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Recent problems solved by 'RAY100'
RAY100 answered: 1636 problems
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1 solutions
Answer 163973 by RAY100(1637)   on 2009-09-26 16:12:56 (Show Source):
You can put this solution on YOUR website!Let x = angle,,,,,,complement = 90-x,,,,,,supplement = 180-x
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S=4+2c,,,,,180-x = 4 + 2(90-x)
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180-x = 4+180-2x
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x=4
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check,,,,x=4,,,c=90-4=86,,,,,s=180-4=176,,,,,176=4+2*86,,,ok
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Numbers_Word_Problems/217497: Given any positive even integer, x, the positive difference between the smallest odd number greater than 7x − 2 and the largest odd number less than 3x + 5 can be written in the form ax + b. What is a + b?
1 solutions
Answer 163972 by RAY100(1637) on 2009-09-26 16:06:23 (Show Source):
You can put this solution on YOUR website!Given x is an even integer,,,7x-2 is also even,,,smallest odd integer larger is 7x-2 +1 = 7x-1
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3x+5 is odd integer,,,,,largest odd number less is,,,,,3x+5 -2 = 3x+3
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(7x-1)-(3x+3) = 4x -4,,,,,ax+b
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a=4,,,,b=-4,,,,,,,a+b = 0
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Numbers_Word_Problems/217493: What is the smallest whole number that has a remainder of 1 when divided by 4, a remainder of 1 when divided by 3, and a remainder of 2 when divided by 5?
1 solutions
Answer 163967 by RAY100(1637) on 2009-09-26 15:50:13 (Show Source):
You can put this solution on YOUR website!5,,,,4,,,,7,,,,
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check,,,5/4=1R1,,,,4/3=1R1,,,,7/5=1R2
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Functions/217482: find the distance between P(-8,4) and Q(3,-2).
1 solutions
Answer 163965 by RAY100(1637) on 2009-09-26 15:44:53 (Show Source):
You can put this solution on YOUR website!P(-8,4),,,,,Q(3,-2)
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Remember the distance formula,,,d= sqrt{(y2-y1)^2 + (x2-x1)^2}
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d=sqrt{ (4-(-2))^2 + (-8-3)^2}
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d = sqrt{ 6^2 + (-11)^2)
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d= sqrt{ 36+121}
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d=sqrt { 157}
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d= 12.53
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checking,,,a rough sketch shows the legs of a rt triangle to be 11 and 6,,,,,and the hypotenuse = sqrt( 121+36) =12.53,,,,,ok
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Polynomials-and-rational-expressions/217390: (x2+3xy-8y2)-(6x3+8xy+xy2)=?
1 solutions
Answer 163932 by RAY100(1637) on 2009-09-26 11:40:43 (Show Source):
You can put this solution on YOUR website!(x^2+3xy-8y^2) - (6x^3 +8xy+xy^2),,,,distribute the -1
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x^2 +3xy -8y^2 -6x^3 -8xy -xy^2,,,,rearrange
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-6x^3 + x^2 -8xy+3xy -xy^2 - 8y^2,,,combine like terms
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-6x^3 +x^2 -5xy -xy^2 -8y^2,,,,,,
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Triangles/217386: The sides of a triangle are 15, 20, and 25. What is the length of the shortest altitude?
1 solutions
Answer 163928 by RAY100(1637) on 2009-09-26 11:23:27 (Show Source):
You can put this solution on YOUR website!Checking, we find that 15^2 +20^2 =25^2,,,,therefore this is a rt triangle, with legs 15, and 20, and hypotenuse 25
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On a right triangle, the legs are also altitudes, so 15, and 20 are altitudes.
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We need to check the altitude from the hypotenuse to the opposite vertex, however.
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Perhaps the easiest way is to establish the Area of the triangle, and then calculate that altitude.
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Area = 1/2 *b*h,,,and for square legs,,,A= 1/2*15*20 = 150
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For the hypotenuse as a base,,A= 1/2 *b*h,,,,150 = 1/2 *25 *h,,,h=12
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As it turns out, this last altitude is the smallest,,,,,,12
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Human-and-algebraic-language/217329: one number is 48 less than another number. If the sum of the two numbers is -164, then what is the smaller of the two numbers?
1 solutions
Answer 163889 by RAY100(1637) on 2009-09-25 22:58:23 (Show Source):
You can put this solution on YOUR website!Let x & y = numbers
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x+y=-164
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x= y-48,,,,,,subst
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(y-48) +y = -164
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2y = -116
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y= -58
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x=y-48=(-58)-48 = -106
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smaller of numbers is x=-106
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check,,,,,,x+y=-164,,,,,,(-106)+(-58) = -164,,,,,,ok
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x=y-48,,,,,,,,(-106) =(-58)-48 = -106,,,,,ok
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Linear-systems/217289: Consider the following.
g(y) = 7 − 2y
Evaluate the function at each specified value of the independent variable and simplify. (If the function is undefined at the specified value, enter UNDEFINED.)
(a) g(0)
(b) g(7/2)
(c) g(s + 2)
1 solutions
Answer 163873 by RAY100(1637) on 2009-09-25 21:42:23 (Show Source):
You can put this solution on YOUR website!g(y) = 7-2(y)
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g(0) = 7 - 2(0)=7,,,,,subst 0 for y
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g(7/2) = 7-2(7/2) = 7-7=0,,,,subst (7/2) for y
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g(s+2) =7-2(s+2) =7-2s-2(2) = 7-2s -4 = 3-2s ,,,,,subst (s+2) for y
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Equations/217301: the sum of 5 consecutive numbers is 195. what are the numbers?
1 solutions
Answer 163863 by RAY100(1637) on 2009-09-25 21:24:11 (Show Source):
You can put this solution on YOUR website!Let x, x+1,,x+2,,x+3,,x+4,,,be consecutive integers
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sum of these is,,,,,5x + 10 = 195
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5x = 185
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x= 37
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numbers are 37,38,39,40,41
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check,,,,sum of numbers = 195,,,ok
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Permutations/217296: Kindly answer this question please!!! Thanks!!! A housing contractor will build a house with 2,3, or 4 bedrooms, 1,or 2 bathrooms and a single garage. How many choices does he offer?
1 solutions
Answer 163858 by RAY100(1637) on 2009-09-25 21:17:20 (Show Source):
You can put this solution on YOUR website!bedroom choices =3
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bathroom choices =2
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garage choices = 1
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Total choices = 3*2*1=6
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listing, 2 bedroom, 1 bathroom, 1 garage
2 bedrooms, 2 bathrooms, 1 garage
3 bedroom, 1 bathroom, 1 garage
3 bedrooms, 2 bathrooms, 1 garage
4 bedroom, 1 bathroom, 1 garage
4 bedrooms, 2 bathrooms, 1 garage
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Percentage-and-ratio-word-problems/217128: There are 385 surfers in Surf City. Two thirds of the boys are surfers and one-twelfth of the girls are surfers. If there are two girls for every boy, then how many boys and how many girls are there in Surf City?
1 solutions
Answer 163773 by RAY100(1637) on 2009-09-25 13:00:38 (Show Source):
You can put this solution on YOUR website!Let b= # boys,,,,G= # girls
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2b=g,,,,,,,or b = g/2
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(2/3)b + (1/12)g =385
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(2/3) (g/2) + (1/12) g = 385
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(1/3)g +(1/12)g =385
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(4/12)g +(1/12)g = 385
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(5/12)g=385
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g=924,,,,,,,,b=g/2=462
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check
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(2/3)(462) +(1/12)(924) = 385
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308 + 77 = 385,,,,,ok
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Quadratic_Equations/217107: I am having difficulty with a question. The problems is as follows: A parabola has an x-intercept at 2, its axis of symmetry is the l ine x=4, and the y-coordinate of its vertex is 6. Determone the equation of the parabola.
I am setting up my equation - y = ax^2 + bx + c and plugging in the numbers as follows: y = 4a^2 + 2b + 8. Am I on the right track?
Thanks,
Lori
1 solutions
Answer 163744 by RAY100(1637) on 2009-09-25 11:13:02 (Show Source):
You can put this solution on YOUR website!a rough sketch helps,,,,,
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On x-y coordinates, line if symmetry is x=4, so draw a vertical at +4
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We also know that the vertex is on the line of symmetry so (4,?) is vertex
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But they give y=6 at vertex,,,,,therefore vertex is (4,6),,,might draw point
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Since x intercept is 2,,,(1) we know(2,0) is point on curve,
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(2) drawing point on rough graph, shows it to be curve pointing down.
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The basic eqn is probably a y parabola pointing down ,,,,,,from sketch
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base eqn is y=x^2 +b
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expanded form is (y-k) = A(x-h)^2
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we know vertex is (4,6) ,,,therefore h=4,,,k=6
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subst,,,,(y-6)=A(x-4)^2,,,,,subst (2,0)
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{(0)-6} =A {(2)-4}^2
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-6 =A(-2)^2
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-6 =A(4)
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A=-6/4 = -3/2=-1.5,,,,,,note negative confirms pointing down parabola
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combining,,,,(y-6)=-1.5(x-4)^2,,,,,answer
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checking,,,,(2,0),,,,(0-6) =-1.5(2-4)^2,,,-6=-1.5(-2)^2 =-1.5*4=-6,,,ok
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and (4,6),,,,,,6-6= -1.5(4-4)^2,,,,or 0=0,,,,,ok
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in standard form,,,(y-6) = -1.5(x-4)^2
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y-6 =-1,5{x^2-8x+16) = -1.5x^2 +12x -24
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y= -1.5x^2 +12x -18,,,,,std form answer
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checking,,,vertex x = -b/2a = -12/(2*-1.5) = +4 ,,,,,ok
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y=-1.5(4)^2 +12(4) -18 = -24 +48-18=6,,,,ok
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Distributive-associative-commutative-properties/217099: 10-4n-16-n
1 solutions
Answer 163740 by RAY100(1637) on 2009-09-25 10:47:06 (Show Source):
You can put this solution on YOUR website!10-4n-16-n,,,,rearrange terms
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10-16-4n-n,,,,,simplify by combining like terms
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-6 -5n,,,,,,answer
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Equations/217098: is 3 a solution to the equation 2x-4=x-1
1 solutions
Answer 163737 by RAY100(1637) on 2009-09-25 10:38:12 (Show Source):
You can put this solution on YOUR website!2x-4 = x-1,,,,,,,add 4 to both sides
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2x-4+4 = x-1+4
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2x=x+3,,,,,,now, substract x both sides
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2x-x = x+3-x
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x=3,,,,,answer
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check
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2x-4 = x-1,,,,subst x=3
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2(3)-4 = (3)-1
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2=2,,,,,,ok
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Linear-equations/217087: find the equation, in standard form, with all integer coefficients, of the line perpendicular to x + 3y=6 and passing through (-3,5).
1 solutions
Answer 163735 by RAY100(1637) on 2009-09-25 10:33:57 (Show Source):
You can put this solution on YOUR website!base eqn,,,x+3y =6,,,,,change to slope intercept form,,,,3y=-x+6,,,y=(-1/3)x +2,,,,,with m1 = (-1/3) and y intercept = +2
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We know a perpendicular has negative reciprocal slope,,,(m2=-1/m1),,,,therefore the slope of the perpendicular to the base eqn is,,,,,,,,m2= +3
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For the perpendicular line eqn,,,,start with y=mx+b,,,,and y=3x +b
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To find b,,,,,subst ( -3,5) into eqn
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(5)= (+3)(-3) +b
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5=-9=b
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14=b,,,,,,,,subst back into eqn
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y=3x + 14,,,,,,answer to perpendicular line in slope int form
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-14 = 3x-y,,,,,or 3x-y = -14,,,,in standard form
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check, m2= -1/m1,,,,,,,3=-1/(-1/3)= +3,,,,ok
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(-3,5),,,,check fit,,,,,(5) = 3(-3) +14,,,,,,5=-9+14,,,,,,ok
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Miscellaneous_Word_Problems/217089: On three consecutive passes, a football team gains 10 yards, looses 37 yards, and gains 11 yards. What number represents the total net yardage?
The total net yardage is ____ yards
my answer is -16 is that correct?
1 solutions
Answer 163734 by RAY100(1637) on 2009-09-25 10:20:36 (Show Source):
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Unit_Conversion_Word_Problems/216664: walt reads 18 yards worth of pages in a book in 3 hours, how many miles of book pages will he read in one day
1 solutions
Answer 163581 by RAY100(1637) on 2009-09-24 14:58:49 (Show Source):
You can put this solution on YOUR website!Rate = 18 yds / 3 hrs * 1mile/ 1760 yards = .03409 mi/hr
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now the question is how many hours does he read per day
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easy to say 24 but not realistic, .03409mi/hr * 24 hrs = .082 miles
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more likely 4 hrs,,,,.03409 mi/hr * 4 hrs = .0136 mi
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percentage/216666: 30 students is 60% of how many students?
1 solutions
Answer 163577 by RAY100(1637) on 2009-09-24 14:48:24 (Show Source):
You can put this solution on YOUR website!Let x = total students
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30 = 60% of x = .6x,,,,,,,,,,divide thru by .6
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50 = x
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checking,,,,,,30/50 = .6 = 60%,,,,,ok
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Numbers_Word_Problems/216663: The sum of half a number and that number's reciprocal is the same as 51 divided by the number. The number is negative. Find the number.
1 solutions
Answer 163576 by RAY100(1637) on 2009-09-24 14:45:13 (Show Source):
You can put this solution on YOUR website!Let n= number
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(n/2) +(1/n) = (51/n),,,,,multiply thru by 2n
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n^2 + 2 = 2*51 =102
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n^2 = 100
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n=+/- 10,,,,,since problem says negative,,,,n=-10
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checking, (-10)/2 + (-1/10) = 51/(-10)
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-5 -.1 = -5.1,,,,,,,ok
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Quadratic-relations-and-conic-sections/216628: write the standard form of the equation of the circle that passes through the points at (4,5),(-2,3), and (-4,-3).
a)(x-5)^2 + (y+4)^2 = 49
b)(x-3)^2 + (y+2)^2 = 50
c)(x+4)^2 + (y-2)^2 = 36
d)(x-2)^2 + (y+2)^2 = 25
1 solutions
Answer 163573 by RAY100(1637) on 2009-09-24 14:31:59 (Show Source):
You can put this solution on YOUR website!The formal method of solution is to start with the basic eqn of a circle,,(x-h)^2 +(y-k)^2 = r^2, where center is (+h,+k) and radius is r
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(1) for (4,5) this becomes,,,,(4-h)^2 +(5-k)^2 = r^2
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(2) for (-2,3) this becomes,,,,(-2-h)^2 +(3-k)^2 = r^2
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(3) for (-4,-3) this becomes,,,(-4-h)^2 + (-3-k)^2 =r^2
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with 3 unknowns and 3 equations, we can solve for h,k,&r
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However, this is a lot of work,,,,A rough sketch on graph paper helps
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Reviewing the answers, we find
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a) (5,-4) @r=7
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b) (3,-2) @ r=sqrt50
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c) (-4,2) @ r= 6
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d) (2,-2) @ r=5
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from sketch (b) is most likely,,,,(radius fits)
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subst in each of the 3 above eqns confirms that (b) is the answer
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for example, subst (3,-2) @ r=sqrt50 in eqn (1)
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{4-(3)}^2 +{5-(-2)}^2 = (sqrt50)^2
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1^2 +7^2 =50
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1+49 =50,,,,,ok
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Likewise for all 3 eqns,,,,,honest
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