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# Recent problems solved by 'lwsshak3'

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 Quadratic-relations-and-conic-sections/616031: Can someone help me with this question for my review? x^2/36-y^2/16=1 center: vertices: conjugate points: foci: asymptotes: I don't know how to start, it's overwhelming X_X IM STUCK....1 solutions Answer 387468 by lwsshak3(6518)   on 2012-05-29 22:38:22 (Show Source): You can put this solution on YOUR website!x^2/36-y^2/16=1 This is an equation of a hyperbola with horizontal transverse axis. Its standard form: (x-h)^2/a^2-(y-k)^2/b^2=1, (h,k)=(x,y) coordinates of the center For given equation:x^2/36-y^2/16=1 center: (0,0) .. a^2=36 a=√36=6 vertices: (0±a,0)=(0±6,0)=(-6,0) and (6,0) .. b^2=16 b=√16=4 conjugate points: (0,0±b)=(0,0±4)=(0-4) and (0,4) .. c^2=a^2+b^2=36+16=52 c=√52≈7.2 foci: (0±c,0)=(0±7.2,0)=(-7.2,0) and (7.2,0) .. slope of asymptotes for hyperbolas with horizontal transverse axis=±b/a=±4/6=±2/3 asymptotes are straight lines that intersect at the center. Equation for asymptote with negative slope: y=-2x/3+b since y-intercept is at 0, b=0 equation of asymptote: y=-2x/3 .. Equation for asymptote with positive slope: y=2x/3+b since y-intercept is at 0, b=0 equation of asymptote: y=2x/3
 Quadratic-relations-and-conic-sections/616029: If you're given x^2/25+y^2/16=1 What is the foci? - - Given 36x^2+9y^2-324=0 Find the center: vertices: co-vertices: foci: I know it's c^2=a^2+b^2 or subtraction? Sorry, These questions I have trouble with on the review, please help!1 solutions Answer 387461 by lwsshak3(6518)   on 2012-05-29 22:00:29 (Show Source): You can put this solution on YOUR website!x^2/25+y^2/16=1 What is the foci? This is an equation of an ellipse with horizontal major axis Its standard form: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b), (h,k)=(x,y) coordinates of the center For given equation: center: (0,0) a^2=25 b^2=16 c^2=a^2-b^2=25-16=9 c=√9=3 foci: (0±c,0)=(0±3,0)=(-3,0) and (3,0) - - Given 36x^2+9y^2-324=0 36x^2+9y^2=324 divide by 324 x^2/9+y^2/36=1 This is an ellipse with vertical major axis center: (0,0) .. a^2=36 a=√36=6 vertices:(0,0±a)=(0,0±6)=(0,-6) and (0,6) .. b^2=9 b=3 co-vertices:(0±b,0)=(0±3,0)=(-3,0) and (3,0) .. c^2=a^2-b^2=36-9=25 c=√25=5 foci:(0,0±c)=(0,0±5)=(0,-5) and (0,5)
 Proportions/615969: I am 62 and am tutoring a 50-year old woman who needs to pass the entrance exam for a college algebra class at the University of Maine in Augusta this Fall. I have done this question by calulator for an answer of B=1.08, but she reduced the fractions longhand and got B=0.1. Doing it her way step-by-step I see the problem is in the cross-products, but I cannot write it out in a step-by-step fashion to get the right answer either. Would you please write out the step-by-step reduction for me? The question is: 3¼/2 = B/two-thirds, that is 3 and one-quarter over 2 = B over two-thirds. Thank you. I see my student again next Tuesday, June 5th, Bob Gross1 solutions Answer 387422 by lwsshak3(6518)   on 2012-05-29 20:03:51 (Show Source): You can put this solution on YOUR website!3¼/2 = B/two-thirds 3 and 1/4=13/4 rewrite equation: (13/4)/2=B/(2/3) cross-multiply 2B=(2/3)(13/4=26/12 divide by 2 B=26/24=13/12 If an exact answer is wanted, you must leave it in this fraction form. If a decimal answer is wanted, you will get 13/12=1.08333... so, you would probably round it off depending on how many decimal places are wanted. one decimal place=1.1 two decimal places=1.08 three decimal places=1.083 etc. hope this helps
 Travel_Word_Problems/615906: a person drives from town A to Town B at the rate of 40mph and then flies back at the rate of 120mph. if the total traveling time is 11 hours, how far is it in miles from town A to town B?1 solutions Answer 387406 by lwsshak3(6518)   on 2012-05-29 19:22:52 (Show Source): You can put this solution on YOUR website!a person drives from town A to Town B at the rate of 40mph and then flies back at the rate of 120mph. if the total traveling time is 11 hours, how far is it in miles from town A to town B? ** let x=travel time from town A to town B 11-x=travel time on return trip Distance=travel time*speed .. 40x=120(11-x) 40x=1320-120x 40x+120x=1320 160x=1320 x=8.25 hrs 11-x=2.75 hrs distance from town A to town B=8.25*40=330 miles
 Trigonometry-basics/615618: verifying identites csc(x)*cos^2(x)+sin(x)=csc(x)1 solutions Answer 387373 by lwsshak3(6518)   on 2012-05-29 16:53:05 (Show Source): You can put this solution on YOUR website!verifying identites csc(x)*cos^2(x)+sin(x)=csc(x) ** Start with left side: csc(x)*cos^2(x)+sin(x) =csc(x)(1-sin^2x)+sin(x) =cscx-cscxsin^2x+sinx =cscx-(1/sinx)*sin^2x+sinx =cscx-sinx+sinx =cscx verified: left side=right side
 Trigonometry-basics/615675: Find all solutions to the equation. csc theta-sqroot of 2=01 solutions Answer 387369 by lwsshak3(6518)   on 2012-05-29 16:42:09 (Show Source): You can put this solution on YOUR website!Find all solutions to the equation. csc theta-sqroot of 2=0 cscx-√2=0 cscx=√2 1/sinx=√2 sinx=1/√2 x=π/4+2πn and 3π/4+2πn, n=integer
 Trigonometry-basics/615760: find all the solution of the equation in the interval (0,2pi) tan(x+pi)+2 sin(x+pi)=01 solutions Answer 387368 by lwsshak3(6518)   on 2012-05-29 16:34:42 (Show Source): You can put this solution on YOUR website!find all the solution of the equation in the interval (0,2pi) tan(x+pi)+2 sin(x+pi)=0 tan(x+π)/sin(x+π)=-2 [sin(x+π)/cos(x+π)]/sin(x+π)=-2 sin(x+π) cancels out 1/cos(x+π)=-2 cos(x+π)=-1/2 x+π=2π/3 and 4π/3 (in quadrants II and III where cos<0) x+π=2π/3 x=2π/3-π=-π/3 and x+π=4π/3 x=4π/3-π=π/3 ans: x=-π/3 and π/3
 Trigonometry-basics/615761: Find all the solution of the equation in the interval (0,2pi) sec^2x-1=0 & sinx-2=cosx-2 1 solutions Answer 387360 by lwsshak3(6518)   on 2012-05-29 15:57:33 (Show Source): You can put this solution on YOUR website!Find all the solution of the equation in the interval (0,2pi) sec^2x-1=0 tan^2x=1 tan x=±√1=±1 x=π/4, 3π/4, 5π/4, and 7π/4 .. sinx-2=cosx-2 sinx=cosx sinx/cosx=1 tanx=1 x=π/4 and 5π/4 in quadrants I and III where tan>0
 Trigonometry-basics/615765: solve the equation √3 cscx-2= 0 Solve the equation tanx+ √3 = 0 1 solutions Answer 387352 by lwsshak3(6518)   on 2012-05-29 15:43:54 (Show Source): You can put this solution on YOUR website!interval:(0 to π) solve the equation √3 cscx-2= 0 cscx=2/√3 1/cosx=2/√3 cosx=√3/2 x=π/6 .. Solve the equation tanx+ √3 = 0 tanx=-√3 x=2π/3 (reference angle in quadrant II where tan<0)
 Trigonometry-basics/615794: using periodic function, find the value of sin 17pie - 3 convert 144degrees int radians1 solutions Answer 387347 by lwsshak3(6518)   on 2012-05-29 15:28:54 (Show Source): You can put this solution on YOUR website!using periodic function, find the value of sin 17pie - 3 convert 144degrees int radians ** 17π/3=5π+(2/3)π which gives you an angle of 5π/3 in standard position or a reference angle of π/3 in quadrant III. sin(17π/3)=sin(π/3) =-√3/2 (in quadrant III where sin<0) .. 144º=(144/180)π=0.8π radians
 Quadratic-relations-and-conic-sections/615650: How do you find the equation, vertex, focus, directrix, and latus rectum of the following: -14x+2y^2-8y=201 solutions Answer 387278 by lwsshak3(6518)   on 2012-05-29 03:49:10 (Show Source): You can put this solution on YOUR website!How do you find the equation, vertex, focus, directrix, and latus rectum of the following: -14x+2y^2-8y=20 complete the square 2(y^2-4y+4)=20+14x+8 2(y-2)^2=14x+28 divide by 2 (y-2)^2=7x+14 (y-2)^2=7(x+2) This is an equation of a parabola that opens rightwards. Its standard form: (y-k)^2=4px, (h,k)=(x,y) coordinates of the vertex For given equation:(y-2)^2=7(x+2) vertex:(-2,2) axis of symmetry: y=2 4p=7 p=7/4 Focus: (-2+p,2)=(-2+7/4,2)=(-1/4,2) (p distance to the right of the vertex on the axis of symmetry) Directrix: x=(-2-p)=(-2-7/4)=-15/4 (p distance to the left of the vertex on the axis of symmetry) latus rectum: length of latus rectum=4p=7 2p=7/2 end points: (-1/4,2±2p) =(-1/4,2±7/2) =(-1/4,-1.5) and (-1/4,5.5)
 Trigonometry-basics/615537: A point on the rim of a wheel has a linear speed of 18 cm/s. If the radius of the wheel is 20 cm, what is the angular speed of the wheel in radians per second?1 solutions Answer 387249 by lwsshak3(6518)   on 2012-05-28 21:02:02 (Show Source): You can put this solution on YOUR website!A point on the rim of a wheel has a linear speed of 18 cm/s. If the radius of the wheel is 20 cm, what is the angular speed of the wheel in radians per second? ** cm=centimeter, rev=revoltion, r=radius 18cm/sec *rev/2πr*2π radian/rev cm, rev, 2π cancel out, leaving 18/r radians/sec angular speed of wheel=18/20=9/10 radians/sec
 Equations/615541: how do you find the vertices, co-vertices, foci, and asymptotes of: 9(x+2)^2 -16(y-1)^2=-1441 solutions Answer 387248 by lwsshak3(6518)   on 2012-05-28 20:44:17 (Show Source): You can put this solution on YOUR website!how do you find the vertices, co-vertices, foci, and asymptotes of: 9(x+2)^2 -16(y-1)^2=-144 divide by -144 -(x+2)^2/16+(y-1)^2/9=1 (y-1)^2/9-(x+2)^2/16=1 This is an equation of a hyperbola with vertical transverse axis. Its standard form: (y-k)^2/a^2-(x-h)^2/b^2=1, (h,k)=(x,y) coordinates of center For given equation: (y-1)^2/9-(x+2)^2/16=1 center: (-2,1) a^2=9 a=3 vertices:(-2,1±a)=(-2,1±3)=(-2,-2) and (-2,4) .. b^2=16 b=4 co-vertices:(-2±b,1)=(-2±4,1)=(-6,1) and (2,1) .. c^2=a^2+b^2=9+16=25 c=√25=5 foci::(-2,1±c)=(-2,1±5)=(-2,-4) and (-2,6) .. Asymptotes are straight lines that intersect at the center slopes of asymptotes=±a/b=±3/4 .. Equation of asymptote with negative slope y=mx+b, m=slope, b=intercept y=-3x/4+b Solve for b using coordinates of center 1=-3*-2/4+b b=1-6/4=-2/4=-1/2 Equation: y=-3x/4-1/2 .. Equation of asymptote with positive slope y=mx+b, m=slope, b=intercept y=3x/4+b Solve for b using coordinates of center 1=3*-2/4+b b=1+6/4=10/4=5/2 Equation: y=3x/4+5/2
 Rational-functions/615579: draw asymptotes (if any), to graph the rational function, plot at least 2 points on each piece of the graph x^2+5x+5/x+21 solutions Answer 387244 by lwsshak3(6518)   on 2012-05-28 19:54:18 (Show Source): You can put this solution on YOUR website!draw asymptotes (if any), to graph the rational function, plot at least 2 points on each piece of the graph x^2+5x+5/x+2 ** I don't have the means to plot a graph for you, but I can provide information with which you can plot the curve yourself. When degree of numerator is one unit higher than that of the denominator, you will have slant or oblique asymptotes, as in this case. To find equation of slant asymptote, divide numerator by denominator by long division or synthetic division. The quotient is the equation of the slant asymptote. (x^2+5x+5)/(x+2)=(x+3)+remainder=1 equation of slant asymptote: y=x+3 .. To find vertical asymptote, set denominator=0, then solve for x x+2=0 x=-2=vertical asymptote .. y-intercept set x=0,then solve for y f(0)=(x^2+5x+5)/(x+2)=5/2 y-intercept=5/2 .. x-intercepts set y=0 x^2+5x+5=0 solve by quadratic formula: x=-3.62 and -1.38 .. number line <....-.....-3.62...+...-2...-...-1.38...+....> see graph below:
 Trigonometry-basics/614375: use the sum and difference formulas to solve the equation on [0,2pi): cos(x+5pi/6)-cos(x-5pi/6)=11 solutions Answer 387122 by lwsshak3(6518)   on 2012-05-28 04:21:03 (Show Source): You can put this solution on YOUR website!use the sum and difference formulas to solve the equation on [0,2pi): cos(x+5pi/6)-cos(x-5pi/6)=1 ** cos(x+5pi/6)-(cos(x-5pi/6)=1 cosxcos5π/6-sinxsin5π/6-(cosxcos5π/6+sinxsin5π/6)=1 cosxcos5π/6-sinxsin5π/6-cosxcos5π/6-sinxsin5π/6)=1 -2sinxsin5π/6=1 sin(5π/6)=1/2 in quadrant II sinx=1/-2sin5π/6=1/(-2*(1/2))=1/-1=-1 x=3π/2
 Trigonometry-basics/615248: Use difference of two angles identity to find the exact value of sin 15 degrees. *I used Sin(A - B)= Sin A cos B - cos A sin B, but came to radical 2 x radical 3 divided by 4 - radical 2 divided by 4....I dont not know how to simplifiy it further. 1 solutions Answer 387121 by lwsshak3(6518)   on 2012-05-28 03:46:23 (Show Source): You can put this solution on YOUR website!Use difference of two angles identity to find the exact value of sin 15 degrees. sin 15º=sin(45-30) =(sin45cos30-cos45sin30) =√2/2*√3/2-√2/2*1/2 =√6/4-√2/4 =(√6-√2)/4
 Trigonometry-basics/615270: verify the identity tanx(1-sinx^2x)=1/2sin2x1 solutions Answer 387120 by lwsshak3(6518)   on 2012-05-28 03:37:50 (Show Source): You can put this solution on YOUR website!verify the identity tanx(1-sinx^2x)=1/2sin2x ** Start with left side tanx(1-sinx^2x) =(sinx/cosx)(cos^2x) =sinxcosx =(1/2)sin2x verified: left side=right side
 Linear_Equations_And_Systems_Word_Problems/615352: Hi... I need help to solve this problem.. Two cars are at a distance of 600 km. These are moving in opposite direction and if there is a difference of 6 km/h in their speeds and after 4 hours distance between them is 123km then find the speed of each car . (form linear equatins) i will b very thankful ..1 solutions Answer 387119 by lwsshak3(6518)   on 2012-05-28 03:18:09 (Show Source): You can put this solution on YOUR website!Two cars are at a distance of 600 km. These are moving in opposite direction and if there is a difference of 6 km/h in their speeds and after 4 hours distance between them is 123km then find the speed of each car ** let x=speed of slower car x+6=speed of faster car distance traveled=600-123=477 km travel time=4 hrs Distance=travel time*speed 4x+4(x+6)=477 4x+4x+24=477 8x=477-24=453 x=453/8=56.625 x+6=62.625 ans: speed of slower car=56.625 km/hr speed of faster car=62.625 km/hr
 Rate-of-work-word-problems/615335: Jack, Kay, and Lynn deliver advertising flyers in a small town. If each person works alone, it takes Jack 4 hours to deliver all the flyers, and it takes Lynn 1 hour longer than it takes Kay. Working together, they can deliver all the flyers in 40% of the time it takes Kay working alone. How long does it take Kay to deliver all the flyers alone? Thanks1 solutions Answer 387118 by lwsshak3(6518)   on 2012-05-28 02:49:05 (Show Source): You can put this solution on YOUR website!Jack, Kay, and Lynn deliver advertising flyers in a small town. If each person works alone, it takes Jack 4 hours to deliver all the flyers, and it takes Lynn 1 hour longer than it takes Kay. Working together, they can deliver all the flyers in 40% of the time it takes Kay working alone. How long does it take Kay to deliver all the flyers alone? ** let x=hrs Kay takes to do the job alone 1/x= Kay's work rate x+1=hrs Lynn takes to do the job alone 1/(x+1)=Lynn's work rate 4=hrs Jack takes to do the job alone(given) 1/4 =Jack's work rate .4x=hrs to complete the job working together .. .4x/x+.4x/(x+1)+.4x/4=100% of the job .4+.4x/(x+1)+.x=1 multiply by 10 4+4x/(x+1)+x=10 LCD:(x+1) 4x+4+4x+x^2+x=10x+10 x^2-x-6=0 (x-3)(x+2)=0 x=-2 (reject, x>0) or x=3 ans: hrs Kay takes to do the job alone=3
 Probability-and-statistics/615360: hello, im having trouble with this problem : -x/7+4≥3x thank you 1 solutions Answer 387114 by lwsshak3(6518)   on 2012-05-28 02:05:20 (Show Source): You can put this solution on YOUR website!-x/7+4≥3x multiply both sides by 7 -x+28≥21x -22x≥-28 divide both side by -22 and reverse inequality sign x≤28/22=14/11 solution: (-∞,14/11]
 Age_Word_Problems/615365: Average age of 4 sons of a family is 12 years. Average age of sons together with their parents is 28 years. If father is older than mother by 6 years . Find the age of mother?1 solutions Answer 387113 by lwsshak3(6518)   on 2012-05-28 01:56:29 (Show Source): You can put this solution on YOUR website!Average age of 4 sons of a family is 12 years. Average age of sons together with their parents is 28 years. If father is older than mother by 6 years . Find the age of mother? ** let x=age of mother x+6=age of father .. Total age of 4 sons/4=12 Total age of 4 sons=48 .. (Total age of 4 sons+father's age+mother's age)/6=28 (48+x+6+x)/6=28 48+x+6+x=168 2x=168-54=114 x=114/2 x=57 ans: age of mother=57
 Trigonometry-basics/614260: Find the solution(s) on the interval 0 ≤ theta<2(pi) 2cos(theta)+ √3 = 01 solutions Answer 386986 by lwsshak3(6518)   on 2012-05-27 03:51:20 (Show Source): You can put this solution on YOUR website!Find the solution(s) on the interval 0 ≤ theta<2(pi) 2cos(theta)+ √3 = 0 2cosx=-√3 cosx=-√3/2 x=5π/6 and 7π/6 (in quadrants II and III where cos<0)
 Trigonometry-basics/615115: I have a question, what is the smallest positive real number x such that sin(2x+1)=1? Please give me a full explanation.1 solutions Answer 386985 by lwsshak3(6518)   on 2012-05-27 03:41:14 (Show Source): You can put this solution on YOUR website!I have a question, what is the smallest positive real number x such that sin(2x+1)=1? Please give me a full explanation. ** When sin(x)=1 x=π/2 radians so, when sin(2x+1)=1 2x+1=π/2 radians 4x+2=π 4x=π-2 x=(π-2)/4
 logarithm/615132: Please Help Me Condense this expression log5 10+log5 2-log5 4 Show Work1 solutions Answer 386984 by lwsshak3(6518)   on 2012-05-27 03:21:12 (Show Source): You can put this solution on YOUR website! log5 10+log5 2-log5 4 =log5[10*2/4]
 Linear-equations/615149: Write the ordered pair for f(-5) = 8 and identify the x- and y-values.1 solutions Answer 386983 by lwsshak3(6518)   on 2012-05-27 03:17:18 (Show Source): You can put this solution on YOUR website!Write the ordered pair for f(-5) = 8 and identify the x- and y-values. ordered pair=(-5,8) x=-5 y=8