR website! M over 15 + 62 = 23 What is m? ------- If M = m: m/(15+62) = 23 m/77 = 23 m = 23*77 m = 1771
 test/590994: A 720 ml container holds a mixture of red, yellow and white paint in a 5 : 3 : 12 ratio. How much more red paint than yellow is present in the mixture?1 solutions Answer 375437 by Alan3354(30955)   on 2012-03-24 14:26:08 (Show Source): You can put this solution on YOUR website!A 720 ml container holds a mixture of red, yellow and white paint in a 5:3:12 ratio. How much more red paint than yellow is present in the mixture? -------------- Assuming they're in that order, or respectively: 5+3+12 = 20 720/20 = 36 red:5*36 = 180 ml ylw:3*36 = 108 ml wht:12*36 = 432 ml -------- red-ylw = 72 ml
 Graphs/590995: how can I graph this equation? x=9/2 1 solutions Answer 375435 by Alan3354(30955)   on 2012-03-24 14:21:07 (Show Source): You can put this solution on YOUR website!how can I graph this equation? x=9/2 ------------------- It's a straight line, so you need 2 points. Pick 2 values for y. y = 0 --> (9/2,0) y = 10 -->(9/2,10) Draw a line thru the points. Any y values will work.
 Probability-and-statistics/590932: 1. The probability that a bulb produced by a factory will fuse after certain period of time is 0.05. Find the probability that out of 5 such bulbs a. None fuses b. Not more than 2 fuse c. More than 2 fuse 1 solutions Answer 375433 by Alan3354(30955)   on 2012-03-24 14:19:06 (Show Source): You can put this solution on YOUR website!1. The probability that a bulb produced by a factory will fuse after certain period of time is 0.05. Find the probability that out of 5 such bulbs a. None fuses b. Not more than 2 fuse c. More than 2 fuse ---------------------------- What does that mean? How does a bulb "fuse?"
 Length-and-distance/591003: Please Help!! Arrange the quantities in order from smallest to largest. 36 km, 272 m, 624 hm1 solutions Answer 375426 by Alan3354(30955)   on 2012-03-24 14:01:18 (Show Source): You can put this solution on YOUR website!Arrange the quantities in order from smallest to largest. 36 km, 272 m, 624 hm -------- Make them all the same units. I don't know what "hm" is.
 Pythagorean-theorem/590997: The length of the hypotenuse in a right triangle is 82 cm and the length of one leg is 70 cm. What is the length of the other leg rounded to one decimal place?1 solutions Answer 375424 by Alan3354(30955)   on 2012-03-24 13:51:05 (Show Source): You can put this solution on YOUR website!The length of the hypotenuse in a right triangle is 82 cm and the length of one leg is 70 cm. What is the length of the other leg rounded to one decimal place? --------------------
 Length-and-distance/591008: Help please!! Indicate the metric unit that would be best used to express the area of the object. The floor of your garage1 solutions Answer 375423 by Alan3354(30955)   on 2012-03-24 13:49:10 (Show Source): You can put this solution on YOUR website!Indicate the metric unit that would be best used to express the area of the object. ------------- Square meters, probably.
 Length-and-distance/591009: Please HELP!! Find the volume of the shaded solid. Round your answer to 2 decimal places if necessary. Use π = 3.14 when necessary. 6ft, 18ft, 30ft The shape is a cylinder. 6ft on top, 18ft is at the botton, and 30ft is on the left side.1 solutions Answer 375422 by Alan3354(30955)   on 2012-03-24 13:47:42 (Show Source): You can put this solution on YOUR website!Find the volume of the shaded solid. Round your answer to 2 decimal places if necessary. Use π = 3.14 when necessary. 6ft, 18ft, 30ft The shape is a cylinder. 6ft on top, 18ft is at the botton, and 30ft is on the left side. ---------- A cylinder has a constant radius, can't be 6 ft on the bottom and 18 ft on the top. Send a sketch.
 Trigonometry-basics/590939: cosx=3/5 o1 solutions Answer 375387 by Alan3354(30955)   on 2012-03-24 09:35:56 (Show Source): You can put this solution on YOUR website!cosx=3/5 0 < x <3pi/2 find sinx,cosx, and tanx by half angle identities ------------- Cosine is positive, --> Q1 & Q4 --> sine is +4/5 only cos(x) is given tan(x) = sin/cos = 4/3 -------------------------- No half-angles are shown. If you want the half-angles, look at Wikipedia, it's covered well there.
 Polynomials-and-rational-expressions/590956: Would someone teach me how to do these? and, would they be worked exactly the same? Solve: b^2 + b - 6 = 0 c^2 + c = 01 solutions Answer 375386 by Alan3354(30955)   on 2012-03-24 09:29:25 (Show Source): You can put this solution on YOUR website!Would someone teach me how to do these? and, would they be worked exactly the same? Solve: b^2 + b - 6 = 0 There's more than one way. This one can be factored. b^2 + b - 6 = 0 (b + 3)*(b - 2) = 0 ---- If the product is 0, either b+3 = 0 --> b = -3 or b-2 = 0 --> b = 2 =============================== c^2 + c = 0 This one factors also c*(c + 1) = 0 Either c = 0 or c = -1