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# Recent problems solved by 'Schaman_Dempster'

 Functions/587194: I need to find the domain of 2x/(x+5)^2 so I take (x+5)^2 and make it x^2+10x+25 = 0 that is as far as I got then i would put the 25 over and divide by 10 geting x^2=-2.51 solutions Answer 374031 by Schaman_Dempster(26)   on 2012-03-15 06:41:34 (Show Source): You can put this solution on YOUR website!You're almost there. I can see you are setting the denominator to 0 and you have: Using Quadratic formula: for the equation We have a = 1 , b=10, c =25 or or or x =-5 This shows that denominator becomes 0 for x= 5. Therefore, we can say that x =-5 can not be in the domain of the given fucntion. Hence, except for x =-5, all real numbers are the domain. It is represented as: x ϵ R - {-5} or x ϵ (-∞,∞) - {5} Hope this helps~~
 Travel_Word_Problems/587203: If boulder city is 20 miles away and i drive at a constant speed of 70 mph how long would it take me to get there?1 solutions Answer 374030 by Schaman_Dempster(26)   on 2012-03-15 06:33:32 (Show Source): You can put this solution on YOUR website!Distance to be traveled = 20 miles Speed at which you're traveling = 70 miles per hour = 70 miles/ 60 minutes = 7/6 miles per minute Let the time taken by you to reach boulder city be t. We know that Speed = So, 7/6 miles per minute = 20 miles/t 7*t = 6*20 {Cross multiplication} 7t = 120 t = 120/7 or t = 17.14 minutes Hence, it will take 17.14 minutes for you to reach there. Hope this helps~!
 Age_Word_Problems/587206: Tom is thrice as the age of Antonette. if the sum of there age is 54. what are their ages?1 solutions Answer 374029 by Schaman_Dempster(26)   on 2012-03-15 06:28:36 (Show Source): You can put this solution on YOUR website!Let the ages of Tom and Alice be x and y respectively. We know that Tom's age is thrice as Alice's age. So, x = 3y --------------- (1) Also, we know that the sum of their ages is 54. Therefore, x + y = 54 or 3y + y = 54 { Using equation (1) } 4y = 54 or y = 54/4 = 13.5 Plugging back the value of y in equation (1), we get: x = 3*13.5 = 40.5 Hence, Tom's age is 40.5 years and Alice's age is 13.5 years Hope this helps~!
 Volume/587207: A cube is 8 inches on each side. What is the height of a cylinder having the same volume, if its radius is 4 inches?1 solutions Answer 374027 by Schaman_Dempster(26)   on 2012-03-15 06:26:46 (Show Source): You can put this solution on YOUR website!We know that side length of a cube is 8 inches. Volume of the cube = V(cube) = V(cube) = 512 cubic inches WE know that the radius of the cylinder is r = 4 inches and let the height of the cylinder be h inches. Volume of the cylinder = π V(cylinder) = V(cylinder) = 16πh Since the volume of cube and cylinder are same, so V(cylinder) = V(cube) or 16πh = 512 or πh = 512/16 {Dividing both the sides by 16} or πh = 32 or h = 32/π inches If we wish to get the decimal value fo h, we can use the standard value of π = 3.14 Therefore, h = 32/π = 32/3.14 or h = 10.189 or h = 10.2 inches (approximately) Hope this helps~!
 Age_Word_Problems/587208: Tom's age is thrice as Alice's age.If the sum of their ages is 54, What is the age of tom and Alice?1 solutions Answer 374025 by Schaman_Dempster(26)   on 2012-03-15 06:16:39 (Show Source): You can put this solution on YOUR website!Let the ages of Tom and Alice be x and y respectively. We know that Tom's age is thrice as Alice's age. So, x = 3y --------------- (1) Also, we know that the sum of their ages is 54. Therefore, x + y = 54 or 3y + y = 54 { Using equation (1) } 4y = 54 or y = 54/4 = 13.5 Plugging back the value of y in equation (1), we get: x = 3*13.5 = 40.5 Hence, Tom's age is 40.5 years and Alice's age is 13.5 years Hope this helps~!
 Miscellaneous_Word_Problems/585879: The sum of 2 and 3 times the difference of a number and 5 is equal to 4 times the difference of a number and 11 solutions Answer 373522 by Schaman_Dempster(26)   on 2012-03-12 14:32:04 (Show Source): You can put this solution on YOUR website!Let the number be x. Difference of the number and 5 = x -5 2 times the difference of the number and 5 = 2(x - 5) 3 times the difference of the number and 5 = 3(x - 5) Sum of 2 times and 3 times the difference of the number and 5 = 2(x - 5)+ 3(x-5) = 5( x- 5) Difference of the number and 1 is = x -1 4 times the difference of the number and 1 is = 4 (x -1) So, 5 (x -5) = 4(x -1) or 5x - 25 = 4x - 4 or 5x - 4x - 25 = -4 or x - 25 = -4 or x = 25 -4 or x = 21 Hence, the number is 21
 Numbers_Word_Problems/585854: A positive integer is increased by 5, and is equal to 36 times the reciprocal of the inetger. Find the integer.1 solutions Answer 373506 by Schaman_Dempster(26)   on 2012-03-12 13:41:33 (Show Source): You can put this solution on YOUR website!Let the positive integer be x. Reciprocal of the integer would be = Now, we can set up the equation as: or {Multiplying both the sides by x} { Factoring by regrouping} Since we have assumed that the integer is positive or x > 0 Therefore, x =4 Hope this helps~!
 Polynomials-and-rational-expressions/585835: How do you solve this problem x+1 divide x+1 _____________ 6 3 it is 6 under neath th x+1 and the 3 is under x+1 rational expression is simplified1 solutions Answer 373499 by Schaman_Dempster(26)   on 2012-03-12 13:13:07 (Show Source): You can put this solution on YOUR website! ÷ Rule: Whenever we have two fractions divided, then we use "KSS" = Keep Switch Switch. Let me explain this to you a little. We 'keep' the first fraction, switch the operator from division to multiplication and again we switch the second fraction. = = { Cancelling out x+1 from both the fractions } = = Hope this helps~!
 Linear-equations/585405: find the answer to this eqution find an equation of the line. through (-2,-8); paralelle to 3x+2y=51 solutions Answer 373339 by Schaman_Dempster(26)   on 2012-03-11 15:00:00 (Show Source): You can put this solution on YOUR website!Given equation of line is: 3x + 2y = 5 Let us transform this into slope intercept form: y = mx + b 2y = 5 - 3x or y = -3x/2 + 5/2 Comparing it with slope-intercept form: y= mx + b Slope = m = -3/2 If two lines are parallel, then they have equal slopes. So, the slope of the line parallel to 3x + 2y = 5 is -3/2 Using slope-intercept form, we can write the equation of a new line can be written as: y = mx + b y = -3x/2 + b Since this line also passes through (-2,-8) Therefore, -8 = (-3)*(-2)/2 + b -8 = 3 + b b = -8 -3 b = -11 Hence the equation of the line parallel to 3x + 2y =5 is: y = -3x/2 - 11 or 2y = - 3x - 22 { Multiplying both the sides by 2} or 3x + 2y + 22 = 0 Hope this helps~!
 Systems-of-equations/585418: Mary is twice as old as John was 3 years ago. In 5 years John will be 1 year older than Mary is now. Find the ages of both people today.1 solutions Answer 373338 by Schaman_Dempster(26)   on 2012-03-11 14:48:22 (Show Source): You can put this solution on YOUR website!Let the ages of Mary and John be x and y years respectively today. 3 years ago, age of John was (y-3) years Since Mary is twice as old as john was 3 years ago. So, x = 2(y-3) or x = 2y - 6 -------- (1) In 5 years, age of John will be = (y + 5) years "John will be 1 year older than Mary is now" So, (y+5) = x + 1 or x = y + 5 -1 or x = y + 4 --------(2) Using equation (1) and (2), we get: 2y - 6 = y + 4 2y = y + 4 + 6 2y = y + 10 y = 10 Plugging back the value of y in equation (2) x = 10 + 4 x = 14 Hence, Age of Mary today is x= 14 years and age of John today is y=10 years. Hope this helps~!
 Travel_Word_Problems/585408: A pilot can travel 560 miles with the wind in the same amount of time as 360 miles against the wind. Find the speed of the wind if the pilot's speed in still air is 230 miles per hour.1 solutions Answer 373337 by Schaman_Dempster(26)   on 2012-03-11 14:40:39 (Show Source): You can put this solution on YOUR website!Let the speed of the wind be w miles per hour. Let t be the time taken by pilot to travel 560 miles with the wind and also to travel 360 miles against the wind. Case: When traveling with the wind, total speed of pilot = speed of pilot in still air + speed of wind Vt = 230 + w Distance traveled = total speed * time taken 560 = (230 + w)* t ------------ (1) Case: When traveling against the wind, total speed of pilot = speed of pilot in still air - speed of wind Vt = 230 - w Distance traveled = total speed * time taken 360 = (230 - w)* t ------------- (2) Using equation (1) and (2), { Dividing both the sides by 40 } { Cross-multiplication} 3220 - 14w = 2070 + 9w 3220 - 2070 = 14w + 9w 1150 = 23w w = 1150/23 w = 50 Hence, the speed of the wind is 50 miles per hour. Hope this helps~!
 Angles/585411: Two angles are supplementary. If the measure of one angle is 46 more than the measure of the other angle, find the measure of the two angles.1 solutions Answer 373334 by Schaman_Dempster(26)   on 2012-03-11 14:20:43 (Show Source): You can put this solution on YOUR website!Let the two angles be x and y such that x>y. Since they are supplementary angles, therefore x + y = 180 ---------(1) Also, x = y + 46 ------------ (2) Plugging the value of x from equation (2) into equation (1), we get: y + 46 + y = 180 2y + 46 =180 2y = 180 - 46 2y = 134 y = 67 Plugging back the value of y in equation (1), x = 67 + 46 x = 113 Hence, the two angles are 67' and 113' Hope this helps~!
 Volume/585323: a cardboard box has a volume of 157500 cm^3. its base is 45 by 50 cm . what is its height?1 solutions Answer 373279 by Schaman_Dempster(26)   on 2012-03-11 09:35:10 (Show Source): You can put this solution on YOUR website!Given that the volume of a box is 157500 cm^3 and base area is 45 * 50 cm^2 We know that volume formula of a box is Let the height of the box be h cm. So, 157500 =45*50*h 157500 = 2250*h or h = 70 cm Hence the height of the box is 70 cm. Hope that helps~!
 Sequences-and-series/585320: find the terms a2 a3 a4 and a5 of a geometric sequence if a1=10 and the common ratio r=-11 solutions Answer 373278 by Schaman_Dempster(26)   on 2012-03-11 09:31:05 (Show Source): You can put this solution on YOUR website!a1 = 10, r =-1 nth term of a geometric sequence is given by: So, a2 = a1*r^(2-1) = a1*r = 10*(-1) = -10 a3 = a1*r^(3-1) = a1*r^2 = 10*(-1)^2 = 10*1 = 10 a4 = a1*r^(4-1) = a1*r^3 = 10*(-1)^3 = 10*(-1) = -10 a5 = a1*r^(5-1) = a1*r^4 = 10*(-1)^4 = 10*1 = 10 Hope this helps~!
 Triangles/585308: A 60cm piece of wire is bent to form a right triangle. If the hypotenuse is 26cm long, what are legs of the right triangle?1 solutions Answer 373266 by Schaman_Dempster(26)   on 2012-03-11 06:36:15 (Show Source): You can put this solution on YOUR website!Let the other sides of the right triangle be x and y. Since the length of the wire was 60 cm, the whole 60 cm has been bent to form a right triangle and that means 60 cm is as well the perimeter of the triangle. Therefore, x + y + 26 = 60 or x + y = 34 or y = 34 -x ---------------- (1) Using the Pythagoras theorem, x^2 + y^2 = 26^2 x^2 + (34 - x)^2 = 26^2 {Using equation (1)} x^2 + 34^2 + x^2 - 68x = 26^2 2x^2 - 68x + 34^2 - 26^2 = 0 2x^2 - 68x + (34 -26)(34+26) = 0 { a^2 - b^2 = (a+b)(a-b)} 2x^2 - 68x + 8*60 = 0 2x^2 - 68x + 480 = 0 x^2 - 34x + 240 = 0 { Dividing the equation throughout by 2} x^2 - 24x - 10x + 240 = 0 x (x -24) - 10(x-24) =0 (x -10) (x-24) = 0 x =10, x =24 Plugging back the value of x in equation (1), we get: When x =10, y = 34 -10 = 24 When x= 24, y = 34-24 =10 Hence, the two legs of the right triangle are 10 cm and 24 cm.
 Age_Word_Problems/585300: A man is 4 times as old as his son, after 16 years he will be only twice as old as his son. find their present age. 1 solutions Answer 373262 by Schaman_Dempster(26)   on 2012-03-11 06:12:55 (Show Source): You can put this solution on YOUR website!Let the present age of father be x and the son be y. Now, x = 4y ---------- (1) After 16 years, age of father will be x+ 16 age of son will be y +16 Therefore, x + 16 = 2( y + 16) x + 16 = 2y + 32 x = 2y + 16 or 4y = 2y + 16 {Using equation (a)} 2y = 16 y = 8 Plugging back the value of y in equation (1), we get: x = 4*8 = 32 Hence, the present age of father is 32 years and present age of son is 8 years.
 Numbers_Word_Problems/585306: three forth of a number exeeds it s one third by 15 find the number1 solutions Answer 373261 by Schaman_Dempster(26)   on 2012-03-11 06:06:26 (Show Source): You can put this solution on YOUR website!Let the number be x. So, we can set up the equation as: (3/4)x = (1/3)x + 15 Solving for x: 3x = (4/3)x + 60 {Multiplying 4 on both the sides} 9x = 4x + 180 {Multiplying 3 on both the sides} 5x = 180 x = 36 Hope this helps~!