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# Recent problems solved by 'robertb'

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 Exponential-and-logarithmic-functions/451905: Evaluate. log4(256)1 solutions Answer 310720 by robertb(4012)   on 2011-05-19 23:29:31 (Show Source):
 Polynomials-and-rational-expressions/451946: FACTOR: ax+ay+2az+3x+3y+6z1 solutions Answer 310719 by robertb(4012)   on 2011-05-19 23:27:11 (Show Source): You can put this solution on YOUR website!a(x+y+2z) + 3(x+y+2z) = (a+3)(x+y+2z)
 Numbers_Word_Problems/451921: 1/3 of a number exceeds 1/4 by 400.find the number1 solutions Answer 310712 by robertb(4012)   on 2011-05-19 22:37:08 (Show Source): You can put this solution on YOUR website! ==> ==> ==> 4n - 3 = 4800 ==> 4n = 4803 ==> n = 4803/4
 Quadratic-relations-and-conic-sections/451902: Find equation for the ellipse that shares a vertex and focus with the parabola x^2 + y = 100 and has its other focus at the origin? I know what the shape of the two figures together would look like, and i found that 2C is 100, since that is the distance between foci. From that I determined that 2b - c = 100. What I don't get is how to find a and b. Thanks very much!1 solutions Answer 310708 by robertb(4012)   on 2011-05-19 22:24:23 (Show Source): You can put this solution on YOUR website!You say that the ellipse shares a vertex (the point (0, 100)) and a focus with the parabola , or , or . Hence for the parabola, the distance from the vertex to the focus is 1/4. Also, one focus of the ellipse must be (0, 399/4). It was given that the other focus of the ellipse is (0,0) (the origin). The center of the ellipse is then the point (0, 399/8). So , and . Then Then the standard equation is , or .
 Age_Word_Problems/451904: determine the value of x: (3-x):(x+1) = 2:11 solutions Answer 310695 by robertb(4012)   on 2011-05-19 21:19:13 (Show Source): You can put this solution on YOUR website! ==> 3-x = 2(x+1) ==> 3-x = 2x + 2 ==> 1 = 3x ==> x = 1/3
 Rate-of-work-word-problems/451900: When Amos and Bert do a certain job, it takes 13 and 19/23 hours. WHen Bert and Clyde do it, it takes 13 and 1/5 hours. When Amos and Clyde do it, it takes 17 and 5/23 hours. How long does it take each brother to do it alone?1 solutions Answer 310691 by robertb(4012)   on 2011-05-19 21:10:41 (Show Source): You can put this solution on YOUR website! Subtracting the 2nd equation from the 1st, we get . Adding the previous equation to the 3rd equation gives . ==> ==> hours. You can now get the values for b and c.
 Linear_Algebra/451871: I have to write each function in standard form 1. y = (x +4)^2 - 4 2. y = -(2x + 3)^2 + 14 3. y = 2 (3x + 2)^2 - 41 solutions Answer 310685 by robertb(4012)   on 2011-05-19 20:52:47 (Show Source): You can put this solution on YOUR website!1. 2. 3.
 Functions/451874: Problem: f(x) = (3x -1)/ (x + 4)= Domain (- infinity, -4) u (-4, infinity) Find the equations of both vertical and horizontal asymptotes of the function. Please show work or explain in Words.1 solutions Answer 310683 by robertb(4012)   on 2011-05-19 20:47:55 (Show Source): You can put this solution on YOUR website!Considering only the highest powers for the numerator and denominator, the function is reduced to . Letting x approach , f(x) then approaches 3, and hence the horizontal asymptote is y = 3. The vertical asymptote is where x + 4 = 0, or x = -4, which is the equation of the vertical asymptote itself.
 Functions/451878: Problem: g(x)= (x + 7)/(x^2-4)= Domain: (- infinity, -2)u (-2, 2) u (2, infinity) Find the equations of both vertical and horizontal asymptotes of the function. Show work or Explain in words:1 solutions Answer 310672 by robertb(4012)   on 2011-05-19 20:11:44 (Show Source): You can put this solution on YOUR website!Considering only the highest power for the numerator and denominator, the function is reduced to . Letting x approach , the limit of g(x) is 0. Hence the horizontal asymptote is y = 0. The vertical asymptotes are exactly x = 2 and x = -2.
 Exponential-and-logarithmic-functions/451880: Write the logarithmic equation in exponential form. logc(a) = b 1 solutions Answer 310670 by robertb(4012)   on 2011-05-19 20:06:59 (Show Source):
 Exponential-and-logarithmic-functions/451541: If a bacteria culture doubles every 12 hours, then how much bacteria would exist after 2 days if the culture started with 100 cells?1 solutions Answer 310503 by robertb(4012)   on 2011-05-19 03:33:25 (Show Source): You can put this solution on YOUR website!, where t is in hours. After 2 days, or 48 hours, there are bacteria.
 test/451560: How to use Sum Difference identities to fin the exact value: Cos 53 degrees cos 82 degrees - sin 53 degrees sin 82 degrees ? Thank you!1 solutions Answer 310502 by robertb(4012)   on 2011-05-19 03:26:19 (Show Source): You can put this solution on YOUR website!Cos(53 + 82) = cos 135 =
 Quadratic_Equations/4812: why do you factor a quadratic equation before you solve?1 solutions Answer 310498 by robertb(4012)   on 2011-05-19 02:56:38 (Show Source): You can put this solution on YOUR website!Because you want to take advantage of the Zero-Product property, which says a*b = 0 implies either a = 0 or b = 0. Factoring a quadratic expression involves reversing the distributive property of multiplication over addition, the result being the product of two linear factors.
 Inequalities/451463: Solve x-5(4-9x)>= 3(6x+1) Write solution using set builder notation. Show all work1 solutions Answer 310495 by robertb(4012)   on 2011-05-19 02:19:14 (Show Source): You can put this solution on YOUR website! ==> ==> ==>
 Functions/451554: How do i simplify 2i to the 3rd power? 1 solutions Answer 310493 by robertb(4012)   on 2011-05-19 02:11:37 (Show Source): You can put this solution on YOUR website!I'll assume the expression is . Then
 Functions/451555: How do i solve "If f(2)=0 and f(x)=3x^2+kx-4,find k" i need help solving this step by step.1 solutions Answer 310492 by robertb(4012)   on 2011-05-19 02:09:39 (Show Source): You can put this solution on YOUR website! ==> ==> 2k + 8 = 0 ==> 2k = -8 ==> k = -4.
 Rational-functions/451539: Write a function with vertical asymptotes at x=2, x=3, x=4 and a horizontal asymptote at y=51 solutions Answer 310489 by robertb(4012)   on 2011-05-19 01:45:48 (Show Source):
 Expressions-with-variables/451544: solvinging inequality...please help -2(2x – 6) -4x > 3x – 10 + 9 1 solutions Answer 310486 by robertb(4012)   on 2011-05-19 01:35:28 (Show Source): You can put this solution on YOUR website!-4x + 12 - 4x > 3x-1 ==> -8x + 12 > 3x - 1 ==> -8x - 3x > -1 - 12 ==> -11x > -13 ==> x < 13/11.
 Volume/451533: How much water can you fit into a container that's 16 square feet by 2inches tall?1 solutions Answer 310484 by robertb(4012)   on 2011-05-19 01:29:57 (Show Source): You can put this solution on YOUR website!16 sq. ft. * 2 in* (1ft. /12 in.) = 32/12 cu. ft. = 8/3 cu.ft.
 Triangles/451549: what the range for the measure of the third side given the measures of two sides of 82 and 81 solutions Answer 310483 by robertb(4012)   on 2011-05-19 01:23:49 (Show Source): You can put this solution on YOUR website!Let x be the 3rd side of the triangle. From the repeated use of the triangle inequality, 82 + 8 = 90 > x, and 8 + x > 82, or x > 74. Hence 90 > x > 74.
 Money_Word_Problems/451521: Suppose you deposit money in an ivestment account that pays 9% annual interest compounded continuously. About how many years will it take for your initial deposit to double?1 solutions Answer 310479 by robertb(4012)   on 2011-05-19 00:20:24 (Show Source): You can put this solution on YOUR website! ==> ==> ln2 = 0.09t ==> t = ln2/0.09 = 7.7 years, to the nearest tenth of a year.
 Divisibility_and_Prime_Numbers/451192: which of the following is divvisble by 4? 126 285 324 442 5981 solutions Answer 310477 by robertb(4012)   on 2011-05-19 00:16:02 (Show Source): You can put this solution on YOUR website!Only 324 is divisible by 4. In general, any number is divisible by 4 if the number formed by the last two digits (from the right) is divisible by 4.
 Linear-equations/451522: como determino los valores de k para que el sistema de ecuaciones lineal tenga numero infinito kx+y=4 2x-3y=-12 1 solutions Answer 310463 by robertb(4012)   on 2011-05-18 23:25:00 (Show Source): You can put this solution on YOUR website!k must be equal to -2/3 for the system to be dependent, hence an infinite number of solutions. That way, the top equation will be , which if you multiply both sides by -3, will give you exactly the bottom equation.
 Triangles/451434: the legs of a right triangle have lengths x+4 and x+7. The hypotenuse has length 3x. Find the perimeter of the triangle1 solutions Answer 310461 by robertb(4012)   on 2011-05-18 23:20:26 (Show Source): You can put this solution on YOUR website!using the Pythagorean theorem, we get <==> <==> <==> (7x + 13)(x-5) = 0 ==> x = 5 The perimeter is x+4 +x+7 + 3x = 5x + 11 Hence the perimeter is 5*5 + 11 = 25 + 11 = 36. (We cannot accept the other x-value -13/7 for an apparent reason.)
 Mixture_Word_Problems/451435: pure acid is to be added to a 20% solution to obtain 60 liters of a 30% acid solution. what amounts of each should be used?1 solutions Answer 310460 by robertb(4012)   on 2011-05-18 23:07:01 (Show Source): You can put this solution on YOUR website!1.00x + 0.20(60-x) = 0.30*60 ==> x + 12 - 0.20x = 18 ==> 0.80x = 6 ==> x = 7.5 liters of pure acid, and 60 - x = 52.5 liters of the 20% acid.
 Rectangles/451466: The dimensions of a rectangular box are 1 ft x 2 ft x 3 ft. What is the length of each interior diagonal of this box?1 solutions Answer 310457 by robertb(4012)   on 2011-05-18 22:55:41 (Show Source): You can put this solution on YOUR website! feet
 Triangles/451439: Use slope to show that XYZ is a right triangle... where X is (2,4), Z is (-1,0) .. & Y is (3, -3)1 solutions Answer 310456 by robertb(4012)   on 2011-05-18 22:52:46 (Show Source): You can put this solution on YOUR website!Slope of line XZ = Slope of line ZY = Since the product of the two slopes is -1, the triangle formed is a right triangle.
 Linear-equations/451456: Find the x and y intercepts and one other point of the line 2x-y= -71 solutions Answer 310452 by robertb(4012)   on 2011-05-18 22:35:22 (Show Source): You can put this solution on YOUR website!Divide both sides by -7: <==> The x-intercept is -7/2, the y-intercept 7. One other point on the line is (1, 9).
 Quadratic-relations-and-conic-sections/451478: What is the equation of a hyperbola with a vertex of (-3,0) and a Focus of (5,0)1 solutions Answer 310447 by robertb(4012)   on 2011-05-18 22:30:18 (Show Source): You can put this solution on YOUR website!The center of the hyperbola would be (0,0). Here, a = 3, and c = 5, and hence . Therefore the (standard) equation is
 Travel_Word_Problems/451470: how many miles will someone travel if they are going 40mph for 36 minutes?1 solutions Answer 310445 by robertb(4012)   on 2011-05-18 22:25:32 (Show Source): You can put this solution on YOUR website! miles
 Triangles/451483: What is the most condensed formula for the Area of a right triangle if only one angle and the hypotenuse is known?1 solutions Answer 310444 by robertb(4012)   on 2011-05-18 22:20:30 (Show Source): You can put this solution on YOUR website!Let A be the given (acute) angle. Then the side adjacent to angle A will have length c*cosA, where c is the length of the hypotenuse. Then the area of the right triangle is then