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# Recent problems solved by 'robertb'

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 Matrices-and-determiminant/391615: find the determinant of [x y] [z w]1 solutions Answer 277869 by robertb(4012)   on 2011-01-07 03:18:00 (Show Source): You can put this solution on YOUR website!xw - yz
 Trigonometry-basics/391582: How do you solve for x in cos2x = cosx, -pi<=x<=pi?1 solutions Answer 277868 by robertb(4012)   on 2011-01-07 03:16:32 (Show Source): You can put this solution on YOUR website! <==> <==> <==> (2 cosx + 1)(cosx - 1) = 0 ==> cosx = -1/2 or cos x = 1. From cosx = -1/2, x = ,. From cos x = 1, x = 0. The solutions are then 0,,.
 Percentage-and-ratio-word-problems/391596: you purchase a desk for 60% of the original price p. the price is \$32 less then the original price.write and solve an equation to find the original price of the desk.1 solutions Answer 277864 by robertb(4012)   on 2011-01-07 03:02:14 (Show Source): You can put this solution on YOUR website!0.60p = p - 32 ==> -0.40p = -32 ==> p = -32/-0.40 = \$80, the original price of the desk.
 Trigonometry-basics/391597: How do I approach the following question: If x sin A + y cos A = p and x cos A - y sin A = q, find x square + y square.1 solutions Answer 277863 by robertb(4012)   on 2011-01-07 02:57:16 (Show Source): You can put this solution on YOUR website!= q cos A - p sin A = p cos A - q sin A after using Cramer's rule to solve for x and y. Then = = =.
 Quadratic_Equations/391624: Determine whether each pair of functions are inverse functions. f(x)=-4x+1, g(x)=1/4(1-x)1 solutions Answer 277861 by robertb(4012)   on 2011-01-07 02:38:59 (Show Source): You can put this solution on YOUR website!, and . They are inverses, because , and .
 Quadratic_Equations/391626: Determine whether each pair of functions are inverse functions. f(x)=2x, g(x)=-2x1 solutions Answer 277860 by robertb(4012)   on 2011-01-07 02:32:02 (Show Source): You can put this solution on YOUR website!No, not inverse functions, because fog = -4x, and not equal to x. Similarly gof = -4x, and not equal to x.
 Probability-and-statistics/391657: Suppose the variable X has a normal distribution with mean 36 inches and standard deviation 2 inches.What proportion of these values is between 32 and 40 inches? If one of these X values is chosen at random, what is the probability that it is between 34 and 38 inches? 1 solutions Answer 277858 by robertb(4012)   on 2011-01-07 02:22:46 (Show Source): You can put this solution on YOUR website!The values between 32 and 40 inches are within 2 standard deviations from the mean 36, and so covers around 95.4% of the distribution. The values between 34 and 38 inches are within 1 standard deviation from the mean 36, and so covers around 68.2% of the distribution.
 Travel_Word_Problems/391667: You live 50 miles away from mr.jones. You both leave home at 5 and drive toward each other. mr. jones travels at 35 mph and you travel at 40 mph. At what time will you pass mr. jones on the road?1 solutions Answer 277857 by robertb(4012)   on 2011-01-07 02:14:35 (Show Source): You can put this solution on YOUR website! 35t + 40t = 50 ==> 75t = 50 ==> t = 2/3 hr, or 40 minutes. You and Mr. Jones will meet at 5:40.
 Rectangles/391117: If you double all of the sides of a square by what percentage has the area increased?1 solutions Answer 277624 by robertb(4012)   on 2011-01-06 03:53:18 (Show Source): You can put this solution on YOUR website!original area = new area = ==> percentage increase is %. You stated: "When we divide a whole number by a FRACTION [caps mine], our answer is larger than we started with. Explain why." In fact, this is true only if the dividing FRACTION is between 0 and 1 exclusive, and the number we're dividing is positive. Let a, b be positive integers, and let a > b, so that b/a < 1. Then by a multiplicative property of inequality.
 Inequalities/391120: Eight less than a number is no more than 14 and no less than 51 solutions Answer 277623 by robertb(4012)   on 2011-01-06 03:49:27 (Show Source): You can put this solution on YOUR website! ==>
 Travel_Word_Problems/391311: A train travels 80 miles per hour. A plane travels 200 miles per hour. How many hours longer will it take the train to travel 1,600 miles than it will take the plane?1 solutions Answer 277622 by robertb(4012)   on 2011-01-06 03:42:53 (Show Source): You can put this solution on YOUR website! hours longer.
 test/389908: Find the x and y coordinates of the points on x^2 + y^2=16 at which the tangent line(s) are: a) horizontal b) have a slope of 11 solutions Answer 277620 by robertb(4012)   on 2011-01-06 02:39:25 (Show Source): You can put this solution on YOUR website!a) The tangent lines are horizontal at the points (0,4) and (0,-4). b) The tangent lines have slope 1 at the intersection points of the circle with the line y = -x. Solving: ==> , or , . Then the points are (,) and (,).
 Probability-and-statistics/391102: Rebecca rolled a fair number cube twice. What is the probability that she will roll a number divisible by 3 on both rolls?1 solutions Answer 277619 by robertb(4012)   on 2011-01-06 02:30:43 (Show Source): You can put this solution on YOUR website!(1/3)*(1/3) = 1/9
 test/389816: Growth and decay. In march, yoda invested \$1500 into the stock market. In December his stock portfolio was worth \$5200. What was the monthly rate of change in his portfolio? 1 solutions Answer 277618 by robertb(4012)   on 2011-01-06 02:27:10 (Show Source): You can put this solution on YOUR website!I will assume that YOU invested \$1500 AT THE BEGINNING of the month of March, and that at the END of December, YOUR stock portfolio has worth \$5200. So that's after 10 months. YOUR portfolio's monthly rate of change r is then computed as follows: ==> , to 4 decimal places. That is 13.24% per month.
 Functions/391212: For g(x)=4x-9, find g(x) when x=3 and when x=5 1 solutions Answer 277617 by robertb(4012)   on 2011-01-06 02:08:06 (Show Source): You can put this solution on YOUR website!g(3) = 4*3 - 9 = 12 - 9 = 3, g(5) = 4*5 - 9 = 20 - 9 = 11.
 Trigonometry-basics/391223: Solve the following equation for x: sec x =1, for the interval[0,pi]?1 solutions Answer 277616 by robertb(4012)   on 2011-01-06 02:04:57 (Show Source): You can put this solution on YOUR website!sec x = 1 ==> cos x = 1. The only x-value satisfying the last equation in [0,] is x = 0.
 logarithm/391251: If f(g(x))=e^.05x, write formulas for f(x) and g(x).1 solutions Answer 277614 by robertb(4012)   on 2011-01-06 02:02:21 (Show Source): You can put this solution on YOUR website!g(x) could be 0.05x, while f(x) could be .
 test/391281: What is the least number that when divided by 7 has a remainder of 4, and when divided by 8 has a remainder of 5, and when divided by 9 has a remainder of 6?1 solutions Answer 277613 by robertb(4012)   on 2011-01-06 02:00:14 (Show Source): You can put this solution on YOUR website!I will assume that the least number you're asking for is a positive number. Then we have to find the smallest positive integer n that satisfies the simultaneous system of congruences n = 4 mod 7, n = 5 mod 8, n = 6 mod 9. We use the Chinese Remainder Theorem using the extended Euclidean algorithm. (For the statement of the theorem and symbolism go to http://en.wikipedia.org/wiki/Chinese_remainder_theorem). (31)(7) + (-3)(8*9) = 31*7 + -3*72 = 1 ==> e1 = -216 (=-3*72) 8*8 + -1*(7*9) = 8*8 + -1*63 = 1 ==>e2 = -63 (=-1*63), and 25*9 + -4*(7*8) = 25*9 + -4*56 = 1 ==> e3 = -224. ( = -4*56) Then the solution n is the linear combination n = 4*e1 + 5*e2 + 6*e3 = 4*-216 +5*-63 +6*-224 = -2523 mod 504, where 504 = 7*8*9. The least positive integer satisfying n = -2523 mod 504 is 501. Therefore the final answer is 501.
 Triangles/389893: The vertices of ABC are A(-8, 0), B(0, 0), and C(0, -4). If a circle is circumscribed around ABC, where would the center of the circle be located?1 solutions Answer 277551 by robertb(4012)   on 2011-01-05 22:13:16 (Show Source): You can put this solution on YOUR website!The circumscribing circle must have center (-4, -2), which is actually the midpoint of the segment AC.
 Trigonometry-basics/391236: If A and B are two angles in Quadrant 2 such that tan A=-1/2 and tan B=-2/3, find cos(A+B). Thank you so much for all of your help!!!! God Bless!!!!!1 solutions Answer 277545 by robertb(4012)   on 2011-01-05 21:56:04 (Show Source): You can put this solution on YOUR website!tan A = -1/2 ==> ==> ==> . tan B = -2/3 ==> ==> ==> . Now
 Complex_Numbers/389874: please solve algebraically for x: square root (3x+1)+1=x1 solutions Answer 277539 by robertb(4012)   on 2011-01-05 21:44:05 (Show Source): You can put this solution on YOUR website!, ==> , ==> ,after squaring both sides. ==> , or x(x - 5) = 0. ==> x = 0 or x = 5. The 1st x-value will not satisfy the original equation, and the 2nd x-value does. Therefore final answer is x = 5.
 logarithm/391133: Can you help me solve this? I have a really hard time with Logarithms: log(2x+7) base 4 = log(81) base 31 solutions Answer 277528 by robertb(4012)   on 2011-01-05 21:36:48 (Show Source): You can put this solution on YOUR website!log(2x+7) base 4 = log(81) base 3 <==> log(2x+7) base 4 = 4 <==> ==> 2x + 7 = 256, x = 249/2.
 Functions/390984: Let f(x) = sqrt of x and g(x)= 2x+5. Determine the domain of the composite function and then find the composite function. (g*f)(x) Domain: _________ (g*f)(x)= _________1 solutions Answer 277521 by robertb(4012)   on 2011-01-05 21:33:15 (Show Source): You can put this solution on YOUR website!(gof)(x) = g(f(x)) = g() = 2 + 5. The domain of gof is [0, ).
 Trigonometry-basics/391225: Determine the range of y = tan 2x1 solutions Answer 277513 by robertb(4012)   on 2011-01-05 21:27:48 (Show Source): You can put this solution on YOUR website!The range of tan(2x) is still (, ). What changes is its period. From a period of (from tanx), the period becomes .
 Triangles/391156: in equilateral triangle one angle measures 3x+y the other 2x+40 and the third 2y what is the value of x and what is the value of y 1 solutions Answer 277506 by robertb(4012)   on 2011-01-05 21:19:46 (Show Source): You can put this solution on YOUR website!3x+y = 60 2x+ 40 = 60 2y = 60, because equilateral <==> equiangular. Then y = 30 degrees, and x = 10 degrees.
 Trigonometry-basics/391183: Which expression is equivalent to log7 2401 - log3 243 1 solutions Answer 277502 by robertb(4012)   on 2011-01-05 21:11:22 (Show Source): You can put this solution on YOUR website! and , thus log7 2401 - log3 243 = 4 - 5 = -1.
 Miscellaneous_Word_Problems/391200: On a scale drawing, 48 feet is represented by 12 inches.How many feet does a scale 1/4 inch represent? 1 solutions Answer 277499 by robertb(4012)   on 2011-01-05 21:07:48 (Show Source): You can put this solution on YOUR website! <==> , so x = 1 foot.
 Inequalities/391216: solve 5x+3x>-81 solutions Answer 277495 by robertb(4012)   on 2011-01-05 21:05:22 (Show Source): You can put this solution on YOUR website!5x+3x>-8 ==>8x > -8 ==>x > -1 after division by 8, a positive number. In interval notation , (-1, ).
 Rational-functions/391155: can you please help me work out this problem. i need to find the range of this function: {{3+x^2/ 4-x^2}}. i tried writing the problem as two binomials on top and two binomials on the bottom and solve for x but i am not sure if that is what i am suppose to do. so can you please help me solve this problem. Thank you so much for your time. 1 solutions Answer 277492 by robertb(4012)   on 2011-01-05 21:03:14 (Show Source): You can put this solution on YOUR website!I will assume that your function is . To find the range solve for x in terms of y and then state conditions on y that may arise. <==> <==> ==> , using the quadratic formula. Since the values of x must be real, the conditions we should impose on y are and y is not equal to -1. The solution set to this inequality is the union of intervals (, -1)U[3/4, ). This is the RANGE of the function.
 Travel_Word_Problems/390922: A car travels y miles in t hours, what is its speed?1 solutions Answer 277260 by robertb(4012)   on 2011-01-05 05:05:30 (Show Source): You can put this solution on YOUR website!y/t miles per hour average speed
 Travel_Word_Problems/390906: The distance from a star to a planet is 9.1 X 10^18 m. How long does it take light, traveling at 10^16 m/year, to travel from the star to the planet?1 solutions Answer 277259 by robertb(4012)   on 2011-01-05 05:04:23 (Show Source): You can put this solution on YOUR website! years, or 910 years.