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# Recent problems solved by 'lwsshak3'

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 Quadratic_Equations/686234: solve the equation using the quadratic formula method:3a^2x^2-abx-2b^2=0 1 solutions Answer 424722 by lwsshak3(6494)   on 2012-11-28 00:27:25 (Show Source): You can put this solution on YOUR website!solve the equation using the quadratic formula method:3a^2x^2-abx-2b^2=0 use following quadratic formula to solve: a=3a^2, b=-ab, c=-2b^2 I will let you take it from here
 Rational-functions/686232: Please help rationalize the problem below with brief step-by-step explanation. Thank you in advance for your time and assistance! (2)/(3t)^(1/2)1 solutions Answer 424721 by lwsshak3(6494)   on 2012-11-28 00:19:38 (Show Source): You can put this solution on YOUR website!(2)/(3t)^(1/2) (2)/√(3t) multiply top and bottom by √(3t) (2)/√(3t)*√(3t)/√(3t) 2√(3t)/3t
 test/686223: Find the value of k so that the three points lie on the same line. Write the equation in point slope form. The points given are (1,-2) (-2,4) (4,k) 1 solutions Answer 424720 by lwsshak3(6494)   on 2012-11-28 00:11:58 (Show Source): You can put this solution on YOUR website!Find the value of k so that the three points lie on the same line. Write the equation in point slope form. The points given are (1,-2) (-2,4) (4,k) ** y-y1=m(x-x1) using given point (1,-2) y-(-2)=m(x-1) y+2=m(x-1) using given points (1,-2) and (-2,4) to find slope,m m=∆y/∆x=(4-(-2))/(-2-1)=(4+2)/-3=6/-3=-2 y+2=-2(x-1) y+2=-2x+2 y=-2x solving for k k=-2*4=-8 k=-8 see graph below:
 Travel_Word_Problems/685928: you can travel 40 miles on motorcycle in the same time that it takes to travel 15 miles on bicycle. if your motorcycle's rate is 20 miles per hour faster than your bicycle's, fine the average rate for each1 solutions Answer 424657 by lwsshak3(6494)   on 2012-11-27 16:32:22 (Show Source): You can put this solution on YOUR website!you can travel 40 miles on motorcycle in the same time that it takes to travel 15 miles on bicycle. if your motorcycle's rate is 20 miles per hour faster than your bicycle's, fine the average rate for each let x=rate of speed of bicycle x+20=rate of speed of motorcycle travel time= distance/rate of speed (same for both) 40/(x+20)=15/x 40x=15(x+20 40x=15x+300 25x=300 x=12 x+20=32 rate of speed of bicycle=12 mph rate of speed of motorcycle=32 mph
 Expressions-with-variables/685894: Find an equation of the line passing (-7,2) and (4,5)1 solutions Answer 424649 by lwsshak3(6494)   on 2012-11-27 16:19:52 (Show Source): You can put this solution on YOUR website!Find an equation of the line passing (-7,2) and (4,5) Equation of a line: y=mx+b, m=slope, b=y-intercept For given problem: m=∆y/∆x=(5-2)/(4-(-7))=3/11 equation: y=3x/11+b solve for b using one of given coordinates(4,5) 5=3*4/11+b b=5-12/11 b=55/11-12/11=43/11 equation: y=3x/11+43/11 see graph below:
 Quadratic_Equations/685893: Please help me with this question. I'm getting really confused with the 3x. I' not sure where to start. Find all of the exact solutions to the following equation. (Use the parameter k as necessary to represent any integer.) cos(3x) =1/2 1 solutions Answer 424643 by lwsshak3(6494)   on 2012-11-27 16:04:57 (Show Source): You can put this solution on YOUR website!Find all of the exact solutions to the following equation. (Use the parameter k as necessary to represent any integer.) cos(3x) =1/2 3x=π/3+2πk, 5π/3+2πk, k=any integer x=π/9+2πk, 5π/9+2πk, k=any integer
 Exponential-and-logarithmic-functions/685808: Solve the following exponential equation. Exact answers only. 49^x-12*7^x=-36 I have tried and tried on this problem. I do not understand. I would appreciate help on this! Thank you!1 solutions Answer 424637 by lwsshak3(6494)   on 2012-11-27 15:57:15 (Show Source): You can put this solution on YOUR website!Solve the following exponential equation. Exact answers only. 49^x-12*7^x=-36 7^2x-12*7^x=-36 let u=7^x u^2=7^2x u^2-12u+36=0 (u-6)(u-6)=0 u=6=7^x 6=7^x log6=xlog7 x=log6/log7 x≈.9208..
 Geometry_Word_Problems/685869: In an isosceles triangle, the base is 7 more than one-half times the legs. If perimeter is 22 centimeters. Find length of each leg. 1 solutions Answer 424619 by lwsshak3(6494)   on 2012-11-27 14:57:23 (Show Source): You can put this solution on YOUR website!In an isosceles triangle, the base is 7 more than one-half times the legs. If perimeter is 22 centimeters. Find length of each leg. ** let x=length of each leg base+2 legs=perimeter (1/2)x+7+2x=22 x/2+7+2x=22 5x/2=15 5x=30 x=6 length of each leg=6 cm
 logarithm/685867: I need help solving this question. write the following as a single logarithm with coefficient of 1. please show steps. thanks in adavance 3logc(x^4)-2logc(3x) 1 solutions Answer 424614 by lwsshak3(6494)   on 2012-11-27 14:48:21 (Show Source): You can put this solution on YOUR website!write the following as a single logarithm with coefficient of 1. please show steps. thanks in adavance 3logc(x^4)-2logc(3x) logc[(x^4)^3/(3x)^2] logc[(x^12/(9x^2] logc[(x^10/9)]
 Length-and-distance/685863: Two cars leave towns 640 kilometers apart at the same time and travel toward each other. One car's rate is 10 kilometers per hour more than the other's. If they meet in 4 hours, what is the rate of the faster car? 1 solutions Answer 424612 by lwsshak3(6494)   on 2012-11-27 14:44:54 (Show Source): You can put this solution on YOUR website!Two cars leave towns 640 kilometers apart at the same time and travel toward each other. One car's rate is 10 kilometers per hour more than the other's. If they meet in 4 hours, what is the rate of the faster car? ** let x=rate of speed of faster car x-10=rate of speed of slower car distance=rate of speed*travel time 4x+4(x-10)=640 4x+4x-40=640 8x=680 x=85 rate of speed of faster car= 85km/hr
 Mixture_Word_Problems/685848: A metal alloy weighing 12 lb. and containing 20% copper is melted and mixed with 3 lb. of a different alloy which contains 40% copper. What percent of the resulting alloy is copper?1 solutions Answer 424609 by lwsshak3(6494)   on 2012-11-27 14:35:43 (Show Source): You can put this solution on YOUR website!A metal alloy weighing 12 lb. and containing 20% copper is melted and mixed with 3 lb. of a different alloy which contains 40% copper. What percent of the resulting alloy is copper? ** 20%*12+40%*3/12+3=(2.4+1.2)/15=3.6/15=.24 What percent of the resulting alloy is copper? 24%
 logarithm/685036: Solve the logarithmic equation algebraically.Approximate the result to three decimal places. log(4x)-log(14+the square root of x)=21 solutions Answer 424513 by lwsshak3(6494)   on 2012-11-27 02:44:35 (Show Source): You can put this solution on YOUR website!Solve the logarithmic equation algebraically.Approximate the result to three decimal places. log(4x)-log(14+the square root of x)=2 ** log(4x)-log(14+√x)=2 log[4x/(14+x^(1/2))=2 convert to exponential form 10^2=4x/(14+x^(1/2))=100 4x=1400+100x^(1/2) 4x-1400-100x^(1/2)=0 let u=x^(1/2) u^2=x 4u^2-100u-1400=0 u^2-25u-350=0 (u-35)(u+10) u=35=√x x=35^2=1225 or u=-10=√x x=(-10)^2=100 ans: x=1225 or x=100
 logarithm/685592: Solve each equation for x A). ln(2x-3)=-1 B). ln(3x+1)=2 (they are natural)1 solutions Answer 424509 by lwsshak3(6494)   on 2012-11-27 02:05:30 (Show Source): You can put this solution on YOUR website!Solve each equation for x A). ln(2x-3)=-1 2x-3=e^-1=1/e 2x=1/e+3 x=(1/e+3)/2 x=1.6839 .. B). ln(3x+1)=2 3x+1=e^2 3x=e^2-1 x=(e^2-1)/3 x=2.1297
 logarithm/685594: Solve each exponential equation for x. Give an exact solution and also approximate the solution to four decimals a). 4^(3x+2)=9 b). 5^(3x-5)=41 solutions Answer 424508 by lwsshak3(6494)   on 2012-11-27 01:56:21 (Show Source): You can put this solution on YOUR website!Solve each exponential equation for x. Give an exact solution and also approximate the solution to four decimals a). 4^(3x+2)=9 (3x+2)log4=log9 (3x+2)=log9/log4 3x=(log9/log4)-2 x=[(log9/log4)-2]/3 (exact solution) x=-0.1383.. .. b). 5^(3x-5)=4 (3x-5)log5=log4 3x-5=log4/log5 x=[(log4/log5)+5]/3 (exact solution) x=1.9538..
 logarithm/685595: Find all the real number roots of the equation. log2(x+7)-log2(x-3)=31 solutions Answer 424507 by lwsshak3(6494)   on 2012-11-27 01:38:20 (Show Source): You can put this solution on YOUR website!Find all the real number roots of the equation. log2(x+7)-log2(x-3)=3 log2[(x+7)/(x-3)]=3 convert to exponential form (x+7)/(x-3)=2^3=8 x+7=8x-24 7x=31 x=31/7=4.4286..
 logarithm/685596: log5(x-2)= 2 + log5(x-4) 1 solutions Answer 424506 by lwsshak3(6494)   on 2012-11-27 01:32:45 (Show Source): You can put this solution on YOUR website!log5(x-2)= 2 + log5(x-4) log5(x-2)- log5(x-4)=2 log5[(x-2)/(x-4)]=2 convert to exponential form (x-2)/(x-4)=5^2=25 x-2=25x-100 24x=98 x=4.0833..
 logarithm/685597: Solve each exponential equation for x. Give an exact solution and also approximate the solution to four decimals 2*5^(x-1)=11 solutions Answer 424505 by lwsshak3(6494)   on 2012-11-27 01:19:57 (Show Source): You can put this solution on YOUR website!Solve each exponential equation for x. Give an exact solution and also approximate the solution to four decimals 2*5^(x-1)=1 log2+(x-1)log5=log1 log1=0 log2+(x-1)log5=0 log2+(x-1)log5=-log2 x-1=-log2/log5 x=(-log2/log5)+1 (exact solution) x=0.5963..
 logarithm/685605: randy invested his inheritance in an account that paid 6.9% interest, coupounded continuously. after 5 years, he found that he now had \$52,565.56. what was the orginal amount of his inheritance? 1 solutions Answer 424504 by lwsshak3(6494)   on 2012-11-27 01:09:00 (Show Source): You can put this solution on YOUR website!randy invested his inheritance in an account that paid 6.9% interest, coupounded continuously. after 5 years, he found that he now had \$52,565.56. what was the orginal amount of his inheritance? ** Formula for continuous compounding:A= Pe^rt, P=initial investment, r=rate of interest, A=amt after t years 52565.56=Pe^(.069*5)=Pe^.345 P=52565.56/e^.345=37228 orginal amount of his inheritance=\$37,228.00..
 Quadratic-relations-and-conic-sections/684975: E is the ellipse with foci at (4,-2) and (4,8) and whose major axis has length of 20 Find an equation for the indicated conic section 1 solutions Answer 424503 by lwsshak3(6494)   on 2012-11-27 00:50:05 (Show Source): You can put this solution on YOUR website!E is the ellipse with foci at (4,-2) and (4,8) and whose major axis has length of 20 Find an equation for the indicated conic section ** This is an ellipse with vertical major axis. Its standard form of equation:, a>b, (h,k)=(x,y) coordinates of center For given ellipse: center: (4,3) given length of vertical major axis=20=2a a=10 a^2=100 c=5 (distance from center to foci) c^2=25 c^2=a^2-b^2 b^2=a^2-c^2=100-25=75 Equation of given ellipse:
 Trigonometry-basics/685106: Find the exact values of each trigonometric function at 0(theta)=-(7pi/12). For sin cos and tan.1 solutions Answer 424398 by lwsshak3(6494)   on 2012-11-26 16:47:50 (Show Source): You can put this solution on YOUR website!Find the exact values of each trigonometric function at 0(theta)=-(7pi/12). For sin cos and tan. -(7π/12) is in quadrant III where sin<0, cos<0, tan>0 -(7π/12)=[(-3π/12)+(-4π/12)]=[(-π/4)+(-π/3)] sin-(7π/12)=sin[(-π/4)+(-π/3)]=[sin(-π/4)cos(-π/3)]+[cos(-π/4)sin(-π/3)] =[(-√2/2)*(1/2)+√2/2*-√3/2] =[-√2/4-√6/4] =(-√2-√6)/4 sin-(7π/12)=-(√2+√6)/4 check with calculator: sin-(7π/12)=-0.9659.. -(√2+√6)/4=-0.9659.. .. cos-(7π/12)=cos[(-π/4)+(-π/3)]=[cos(-π/4)cos(-π/3)]-[sin(-π/4)sin(-π/3)] =[(√2/2)*(1/2)]-[-√2/2*-√3/2] =[√2/4-√6/4] =(√2-√6)/4 check with calculator: cos-(7π/12)=-0.2588.. (√2-√6)/4=-0.2588.. .. tan-(7π/12)=tan[(-3π/12)+(-4π/12)]=tan[(-π/4)+(-π/3)] =[tan(-π/4)+tan(-π/3)]/[1-tan(-π/4)*tan(-π/3)]=[-1+(-√3)]/[1-(-1*(-√3)] =(-1-√3)/(1-√3) check with calculator: tan-(7π/12)=3.732.. (-1-√3)/(1-√3)=3.732..
 Trigonometry-basics/685119: Find the six trig functions of -pi1 solutions Answer 424390 by lwsshak3(6494)   on 2012-11-26 15:05:29 (Show Source): You can put this solution on YOUR website!Find the six trig functions of -pi sin -π=0 cos -π=-1 tan -π=0 csc -π=undefined sec -π=-1 cot -π=undefined
 Trigonometry-basics/685120: Given that sin(3θ)= (1/5) and (π/2)<3θ<π: Find cos(3θ), sin(6θ), and tan (3θ/2)1 solutions Answer 424388 by lwsshak3(6494)   on 2012-11-26 14:54:31 (Show Source): You can put this solution on YOUR website!Given that sin(3θ)= (1/5) and (π/2)<3θ<π: Find cos(3θ), sin(6θ), and tan (3θ/2) You are working with reference angle 3θ in quadrant II where sin>0, cos<0, and tan<0 sin3θ=opposite side/hypotenuse=1/5 adjacent side=√(5^2-1^2)=√(25-1)=√24 .. cos(3θ)=-√24/5 .. Identity: sin 2s=2sins cos s sin(6θ)=2sin3θcos3θ =2*1/5*-√24/5 =-(2√24)/25 .. Identity: tan s/2= (sin s)/(1+cos s) tan (3θ/2)=sin3θ/1+cos3θ =(1/5)/(1-√24/5) =(1/5)/(5-√24)/5 =1/(5-√24)
 Trigonometry-basics/685127: Solve each equation on the interval (0,2pi): a.) 2sin^(2)x-cos x-1=0, b.) sin 3x cos 2x + cos3x sin2x= (√2/2).1 solutions Answer 424381 by lwsshak3(6494)   on 2012-11-26 14:22:31 (Show Source): You can put this solution on YOUR website!Solve each equation on the interval (0,2pi): a.) 2sin^(2)x-cos x-1=0, b.) sin 3x cos 2x + cos3x sin2x= (√2/2). ** a.) 2sin^(2)x-cosx-1=0 2(1-cos^2x)-cosx-1=0 2-2cos^2x-cosx-1=0 2cos^2x+cosx-1=0 (2cosx-1)(cosx+1)=0 2cosx-1=0 cosx=1/2 x=π/3, 5π/3 or cosx+1=0 cosx=-1 x=π .. b.) sin 3x cos 2x + cos3x sin2x= (√2/2). Identity:sin(s+t)=sin s cos t+cos s sin t sin 3x cos 2x + cos3x sin2x= (√2/2) sin(3x+2x)=sin(5x)=√2/2 5x=π/4, 3π/4 x=π/20, 3π/20
 logarithm/683960: Solve for t 10^(7t) = 18^(2t-5)1 solutions Answer 423996 by lwsshak3(6494)   on 2012-11-24 03:21:06 (Show Source): You can put this solution on YOUR website!Solve for t 10^(7t) = 18^(2t-5) 7tlog10=(2t-5)log18 7t/2t-5=log18/log10≈1.2553 7t=1.2553(2t-5)=2.5105t-6.2764 7t-2.5105t=-6.2764 4.4894t=-6.2764 t≈-6.2764/4.4894 t≈-1.3980
 logarithm/684125: How would I find the inverse of f(x)=log 9 (x)? Does having the parenthesis around x change it? Here is what I did:1) re-write it as y=log 9 (x); 2) identify 9 as the base, y as the exponent, and keeping x on the right side of the equation; 3) re-write it as 9^y=x.1 solutions Answer 423995 by lwsshak3(6494)   on 2012-11-24 03:01:25 (Show Source): You can put this solution on YOUR website!The inverse of the log function is the exponential form: For given problem:y=log 9 (x) Exponential form: base(9) raised to log of number(y)=number(x) 9^y=x so, you were right on.
 logarithm/684196: Can you help me solve. I'm having problems using the laws. thanks in advance. Log2t^3-Logt = Log16+Logt 1 solutions Answer 423994 by lwsshak3(6494)   on 2012-11-24 02:53:43 (Show Source): You can put this solution on YOUR website!Log2t^3-Logt = Log16+Logt log[2t^3/t]=log[16/t] 2t^3/t=16/t 2t^3=16 t^3=8 t=2
 logarithm/684219: Please help me solve this: Write as a single logarithm: 1/3[logsubscript4x-logsubscript4y] + 2logsubscript4(3x-4) 1 solutions Answer 423992 by lwsshak3(6494)   on 2012-11-24 02:48:13 (Show Source): You can put this solution on YOUR website!Write as a single logarithm: 1/3[logsubscript4x-logsubscript4y] + 2logsubscript4(3x-4) 1/3[log4(x)-log4(y)]+2log4(3x-4) log4[(x/y)^(1/3)*(3x-4)^2]
 Trigonometry-basics/683726: Write the expression as the sine, cosine, or tangent of an angle. sin 48° cos 15° - cos 48° sin 15° And also: Find all solutions to the equation. cos x = sin x And: Verify the identity. 4 csc 2x = 2 csc2x tan x 1 solutions Answer 423991 by lwsshak3(6494)   on 2012-11-24 02:34:42 (Show Source): You can put this solution on YOUR website!Write the expression as the sine, cosine, or tangent of an angle. sin 48° cos 15° - cos 48° sin 15° Identity: sin(s-t)=sin s cos t-cos s sin t sin 48° cos 15° - cos 48° sin 15°=sin(48º-15º)=sin 33º .. And also: Find all solutions to the equation. cos x = sin x tan x=cos x/sin x=1 x=45º+360ºk, x=225º+360ºk, k=integer .. And: Verify the identity. 4 csc(2x) = 2 csc^2x tan x start with right side 2csc^2x tanx =2/sin^2x*sinx/cosx =2/sinx cosx multiply top and bottom by 2 =4/2sinx cosx =4/sin(2x) =4csc(2x) verified: right side=left side
 Travel_Word_Problems/683843: A man drove 156 km at a constant rate. If he had driven 5km/hr. faster he would made the trip in 12 minutes less time. How fast did he drive? ans. 60 KPH help me with solution pls..1 solutions Answer 423769 by lwsshak3(6494)   on 2012-11-22 02:35:22 (Show Source): You can put this solution on YOUR website!A man drove 156 km at a constant rate. If he had driven 5km/hr. faster he would made the trip in 12 minutes less time. How fast did he drive? ans. 60 KPH ** let x=how fast he drove x+5=speed in 12 min less time 156/x-156/(x+5)=12 min=12/60 hr=0.2 hr 156/x-156/(x+5)=.2 LCD: x(x+5) 156(x+5)+156x=x(x+5)(.2) 156x+780+156x=.2x^2+x .2x^2+x-780=0 2x+10x-7800=0 x+5x-3900=0 (x+65)(x-60)=0 x+65=0 x=-65(reject, x>0) or x-60=0 x=60 how fast he drove=60 km/hr
 logarithm/683608: log(2x)=1.7 Solve for x1 solutions Answer 423767 by lwsshak3(6494)   on 2012-11-22 01:44:59 (Show Source): You can put this solution on YOUR website!log(2x)=1.7 Solve for x 2x=10^1.7 x=(10^1.7)/2 x≈25.0594
 logarithm/683829: 2. Solve the following exponential equation. Exact answers only. 49^x-12*7^x=-361 solutions Answer 423766 by lwsshak3(6494)   on 2012-11-22 01:37:41 (Show Source): You can put this solution on YOUR website!2. Solve the following exponential equation. Exact answers only. 49^x-12*7^x=-36 7^2x-12*7^x+36=0 let u=7^x u^2=7^2x u^2-12u+36=0 (u-6)(u-6)=0 u=6=7^x xlog7=log6 x=log6/log7