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# Recent problems solved by 'lwsshak3'

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 Equations/695472: Factorise x^3+3x^2-4x-12 completely.1 solutions Answer 428504 by lwsshak3(6460)   on 2012-12-18 01:53:16 (Show Source): You can put this solution on YOUR website!Factorise x^3+3x^2-4x-12 completely. x^3+3x^2-4x-12 x^2(x+3)-4(x+3) (x^2-4)(x+3) (x+2)(x-2)(x+3)
 Length-and-distance/695474: Write the equation of a line that passes through the points (4,4) and (-2,1). Your answer should be in slope intercept form (y = mx + b) im so confused i have no clue how to do any of this..1 solutions Answer 428502 by lwsshak3(6460)   on 2012-12-18 01:45:19 (Show Source): You can put this solution on YOUR website!Write the equation of a line that passes through the points (4,4) and (-2,1). Your answer should be in slope intercept form (y = mx + b) ** equation of a line: y=mx+b, m=slope, b=y-intercept slope=∆y/∆x=(4-1)/(4-(-2))=3/6=1/2 equation y=(1/2)x+b solve for b using coordinates of one of the given points(4,4) (either point can be used) 4=(1/2)4+b b=2 equation of given line: y=x/2+2
 Percentage-and-ratio-word-problems/695481: the ratio of two no is 3:5, and their difference is 46. find the larger no?1 solutions Answer 428501 by lwsshak3(6460)   on 2012-12-18 01:36:01 (Show Source): You can put this solution on YOUR website!the ratio of two no is 3:5, and their difference is 46. find the larger no. let x=larger no. y=smaller no. 3/5=y/x x-y=46 y=x-46 3/5=(x-46)/x 3x=5x-230 2x=230 x=115 larger no.=115
 Travel_Word_Problems/695475: A plane leaves the airport and flies East at 200 mph. 2 hours later, another plane leaves and flies West at 150 mph. Write and solve a system of linear equations that can be used to determine when the planes are 750 miles apart.1 solutions Answer 428500 by lwsshak3(6460)   on 2012-12-18 01:26:08 (Show Source): You can put this solution on YOUR website!A plane leaves the airport and flies East at 200 mph. 2 hours later, another plane leaves and flies West at 150 mph. Write and solve a system of linear equations that can be used to determine when the planes are 750 miles apart. ** let x-2=travel time of plane flying East x=travel time of plane flying West(when planes are 750 miles apart) distance=*travel time*speed equation: 150(x-2)+200x=750 150x-300+200x=750 350x=1050 x=3 planes are 750 miles apart after 3 hrs
 Travel_Word_Problems/695477: The speed of a stream is 3 km/h. A boat travels 4 km upstream in the same time it takes to travel 10 km downstream. What is the speed of the boat.1 solutions Answer 428499 by lwsshak3(6460)   on 2012-12-18 00:59:03 (Show Source): You can put this solution on YOUR website!The speed of a stream is 3 km/h. A boat travels 4 km upstream in the same time it takes to travel 10 km downstream. What is the speed of the boat. ** let x=speed of the boat in still water x-3=speed upstream x+3=speed downstream travel time=distance/speed (same for upstream and downstream) 4/(x-3)=10/(x+3) 10x-30=4x+12 6x=42 x=6 speed of the boat in still water=6 km/hr
 Age_Word_Problems/695458: The ratio of the ages of Rajesh to that of Ramesh is 5 : 8. After 10 years the new ratio of their ages will be 7 : 10. What is the age of Ramesh at present?1 solutions Answer 428498 by lwsshak3(6460)   on 2012-12-18 00:48:32 (Show Source): You can put this solution on YOUR website!The ratio of the ages of Rajesh to that of Ramesh is 5 : 8. After 10 years the new ratio of their ages will be 7 : 10. What is the age of Ramesh at present? ** let y=Rajesh's present age let x=Ramesh's present age y/x=5/8 y=5x/8 .. After 10 years: y+10=Rajesh's age x+10=Ramesh's age (y+10)/(x+10)=7/10 7x+70=10y+100 7x+70=10(5x/8)+100 7x+50x/8=30 56x+50x=240 6x=240 x=40 Ramesh's present age=40
 Travel_Word_Problems/695463: A bus leave Sacramento traveling South at 40 mph. A half hour hour later, a car leaves from the same location on the same route at 60 mph. How far from Sacramento will the car overtake the bus?1 solutions Answer 428496 by lwsshak3(6460)   on 2012-12-18 00:14:31 (Show Source): You can put this solution on YOUR website!A bus leave Sacramento traveling South at 40 mph. A half hour hour later, a car leaves from the same location on the same route at 60 mph. How far from Sacramento will the car overtake the bus? ** let x=travel time of car (x+.5)=travel time of bus distance=speed*travel time(the same for car and bus) .. 60x=40(x+.5) 60x=40x+20 20x=20 x=1 distance car overtakes bus=60x=60 miles
 Trigonometry-basics/694532: I don't know how to find the exact value of cos 23pi/12 using the properties of special triangles1 solutions Answer 428052 by lwsshak3(6460)   on 2012-12-15 17:27:47 (Show Source): You can put this solution on YOUR website!find the exact value of cos 23pi/12 using the properties of special triangles Use cos half-angle identity cos(x/2)=±√[(1+cos(x)/2] cos(23π/12)=cos(23π/6)/2)=√[(1+cos(23π/6)/2] For cos(23π/6) use reference angle π/6 in quadrant IV where cos>0 cos(23π/6)=cos(π/6)=√3/2 cos(23π/12) =cos(23π/6)/2) =√[(1+cos(23π/6)/2] =√[(1+√3/2/2] calculator check: cos(23π/12)≈0.9659.. √[(1+√3/2/2]≈0.9659..
 absolute-value/693974: |4x-2 divided by 5| = |6x+3 divided by 2|1 solutions Answer 427963 by lwsshak3(6460)   on 2012-12-15 03:30:57 (Show Source): You can put this solution on YOUR website!|4x-2 divided by 5| = |6x+3 divided by 2| |(4x-2)/5|=|(6x+3)/2| solve for 2 equations (4x-2)/5=(6x+3)/2 5(6x+3)=2(4x-2) 30x+15=8x-4 22x=-19 x=-19/22 check: |(4x-2)/5|=|(6x+3)/2| |(4(-19/22)-2)/5|=|(6(-19/22)+3)/2| |-1.0909|=|-1.0909| 1.0909=1.0909 check ok .. (4x-2)/5=-(6x+3)/2 -5(6x+3)=2(4x-2) -30x-15=8x-4 -38x=11 x=-11/38 check: |(4x-2)/5|=|(6x+3)/2| |(4(-11/38)-2)/5|=|(6(-11/38)+3)/2| |-.6316|=|.6316| .6316=.6316 check ok solution: x=-19/22, -11/38
 absolute-value/694488: |10x+65|=7x+25 1 solutions Answer 427960 by lwsshak3(6460)   on 2012-12-15 03:08:41 (Show Source): You can put this solution on YOUR website!|10x+65|=7x+25 solve for 2 possibilities .. 10x+65=7x+25 3x=-40 x=-40/3 check: (10x+65)=7x+25 |10*-40/3+65|=7*-40/3+25 |10*-40/3+65|=7*-40/3+25 |-68.33|=-68.33 68.33≠-68.33 does not check, no solution .. -(10x+65)=7x+25 -10x-65=7x+25 -17x=90 x=-90/17 check: |10x+65|=7x+25 |10*-90/17+65|=7*-90/17+25 |12.06|=-12.06 12.06≠-12.06 does not check, no solution
 Exponential-and-logarithmic-functions/694003: how do you solve these equations 1) e^-x=5 2) 11^5x=33 3) 4e^2x=171 solutions Answer 427957 by lwsshak3(6460)   on 2012-12-15 02:06:54 (Show Source): You can put this solution on YOUR website!how do you solve these equations 1) e^-x=5 -xlne=ln5 x=-ln5 .. 2) 11^5x=33 5xlog11=log33 5x=log33/log11 x=(log33/log11)/5 x≈0.2916 .. 3) 4e^2x=17 ln4+2xlne=ln17 2x=ln17-ln4 x=(ln17-ln4)/2 x≈.7235
 Quadratic-relations-and-conic-sections/694194: what is the vertex, axis of symmetry, and direction of opening for y=x^2-18x+79?1 solutions Answer 427927 by lwsshak3(6460)   on 2012-12-14 20:30:35 (Show Source): You can put this solution on YOUR website!what is the vertex, axis of symmetry, and direction of opening for y=x^2-18x+79? complete the square y=(x^2-18x+81)+79-81 y=(x-9)^2-3 This is an equation of a parabola that opens upwards. (lead coefficient positive) Its standard form: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex. For given equation: y=(x-9)^2-3 vertex:(9,-3) Axis of symmetry: x=9
 Quadratic-relations-and-conic-sections/694199: Identify the center and foci of the ellipse. (x-2)^2/16 + (y-7)^2/169 =11 solutions Answer 427925 by lwsshak3(6460)   on 2012-12-14 20:15:24 (Show Source): You can put this solution on YOUR website!Identify the center and foci of the ellipse. This is an equation of an ellipse with vertical major axis.(y-denominator > x-denominator Its standard form: , a>b, (h,k)=(x,y) coordinates of center For given equation: center: (2,7) a^2=169 b^2=16 c^2=a^2-b^2=169/16=153 c=√153≈12.4 foci: (2,7±c)≈(2,7±12.4)≈(2,-5.4 and (2,19.4)
 Quadratic-relations-and-conic-sections/694390: graph y= 1/2(x-1)(x+2)1 solutions Answer 427916 by lwsshak3(6460)   on 2012-12-14 19:11:03 (Show Source): You can put this solution on YOUR website!graph y= 1/2(x-1)(x+2) y=(1/2)(x^2+x-2) complete the square: y=(1/2)(x^2+x+1/4)-1-1/8 y=(1/2)(x+1/2)^2-9/8 This is an equation of a parabola that opens upwards. Its standard form of equation:y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex for given equation:y=(1/2)(x+1/2)^2-9/8 vertex: (-1/2,-9/8) see graph below:
 Quadratic-relations-and-conic-sections/694202: Use the information provided to write the standard form equation of each hyperbola. Vertices: (-2, 8), (-2,-2) Endpoints of Conjugate Axis:(8,3) (-12,3)1 solutions Answer 427914 by lwsshak3(6460)   on 2012-12-14 19:02:48 (Show Source): You can put this solution on YOUR website!Use the information provided to write the standard form equation of each hyperbola. Vertices: (-2, 8), (-2,-2) Endpoints of Conjugate Axis:(8,3) (-12,3) ** This is a hyperbola with vertical transverse axis (y-coordinates of vertices change but x-coordinates do not) Its standard form of equation: , (h,k)=(x,y) coordinates of center For given hyperbola: center: (-2,3) (midpoints of changing x and y-coordinates) length of vertical transverse axis=10(-2 to 8)=2a a=5 a^2=25 length of conjugate axis=20 (-12 to 8)=2b b=10 b^2=100 Equation of given hyperbola:
 Quadratic-relations-and-conic-sections/694423: Graph the quadratic function f(x)=5-x^2 and identify the Vertex. Give the Domain and Range.1 solutions Answer 427908 by lwsshak3(6460)   on 2012-12-14 18:38:50 (Show Source): You can put this solution on YOUR website!Graph the quadratic function f(x)=5-x^2 and identify the Vertex. Give the Domain and Range This is an equation of a parabola that opens downwards. (negative lead coefficient) Its standard form: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex. For given equation: y=-x^2+5 (rewritten) vertex(0,5) domain: (-∞,∞) range: (-∞,5] see graph below:
 Age_Word_Problems/693739: How old is Anna if she's 3yrs older than chuck, and in 5yrs, her age and chucks age would equal 54?1 solutions Answer 427681 by lwsshak3(6460)   on 2012-12-13 16:35:58 (Show Source): You can put this solution on YOUR website!How old is Anna if she's 3yrs older than chuck, and in 5yrs, her age and chucks age would equal 54? ** let x=anna's present age x-3=chuck's present age .. in 5 yrs x+5=anna's age x-3+5=x+2=chuck's age .. (x+5)+(x+2)=54 2x+7=54 2x=47 x=23.5 anna's present age=23.5
 Age_Word_Problems/693994: Eighteen years ago Alan was twice as old as Tony. Alan is eight years older than Tony. Find Tony's age now. 1 solutions Answer 427680 by lwsshak3(6460)   on 2012-12-13 16:21:13 (Show Source): You can put this solution on YOUR website!Eighteen years ago Alan was twice as old as Tony. Alan is eight years older than Tony. Find Tony's age now. ** let x=tony's age now x+8=alan's age now .. 18 years ago x-18=tony's age x+8-18=x-10 .. x-10=2(x-18) x-10=2x-36 x=26 tony's age now=26
 Rational-functions/693581: Determine wheather the following relation represents a function. If the relation is a function, then state its domain and range (2,8),(-2,8),(8,10),(2,17) 1 solutions Answer 427666 by lwsshak3(6460)   on 2012-12-13 15:12:58 (Show Source): You can put this solution on YOUR website!Determine wheather the following relation represents a function. If the relation is a function, then state its domain and range (2,8),(-2,8),(8,10),(2,17) This relation is not a function because (2,8)and (2,17) show that you have 2 different y=values for the same x-value.
 Rational-functions/693642: X =(y+2)^2 Solve and state the domain and range, and write in interval notation. Is this equation a function?1 solutions Answer 427665 by lwsshak3(6460)   on 2012-12-13 15:00:33 (Show Source): You can put this solution on YOUR website!X =(y+2)^2 Solve and state the domain and range, and write in interval notation. Is this equation a function? This is a parabola that opens rightwards with the vertex at (0,0) Its standard form of equation: (y-k)^2=4p(x-h)X (y+2)^2=x This is a sqrt function where the radican x≥0 domain: [0,∞) range: (-∞,∞) equation is not a function. To be a function, for each x-value, there can be only one y-value, and given equation has 2 different y-values for each x.
 Exponential-and-logarithmic-functions/693876: how do you factor: x to the 4th power -5x to the 2nd power-14?1 solutions Answer 427648 by lwsshak3(6460)   on 2012-12-13 14:20:11 (Show Source): You can put this solution on YOUR website!how do you factor: x to the 4th power -5x to the 2nd power-14? x^4-5x^2-14 (x^2-7)(x^2+2)
 Exponential-and-logarithmic-functions/693680: Solve 1n 2 + 1n x = 5. Round to the nearest thousandth, if necessary.1 solutions Answer 427646 by lwsshak3(6460)   on 2012-12-13 14:16:01 (Show Source): You can put this solution on YOUR website!Solve 1n 2 + 1n x = 5. Round to the nearest thousandth ln[2x]=5 e^5=2x x=e^5/2 x≈74.207
 Quadratic-relations-and-conic-sections/693238: Write in standard form.It is a Hyperbola. The vertices are (0,+-1) and the foci are (0, +-5). 1 solutions Answer 427554 by lwsshak3(6460)   on 2012-12-13 03:05:29 (Show Source): You can put this solution on YOUR website!Write in standard form.It is a Hyperbola. The vertices are (0,+-1) and the foci are (0, +-5). ** This is a hyperbola with horizontal transverse axis. Its standard form of equation: , (h,k)=(x,y) coordinates of center For given hyperbola: center:(0,0) a=1 (distance from center to vertices on transverse axis) a^2=1 c=5 (distance from center to foci on transverse axis) c^2=25 c^2=a^2+b^2 b^2=c^2-a^2=25-1=24 Equation of given hyperbola:
 Quadratic-relations-and-conic-sections/693239: Write in standard form. It is a ellipse. The center is (0,0) and the foci is (+-3,0) and the major axis is 12.1 solutions Answer 427553 by lwsshak3(6460)   on 2012-12-13 02:53:26 (Show Source): You can put this solution on YOUR website!Write in standard form. It is a ellipse. The center is (0,0) and the foci is (+-3,0) and the major axis is 12. ** This is an ellipse with horizontal major axis. Its standard form of equation: , a>b, (h,k)=(x,y) coordinates of center. For given ellipse: Given center: (0,0) length of horizontal major axis=12=2a a=6 a^2=36 c=3 (distance from center to foci) c^2=9 c^2=a^2-b^2 b^2=a^2-c^2=36-9=25 b=5 Equation of given ellipse:
 Quadratic-relations-and-conic-sections/693240: Write in standard form. It is a parabola. The vertex is (0,0) and the focus is (-6,0).1 solutions Answer 427552 by lwsshak3(6460)   on 2012-12-13 02:42:48 (Show Source): You can put this solution on YOUR website!Write in standard form. It is a parabola. The vertex is (0,0) and the focus is (-6,0). This is a parabola that open leftwards. Its standard form of equation: (y-k)^2=-4p(x-h), (h,k)=(x,y) coordinates of the vertex For given parabola: given vertex: (0,0) Axis of symmetry: y=0 or x-axis From focus: p=6 (distance from focus to vertex on the axis of symmetry) 4p=24 Equation: y^2=-24x
 Quadratic-relations-and-conic-sections/693660: Find an equation of the ellipse that has center (1,3) , a major axis of length 12 , and endpoint of minor axis (0,3) .1 solutions Answer 427551 by lwsshak3(6460)   on 2012-12-13 02:31:43 (Show Source): You can put this solution on YOUR website!Find an equation of the ellipse that has center (1,3) , a major axis of length 12 , and endpoint of minor axis (0,3) . ** Standard form of equation for an ellipse with vertical major axis: , a>b, (h,k)=(x,y) coordinates of center. given center: (1,3) given length of vertical major axis:=12=2a a=6 a^2=36 length of minor axis=6=2b b=3 b^2=9 equation of given ellipse:
 Trigonometry-basics/693314: A square of side x is inscribed in a circle. Express the area A of the circle as a function of x.1 solutions Answer 427550 by lwsshak3(6460)   on 2012-12-13 02:12:11 (Show Source): You can put this solution on YOUR website!A square of side x is inscribed in a circle. Express the area A of the circle as a function of x. ** Use sector area formula to solve: area of one of 4 sectors=(1/2)r^2A diameter of circle=(√2/2)x r=√2/4)x r^2=(2/16)x^2=(x^2)/8 A=π/2(central angle) Area of circle=4*(1/2)(x^2/8)*π/2=πx^2/8
 Trigonometry-basics/693416: Find all solutions of the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.) 4 cos θ + 1 = 01 solutions Answer 427549 by lwsshak3(6460)   on 2012-12-13 02:02:55 (Show Source): You can put this solution on YOUR website!Find all solutions of the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.) 4 cos θ + 1 = 0 cos θ=-1/4 reference angle≈1.32 in quadrants II and III where cos<0 θ≈1.82+2πk, 4.46+2πk, k=any integer
 Trigonometry-basics/693461: the question asks,"cos^-1 0.5=?" and also "The sine is positive in __?" A q2 and q3 B q1 and q2 C q1 and q3 1 solutions Answer 427548 by lwsshak3(6460)   on 2012-12-13 01:53:05 (Show Source): You can put this solution on YOUR website!he question asks,"cos^-1 0.5=?" and also "The sine is positive in __?" A q2 and q3 B q1 and q2 C q1 and q3 .. cos^-1 0.5= 30º or π/6 The sine is positive in q1 and q2 (top half of the unit circle)
 Trigonometry-basics/693620: if sin theta=12/13 and tan <0, find the exact values of the remaining trigonometric functions of theta.1 solutions Answer 427547 by lwsshak3(6460)   on 2012-12-13 01:48:34 (Show Source): You can put this solution on YOUR website!if sin theta=12/13 and tan <0, find the exact values of the remaining trigonometric functions of theta. ** use x for theta O for opposite side A for adjacent side H for hypotenuse if sin theta=12/13 and tan <0, reference angle must be in quadrant II .. sin x=12/13=O/H O=12, H=13 A=√(H^2-O^2)=√(13^2-12^2)=√(169-144)=√25=5 cos x=A/H=-5/13 tan x=O/A=-12/5 csc x=13/12 sec x=-13/5 cot x=-5/12