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# Recent problems solved by 'venugopalramana'

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 Polynomials-and-rational-expressions/14331: I Need Help Solving This Problem.... x/5 - x+2/3 = 1/151 solutions Answer 7461 by venugopalramana(3286)   on 2005-10-12 11:59:54 (Show Source): You can put this solution on YOUR website! lcm is 15. hence Multiplying both sides with 15 , we get .... -2x-10=1 -2x=1+10=11 x=11/2
 Equations/14354: Find an equation of the line (in either general form or slope intercept form) that contains the centers of the following two circles: x^2+y^2-4x+6y+4 = 0 and x^2+y^2+6x+4y+9 = 01 solutions Answer 7452 by venugopalramana(3286)   on 2005-10-12 06:47:47 (Show Source): You can put this solution on YOUR website!The equation of a circle with centre as (h,k) and radius r is given by the formula . So we have to write the given equation in this form to get the centre of the circle. OR ...Note that we have added and subtracted 4 and 9 to make up the squares mentioned in brackets. Hence Hence (2,-3)is the centre of this circle .Similarly the centre of the second circle is obtained from OR ...Note that we have added and subtracted 9 and 4 to make up the squares mentioned in brackets. Hence Hence the centre of the second circle is (-3,-2) The equation of line joining 2 ponts (x1,y1) and (x2,y2)is given by the formula Substituting (2,-3) and (-3,-2) in the above formula we get Y-(-3)=(-2-(-3))*(X-2)/(-3-(-2)) Y+3=(X-2)/(-5) -5Y-15=X-2 X+5Y+13=0
 Linear-equations/14337: Can you pleae help me with these two questions: The table of ordered pairs shown was generated by a graphing calculator a. What is the x intercept b. Find the slope of the line. x y 0 1 -2 0 -4 -11 solutions Answer 7451 by venugopalramana(3286)   on 2005-10-12 06:11:22 (Show Source): You can put this solution on YOUR website! X intercept of a line is the distance (to be measured along the positive direction of the X axis) from origin to the point where the line meets the X axis .As the intersecting point is on the X axis ,it is characterised by the fact that its Y coordinate is zero.From the table we find that when Y =0 , X = -2 . Hence the X intercept is -2. Slope of a line is given by the formula Difference in Y coordinates of any 2 points on the line / Difference in X coordinates of the same 2 points on the line . If we take the 2 points as A (0,1) and B (-2,0) from the given ordered pairs... slope = (0-1)/(-2-0)= -1/(-2)=1/2
 Linear-equations/14313: 1. Two points, as we know, determine a line segment. To compute the slope of the line, we can take the points in either order. Explain WHY this is so. Give an example to help explain. 1 solutions Answer 7450 by venugopalramana(3286)   on 2005-10-12 05:58:37 (Show Source): You can put this solution on YOUR website!If the points are taken as P with coordinates (p,q) and A with coordinates (a,b) then the slope of the line PA is given by the formula Difference in Y coordinates / Difference in X coordinates = (b-q)/(a-p)...It does not matter for this purpose whether we take the coordinates of A first or those of P first as long as we take the same order for calculating the difference of both Y and X cordinates of the 2 points.It is easy to see that Slope of PA = (b-q)/(a-p) = (-(q-b))/(-(p-a))= (q-b)/(a-p)= Slope of AP Viewing it from the physical sence , slope of a line is the Tangent of the angle the line makes with X axis in the positive (anticlockwise)direction. The line afterall makes the same angle with X axis , whether we look at it as PA or AP and hence its tangent which is the slope of the line is also same whichever way we take the line segment.
 Triangles/14649: You have a triangle with sides 6, 7 and x. What is the maximum that x can be and why?1 solutions Answer 7430 by venugopalramana(3286)   on 2005-10-11 23:35:22 (Show Source): You can put this solution on YOUR website!There seems to be an error in your problem .There are 2 basic (inter-related)rules governing the dimensions of the 3 sides of a triangle for it to exist,that is for you to physically draw a triangle with those dimensions.They are 1. Sum of any 2 sides shall be greater than the third side and 2. Difference of any 2 sides shall be less than the third side. Otherwise, what happens is that when you attempt to draw such a triangle , you will not be able to get the third vertex after having started with any 2 sides and 2 vertices. Hence ,in our present problem ,since 2 sides are 6 & 7 b,the third side x shall be greater than 13 or less than 1 (ofcourse it cannot be zero or negative).That is x should lie between 9 and 1 or should be greater than 13. Hence it is not correct to say that x has a maximum value .We can however say it has a minimum of zero in the lower range of number line and in that vicinity a local maximum of one and then again a minimum of 13 in the upper range of number line with no limit on maximum higher value beyond that.