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# Recent problems solved by 'Alan3354'

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 Sequences-and-series/285528: In numbering the pages of a book, a total of 510 digits were printed. If the first page is numbered 1, how many pages does the book have? (A)170 (B) 199 (C) 200 (D) 206 (E) 198 1 solutions Answer 207157 by Alan3354(30993)   on 2010-03-26 20:41:36 (Show Source): You can put this solution on YOUR website!In numbering the pages of a book, a total of 510 digits were printed. If the first page is numbered 1, how many pages does the book have? (A)170 (B) 199 (C) 200 (D) 206 (E) 198 ------------------- 1 to 9 = 9 digits 10 to 99 = 180 digits ---------------------- 189 used, 321 left of 3 each 321/3 = 107 pages starting at 100 ---> 206 pages total Why couldn't you figure that out?
 Finance/285669: A) round 64,982.7866 to the nearest hundred. b)round 97,840.(27) ̅ to the nearest ten-thousandth. 1 solutions Answer 207074 by Alan3354(30993)   on 2010-03-26 18:11:27 (Show Source): You can put this solution on YOUR website!A) round 64,982.7866 to the nearest hundred. 65000 ---------- b)round 97,840.(27) ̅ to the nearest ten-thousandth. What does that mean? What's the (27) ? If it's repeating, .27272727... Then it's 97840.2727
 test/285649: ∫e^√x / √x dx= (A) 2e^√x+C (B) 1/2e^√x+C (C) e^√x+C (D) 2√xe^√x+C (E) (1/2)*e^√x/√x+C1 solutions Answer 207073 by Alan3354(30993)   on 2010-03-26 18:00:51 (Show Source): You can put this solution on YOUR website!It's A
 Quadratic_Equations/285663: y^2-4y=01 solutions Answer 207071 by Alan3354(30993)   on 2010-03-26 17:49:07 (Show Source): You can put this solution on YOUR website!Do you have a question? Solve for y? y*(y-4) = 0 y = 0, y = 4
 Angles/285662: How do I find the exact ratio of sec pi/6?1 solutions Answer 207070 by Alan3354(30993)   on 2010-03-26 17:47:38 (Show Source): You can put this solution on YOUR website!It's a value. If you're allowed to start with the cosine, it's sec(pi/6) = 1/cos(pi/6) = 1/(sqrt(3)/2) =
 Points-lines-and-rays/285651: It has been a really long time since high school so I am not sure what to do or where to look to learn how to do this! Thanks Given two points (x1, y1) and (x2, y2), derive the equation of the line that passes through those two points and write it in the form y = mx + b. This is called the slope-intercept form of the equation of the line because the two parameters m and b represent the slope and y-intercept of the line. 1 solutions Answer 207068 by Alan3354(30993)   on 2010-03-26 17:30:30 (Show Source): You can put this solution on YOUR website!Given 2 points example. Find the equation of the line thru the points (2,1) and (3,5) --------------------- This is a 2 step process. First find the slope of the line thru the points. slope, m = diffy/diffx m = (5-1)/(3-2) m = 4 --------- Now use y = mx + b with either point to find b, the y-intercept. y = mx + b 5 = 4*3 + b b = -7 ------- y = mx + b y = 4x - 7 is the answer. ------------------------ For further assistance, or to check your work, email me via the thank you note.
 logarithm/285641: Log9 1 = x. solve.1 solutions Answer 207067 by Alan3354(30993)   on 2010-03-26 17:23:55 (Show Source): You can put this solution on YOUR website!The log of 1 to any base is zero (0). for all values of b>0. by convention. Negative numbers I'm not sure about.
 logarithm/285549: The Richter magnitude m of an earthquake is given by the formula: m = log (A/A₀), where A is the maximum amplitude of the earthquake and is a constant. What is the magnitude on the Richter scale of an earthquake with an amplitude that is a million times A₀?1 solutions Answer 207043 by Alan3354(30993)   on 2010-03-26 15:11:43 (Show Source): You can put this solution on YOUR website!1 million = 10^6 --> A₀ + 6
 Geometric_formulas/285624: if the radius of a circle is tripled, the diameter is also tripled. true or false? I think it is true1 solutions Answer 207042 by Alan3354(30993)   on 2010-03-26 15:05:27 (Show Source): You can put this solution on YOUR website!It's true. d = 2r 3d = 2*3r = 6r ---------------- More formally, the diameter is directly related to the radius. The area is related to the square of the radius, so 3x the radius --> 9x area.
 Linear-equations/285622: Find an equation of the line containing the given pair of points. (-5,-2) and (-3,-1). The equation of the line in slope-intercept form is y=1 solutions Answer 207041 by Alan3354(30993)   on 2010-03-26 15:04:07 (Show Source): You can put this solution on YOUR website!Given 2 points example. Find the equation of the line thru the points (2,1) and (3,5) --------------------- This is a 2 step process. First find the slope of the line thru the points. slope, m = diffy/diffx m = (5-1)/(3-2) m = 4 --------- Now use y = mx + b with either point to find b, the y-intercept. y = mx + b 5 = 4*3 + b b = -7 ------- y = mx + b y = 4x - 7 is the answer. ------------------------ For further assistance, or to check your work, email me via the thank you note.
 Travel_Word_Problems/285569: james is hiding within a 7 miles of his home. what is the approximate area, in square miles, of the region in which he may be hiding? 1 solutions Answer 207040 by Alan3354(30993)   on 2010-03-26 14:53:58 (Show Source): You can put this solution on YOUR website!He would be inside a circle 7 miles in radius. Area = pi*7^2 = 49pi Area =~ 154 sq miles
 Geometric_formulas/285620: Ray SU bisects angle RST. The measure of angle RSU=6x-3 and the measure of angle UST=5x+4. Find the measure of RSU. 1 solutions Answer 207037 by Alan3354(30993)   on 2010-03-26 14:45:39 (Show Source): You can put this solution on YOUR website!Ray SU bisects angle RST. The measure of angle RSU=6x-3 and the measure of angle UST=5x+4. Find the measure of RSU. --------------- Since it bisects it, 6x-3 = 5x+4 x = 7 RSU = 6*7 - 3 = 39 degrees
 Equations/285615: Find the missing factor: 6x^4=(3x^3)(____) I have no idea whereabouts on how to do this.1 solutions Answer 207036 by Alan3354(30993)   on 2010-03-26 14:43:03 (Show Source): You can put this solution on YOUR website!Find the missing factor: 6x^4=(3x^3)(F) ---------- F = 2x
 Trigonometry-basics/285552: simplify tan (pi/4 -x) 1 solutions Answer 207025 by Alan3354(30993)   on 2010-03-26 14:16:21 (Show Source): You can put this solution on YOUR website!cot(x)
 Rational-functions/285613: 1 + 2/x = 3/ x^2 x/ x-1 + x = 4x - 3/ x - 1 Please help....I am so lost. I have no idea even where to start.1 solutions Answer 207024 by Alan3354(30993)   on 2010-03-26 14:14:46 (Show Source): You can put this solution on YOUR website!1 + 2/x = 3/ x^2 Get rid of fractions. Multiply thru by x^2 (x+3)*(x-1) = 0 x = -3, 1 ------------- x/ x-1 + x = 4x - 3/ x - 1 It's not clear, use some parenthese.
 Volume/285583: In cubic meters, how much greater is the volume of a cylinder with height 19 m and a radius 16 m than the volume of a square prism with height 19 m and base 16 m on a side?1 solutions Answer 207022 by Alan3354(30993)   on 2010-03-26 14:11:52 (Show Source): You can put this solution on YOUR website! In cubic meters, how much greater is the volume of a cylinder with height 19 m and a radius 16 m than the volume of a square prism with height 19 m and base 16 m on a side? --------------------- Find the volumes and see. Cylinder: r = 16, h = 19 ---------------- Prism: Vol = 16*16*19 --------------
 Triangles/285435: Kim throws a boccie ball 25 yards ahead, then turns 15 degrees and throws another boccie ball 25 yards straight ahead. How far apart, to the nearest yard, will the two balls land?1 solutions Answer 207020 by Alan3354(30993)   on 2010-03-26 13:58:57 (Show Source): You can put this solution on YOUR website!Kim throws a boccie ball 25 yards ahead, then turns 15 degrees and throws another boccie ball 25 yards straight ahead. How far apart, to the nearest yard, will the two balls land? --------------------------------- The origin and the 2 balls form an isosceles triangle. Dropping an altitude from the origin to the side between the two balls gives 2 right triangles with a hypotenuse of 25 yards and an angle at the origin of 7.5 degrees. 1/2 the distance = 25*sin(7.5) =~ 3.263 yards The distance is 2x that, =~ 6.526 yards
 Rational-functions/285589: Write a function that models the variation. {x=3 & y=12} if z=2 z varies directly with y and inversely with x. I tried this problem, and came up with the equation, z=(1/18y)/x Is this correct? If not, how do I solve this problem? Thanks.1 solutions Answer 206997 by Alan3354(30993)   on 2010-03-26 12:10:43 (Show Source): You can put this solution on YOUR website!Write a function that models the variation. {x=3 & y=12} if z=2 z varies directly with y and inversely with x. I tried this problem, and came up with the equation, z=(1/18y)/x Is this correct? If not, how do I solve this problem? --------------- z = ky/x 2 = 12k/3 k = 1/2 --> z = y/2x
 Radicals/285594: What is the sum of the roots of the equation ax(squared) +bx +c =0?1 solutions Answer 206996 by Alan3354(30993)   on 2010-03-26 12:07:48 (Show Source): You can put this solution on YOUR website!-b/a ----- The roots are -b/2a + D -b/2a - D ---------- Add -b/a
 Linear-equations/285591: find the slope and y intercept of the line. write fractional answers in lowest terms. 5y+9x+7 = 18+9x 1 solutions Answer 206995 by Alan3354(30993)   on 2010-03-26 12:06:50 (Show Source): You can put this solution on YOUR website! find the slope and y intercept of the line. write fractional answers in lowest terms. 5y+9x+7 = 18+9x --------------- Solve for y 5y = 11 y = 11/5 Slope = 0 y-intercept = 11/5
 Linear-equations/285593: After graphing 4x-2y=5 and y=x how many points do they intersect?1 solutions Answer 206994 by Alan3354(30993)   on 2010-03-26 12:01:34 (Show Source): You can put this solution on YOUR website!1 They're straight lines, and their slopes are not equal. --> 1
 Money_Word_Problems/285590: What is the slope of the line tangent to the curve y=10x^2+x At the point (1,11)?1 solutions Answer 206992 by Alan3354(30993)   on 2010-03-26 11:47:50 (Show Source): You can put this solution on YOUR website!The slope is 20x + 1 at any point At x = 1, it's 21
 Quadratic-relations-and-conic-sections/285565: Find the center and radius of the circle with equation: x^2 + (y-4)^2 =91 solutions Answer 206989 by Alan3354(30993)   on 2010-03-26 11:34:29 (Show Source): You can put this solution on YOUR website!Find the center and radius of the circle with equation: x^2 + (y-4)^2 =9 --------------- The center is (0,4) The radius is 3
 Quadratic-relations-and-conic-sections/285580: if you have an equation that is x^2=10y, how do you graph that as a parabola?1 solutions Answer 206985 by Alan3354(30993)   on 2010-03-26 11:24:26 (Show Source): You can put this solution on YOUR website! Pick values for x, find y. Plot the points, draw a curve thru them. eg x....y 0...0 1...0.1 2...0.4 3...0.9 ---------- You can sub neg values for x and get the same y to save time.
 Rate-of-work-word-problems/285585: if jane can paint a house in four hours and paul can paint the same house in six hours how long will it take to paint the house together?1 solutions Answer 206984 by Alan3354(30993)   on 2010-03-26 11:19:39 (Show Source): You can put this solution on YOUR website!In one hour, Jane paints 1/4 and Paul paints 1/6. Add those up. What does that tell you?
 Permutations/285587: 2x^2-5x+11 solutions Answer 206983 by Alan3354(30993)   on 2010-03-26 11:18:36 (Show Source): You can put this solution on YOUR website!Do you have a question?
 logarithm/285582: what is 8 to the power of log base 8 of X?1 solutions Answer 206981 by Alan3354(30993)   on 2010-03-26 11:13:51 (Show Source): You can put this solution on YOUR website! = x
 Polynomials-and-rational-expressions/285586: can you give me the answer and show me how to solve 16x-25?1 solutions Answer 206980 by Alan3354(30993)   on 2010-03-26 11:11:51 (Show Source): You can put this solution on YOUR website!Equations are solved. This is not an equation, only an expression. All equations have an equal sign.
 Trigonometry-basics/285553: use pi/3 + pi/4=7pi/12 find the exact value of sin 7pi/121 solutions Answer 206960 by Alan3354(30993)   on 2010-03-26 09:05:03 (Show Source): You can put this solution on YOUR website!use pi/3 + pi/4=7pi/12 find the exact value of sin 7pi/12 ----------------------- sin(pi/3) = 1/2 cos(pi/3) = sqrt(3)/2 sin(pi/4) = sqrt(2)/2 cos(pi/4) = sqrt(2)/2 ---------------- sin(A+B) = sin(A)cos(B) + sin(B)cos(A) sin(7pi/12) = 1/2*sqrt(2)/2 + sqrt(3)/2*sqrt(2)/2 = sqrt(2)/4 + sqrt(6)/4 =
 Miscellaneous_Word_Problems/285441: Please help with the following word problem! A plane flies 390 mph in still air. It makes a round trip of 5040 miles in a total of 13 hours, one way with the jet stream and the other way against the jet stream. Find the speed of the jet stream. I know that Rate X Time = Distance, so using J for jet stream and T for time, I tried (390-J) X (T) = 2520 (1/2 the distance since it was round-trip) and (390+J) X (13-T) = 2520. I also tried (390-J) X (T) = (390+J) X (13-T). I get to a point where I'm not sure what to do with two variables. How would you set this problem up? If I am on the right track, how do I solve for 2 variables? Thank you so much!1 solutions Answer 206918 by Alan3354(30993)   on 2010-03-25 22:35:29 (Show Source): You can put this solution on YOUR website!2520/(390 + J) + 2520/(390-J) = 13 2520*(390-J) + 2520*(390+J) = 13(390-J)(390+J) A quadratic in J email me via the Thank You note if you like
 Polynomials-and-rational-expressions/285449: What is the difference of 2 squares of this question: 16x^2-25? Thank You.1 solutions Answer 206908 by Alan3354(30993)   on 2010-03-25 21:05:43 (Show Source): You can put this solution on YOUR website!it's