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Recent problems solved by 'lwsshak3'

lwsshak3 answered: 6525 problems
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Travel_Word_Problems/650488: A subway travels 60 mph from Glendale to Midtown. Another subway, traveling at 45 mph, takes 11 minutes longer for the same trip. how far apart are Glendale and Midtown. Can you walk thru step by step 1 solutions Answer 407337 by lwsshak3(6527)   on 2012-09-12 20:37:46 (Show Source): You can put this solution on YOUR website! A subway travels 60 mph from Glendale to Midtown. Another subway, traveling at 45 mph, takes 11 minutes longer for the same trip. how far apart are Glendale and Midtown. ** let x=distance between Glendale and Midtown travel time=distance/speed 11 min=11/60 hr .. travel time from Glendale to Midtown at 60 mph=x/60 (faster train takes less time) travel time from Glendale to Midtown at 45 mph=x/45 difference in travel times=x/45-x/60=11 min=11/60 hr x/45-x/60=11/60 LCD:60*45 60x-45x=45*11 15x=495 x=33 distance between Glendale and Midtown=33 miles

Angles/650507: angle a and angle b are supplementary. Twice the measure of angle a is one-half the measure of angle b. find the angle of measure b 1 solutions Answer 407328 by lwsshak3(6527)   on 2012-09-12 20:15:17 (Show Source): You can put this solution on YOUR website! angle a and angle b are supplementary. Twice the measure of angle a is one-half the measure of angle b. find the angle of measure b ** a+b=180º a=180-b .. 2a=b/2 2(180-b)=b/2 360 -2b=b/2 720-4b=b 5b=720 b=144 angle of measure b=144º

Age_Word_Problems/650493: Jake is five years older than laura. Four years ago jake was twice as old as laura was then. How old is jake now? 1 solutions Answer 407325 by lwsshak3(6527)   on 2012-09-12 20:00:03 (Show Source): You can put this solution on YOUR website! Jake is five years older than laura. Four years ago jake was twice as old as laura was then. How old is jake now? ** let x= jake's age now x-5=laura's age now four years ago: jake's age=x-4 laura's age=x-5-4=x-9 (x-4)=2(x-9) x-4=2x-18 -x=-14 x= 14 jake's age now=14

Numbers_Word_Problems/649980: 1. There’s a two digit number, let’s call it the original number. When we reverse the digits, the new number thus formed, is 27 less than the original number. When 2 is subtracted from the original number, it becomes twice the new number. Find the original number. 1 solutions Answer 407155 by lwsshak3(6527)   on 2012-09-12 03:19:59 (Show Source): You can put this solution on YOUR website! There’s a two digit number, let’s call it the original number. When we reverse the digits, the new number thus formed, is 27 less than the original number. When 2 is subtracted from the original number, it becomes twice the new number. Find the original number. ** let u=units digit let t=tens digit original number=10t+u new number=10u+t .. 10t+u=10u+t+27 10t+u-2=2(10u+t)=20u+2t .. 9t-9u=27 8t-19u=2 .. 3t-3u=9 8t-19u=2 .. 24t-24u=72 24t-57u=6 33u=66 u=2 3t=9+3u=9+6=15 t=15/3=5 original number=10t+u=50+2=52

Polynomials-and-rational-expressions/649719: Please help me with this question: Find all real zeros of the polynomial function: f(x)=-6x^4+54x^2 1 solutions Answer 407154 by lwsshak3(6527)   on 2012-09-12 02:45:24 (Show Source): You can put this solution on YOUR website! Find all real zeros of the polynomial function: f(x)=-6x^4+54x^2 set f(x)=0 -6x^4+54x^2=0 6x^4-54x^2=0 x^2(6x^2-54)=0 x^2=0 x=0 or 6x^2-54=0 6x^2=54 x^2=54/6=0 x=±√9=±3 zeros are: 0, 0, -3, 3

Rational-functions/647616: Find two numbers whose difference is 4 and the difference of their squares is 88. 1 solutions Answer 407153 by lwsshak3(6527)   on 2012-09-12 02:27:46 (Show Source): You can put this solution on YOUR website! Find two numbers whose difference is 4 and the difference of their squares is 88. ** let x=one of 2 numbers let y=other number .. x-y=4 x=y+4 .. x^2-y^2=88 (y+4)^2-y^2=88 y^2+8y+16-y^2=88 8y=88-16=72 y=72/8=9 x=y+4=13 numbers are: 9 and 13

Rational-functions/649833: How would I Write An Equation Of A Line That Passes Through (1,6) And Is Perpendicular To The Line x-y=4 1 solutions Answer 407151 by lwsshak3(6527)   on 2012-09-12 02:12:31 (Show Source): You can put this solution on YOUR website! How would I Write An Equation Of A Line That Passes Through (1,6) And Is Perpendicular To The Line x-y=4 ** Equation of a line: y=mx+b, m=slope, b= y-intercept x-y=4 y=x-4 slope, m=1 slope of perpendicular line=-1 (negative reciprocal) equation: y=-x+b solve for b using coordinates of given point (1,6) 6=-1+b b=7 equation of perpendicular line: y=-x+7

Trigonometry-basics/649718: solutions for the interval 0,2 pi sin(x)=(1)/(4sinx) 1 solutions Answer 407150 by lwsshak3(6527)   on 2012-09-12 01:53:23 (Show Source): You can put this solution on YOUR website! solutions for the interval 0,2 pi solve for x sin(x)=(1)/(4sinx) 4sin^2x=1 sin^2x=1/4 sinx=1/2 x=π/6 and 5π/6 (in quadrants I and II where sin>0)

Trigonometry-basics/649994: sin 3pi/8 cos pi/8 + cos3pi/8 sin pi/8 1 solutions Answer 407147 by lwsshak3(6527)   on 2012-09-12 01:47:31 (Show Source): You can put this solution on YOUR website! sin 3pi/8 cos pi/8 + cos3pi/8 sin pi/8 Trig identity: sin(s+t)=sin s cos t + cos s sin t For given problem: sin 3π/8 cos π/8 + cos3 π/8 sin π/8 =sin(3π/8+π/8) =sin(4π/8) =sin(π/2) =1

Trigonometry-basics/649998: in which quadrant does theta lie if tan theta>0 and csc theta<0? 1 solutions Answer 407146 by lwsshak3(6527)   on 2012-09-12 01:37:06 (Show Source): You can put this solution on YOUR website! in which quadrant does theta lie if tan theta>0 and csc theta<0? tan>0 in quadrants I and III. csc<0 in quadrants III and IV (same as its reciprocal, sin.) Therefore, theta lies in quadrant III.

Money_Word_Problems/650054: Sandro invested Php38,000 in the International Bank of the Philippines at 5% interest. How much additional money must he invest at 10% so that the annual income would be equal to 7.5% of his investment? 1 solutions Answer 407145 by lwsshak3(6527)   on 2012-09-12 01:29:25 (Show Source): You can put this solution on YOUR website! Sandro invested Php38,000 in the International Bank of the Philippines at 5% interest. How much additional money must he invest at 10% so that the annual income would be equal to 7.5% of his investment? ** let x=additional money invested at 10% .. 5%(38000)+10%x=7.5%(38000+x) 1900+0.10x=2850+.075x .10x-.075x=2850-1900 .025x=950 x=38000 additional money invested at 10%=Php38,000

Trigonometry-basics/646322: how do i find the exact value of sec 25pi/3? 1 solutions Answer 407062 by lwsshak3(6527)   on 2012-09-11 17:15:50 (Show Source): You can put this solution on YOUR website! how do i find the exact value of sec 25pi/3? ** 25π/3=8π+π/3 this means rotating counter clockwise 4 revolutions+π/3, terminating in quadrant I with reference angle π/3 sec 25π/3 =sec π/3 =1/cos π/3 =1/(1/2) =2

Trigonometry-basics/649591: find the exact angle less than 2pi and is coterminal to - 49pi/6 in terms of pi. 1 solutions Answer 407054 by lwsshak3(6527)   on 2012-09-11 17:04:42 (Show Source): You can put this solution on YOUR website! find the exact angle less than 2pi and is coterminal to - 49pi/6 in terms of pi. ** -49π/6=-8π+π/6 this means rotating clockwise 4 revolutions plus π/6, terminating in quadrant IV with 11π/6. coterminal angle=11π/6

Trigonometry-basics/649399: Calculate how many revolutions the car wheel turns every second (at 100km/h) Given the circumference is 2.325m 1 solutions Answer 406992 by lwsshak3(6527)   on 2012-09-11 14:47:09 (Show Source): You can put this solution on YOUR website! Calculate how many revolutions the car wheel turns every second (at 100km/h) Given the circumference is 2.325m ** cancel out: km, hr, m, leaving: 100*1000*rev/2.325*3600sec ≈11.95 rev/sec

Quadratic-relations-and-conic-sections/648879: The vertex form of the equation of a parabola is y=(x-4)^2+22. What is the standard form of the equation? 1 solutions Answer 406934 by lwsshak3(6527)   on 2012-09-11 03:18:46 (Show Source): You can put this solution on YOUR website! The vertex form of the equation of a parabola is y=(x-4)^2+22. What is the standard form of the equation? ** Standard form of equation for a parabola that opens upwards: (x-h)^2=4p(y-k), (h,k)=(x,y) coordinates of the vertex. .. rewrite given equation in standard form: (x-4)^2=(y-22) vertex: (4,22) 4p=1 p=1/4

logarithm/649102: Please solve 16, base 4 1 solutions Answer 406933 by lwsshak3(6527)   on 2012-09-11 03:04:13 (Show Source): You can put this solution on YOUR website! Please solve 16, base 4 log4(16)=4 (log form) base(4) raised to log of number(4)=number(16) (exponential form)

logarithm/646070: Solve the following logarithmic equation. log(base5)(x+15)+log(base5)(x+134)=4 1 solutions Answer 406932 by lwsshak3(6527)   on 2012-09-11 02:58:29 (Show Source): You can put this solution on YOUR website! Solve the following logarithmic equation. log(base5)(x+15)+log(base5)(x+134)=4 place under single log log5[(x+15)(x+134)]=4 convert to exponential form 5^4=(x+15)(x+134) 625=x^2+149x+2010 x^2+149x+1385=0 solve for x by following quadratic formula: a=1, b=149, c=1385 ans: x≈-139.039 (reject,(x+15)>0) or x≈-9.961

logarithm/649010: How do I solve this problem? What am I supposed to do with the numbers in parenthesis? Multiply them? log b (x+2) + log b (x-4)= log b 24 its similar to this one which I am also having trouble with: log10 (x+6) - log10 (x-3)=1 1 solutions Answer 406931 by lwsshak3(6527)   on 2012-09-11 02:27:25 (Show Source): You can put this solution on YOUR website! log b (x+2) + log b (x-4)= log b 24 its similar to this one which I am also having trouble with: log10 (x+6) - log10 (x-3)=1 ** log b (x+2) + log b (x-4)= log b 24 logb[(x+2)(x-4)]=logb(24) (x+2)(x-4)=24 x^2-2x-8=24 x^2-2x-32=0 solve for x by following quadratic formula: a=1, b=-2, c=-32 ans: x≈-4.744 ( reject, (x+2)>0) or x≈6.744 note: base does not enter into calculations. .. log10 (x+6) - log10 (x-3)=1 place under single log log10[(x+6)/(x-3)]=1og10(10) [(x+6)/(x-3)=10 x+6=10x-30 9x=36 x=4

Trigonometry-basics/649335: Find the exact value of trig functions of theta sin (theta) = - 3/7 given that theta is in quadrant IV I don't understand how to rationalize the problem once I get to: cos = the square root of 1 - 3/49 1 solutions Answer 406930 by lwsshak3(6527)   on 2012-09-11 01:39:00 (Show Source): You can put this solution on YOUR website! Find the exact value of trig functions of theta sin (theta) = - 3/7 given that theta is in quadrant IV ** You are working with a reference angle and right triangle in given quadrant IV sin=opp side/hypotenuse=-3/7 adjacent side=√(7^2-3^2)=√(49-9)=√40 .. Trig Functions: sin theta=-3/7 cos theta=√40/7 tan theta=-3/√40=-(3√40)/40 csc theta=-7/3 sec theta=7/√40=(7√40)/40 cot theta=-√40/3

Trigonometry-basics/648990: Find all angles θ between 0° and 180° satisfying the given equation. (Enter your answers as a comma-separated list. Round your answers to the nearest degree.) cos theta= sqr 3/2 1 solutions Answer 406928 by lwsshak3(6527)   on 2012-09-11 01:26:20 (Show Source): You can put this solution on YOUR website! Find all angles θ between 0° and 180° satisfying the given equation. (Enter your answers as a comma-separated list. Round your answers to the nearest degree.) cos theta= sqr 3/2 ** cos theta=√3/2 theta=30º in quadrant I where cos>0

Trigonometry-basics/648102: Consider the angle theta = -1283 degrees A. Find two other coterminal angles to theta. B. What quadrant is theta in? Provide reasoning. C. Is cos theta positive or negative? How do you know? D. Which is greater sin theta or co-secant theta? How do you know? 1 solutions Answer 406851 by lwsshak3(6527)   on 2012-09-10 16:33:55 (Show Source): You can put this solution on YOUR website! Consider the angle theta = -1283 degrees This means going around the circle clockwise 1080º+203º 3*360+203=1283º This positions the angle in quadrant IV .. A. Find two other coterminal angles to theta. 360+203=563º and 720+203=923º .. B. What quadrant is theta in? Provide reasoning. Quadrant IV as explained above. .. C. Is cos theta positive or negative? How do you know? cos is always >0 in quadrant IV .. D. Which is greater sin theta or co-secant theta? How do you know? 203º in quadrant IV makes a reference angle of 360-203=157º sin157º≈-.39 in quadrant IV where sin<0 csc 203=1/sin157=-1/.39≈-2.6. -.39>-2.6 Therefore sin theta>csc theta

Trigonometry-basics/648315: tan of phata if the sin of phata is the square root of 7 divided by 6 1 solutions Answer 406841 by lwsshak3(6527)   on 2012-09-10 15:53:11 (Show Source): You can put this solution on YOUR website! tan of phata if the sin of phata is the square root of 7 divided by 6 ** use x for phata given: sinx=√7/6=opposite side/hypotenuse adjacent side=√[6^2-(√7)^2]=√(36-7)=√29 tanx=opp side/adj side=√7/√26

Trigonometry-basics/648063: find other fundamental identities if tan theta=8/15 and sec theta <0 1 solutions Answer 406838 by lwsshak3(6527)   on 2012-09-10 15:43:27 (Show Source): You can put this solution on YOUR website! find other fundamental identities if tan theta=8/15 and sec theta <0 tan>0 in quadrants I and III sec<0 in quadrants III and IV so, we are working with a reference angle and right triangle in quadrant III opposite side=-8 adjacent side=-15 hypotenuse=√(8^2+15^2)=√(64+225)=√289=17 .. fundamental identities: sin theta=-8/17 cos theta=-15/17 tan theta=8/15 csc theta=-17/8 sec theta=-17/15 cot theta=15/8

Trigonometry-basics/648312: How do you convert radians to degrees without a calculator because I forgot how to convert 7pi/10 into degree measure. 1 solutions Answer 406831 by lwsshak3(6527)   on 2012-09-10 15:30:01 (Show Source): You can put this solution on YOUR website! How do you convert radians to degrees without a calculator because I forgot how to convert 7pi/10 into degree measure. ** Just remember that π(radians)=180º so 7π/10 radians=(7/10)π=(7/10)*180º=126º conversely:126º=(126/180)*π=0.7π=(7/10)π radians

Trigonometry-basics/648163: what is the period of sec(1/4x) 1 solutions Answer 406820 by lwsshak3(6527)   on 2012-09-10 15:12:07 (Show Source): You can put this solution on YOUR website! what is the period of sec(1/4x) equation of sec function: y=sec(Bx) period=2π/B For given function, sec(1/4x): B=1/4 period=2π/(1/4)=8π

Trigonometry-basics/648352: Find the exact value of the six trigonometric functions of θ in standard positions that contains the point (3,-8) 1 solutions Answer 406809 by lwsshak3(6527)   on 2012-09-10 14:40:50 (Show Source): You can put this solution on YOUR website! Find the exact value of the six trigonometric functions of θ in standard positions that contains the point (3,-8) ** You are working with a reference angle and right triangle in quadrant IV. adjacent side=3 opposite side=-8 hypotenuse=√(3^2+8^2)=√9+64=√73 .. sinθ=-8/√73 cosθ=3/√73 tanθ=-8/3 cscθ=-√73/8 secθ=√73/3 cotθ=-3/8

Inequalities/648009: |9x+8/x-10|=11 1 solutions Answer 406529 by lwsshak3(6527)   on 2012-09-09 03:06:08 (Show Source): You can put this solution on YOUR website! solve for x |9x+8/x-10|=11 solve for 2 conditions (9x+8)/(x-10)=11 cross-multiply 9x+8=11x-110 2x=118 x=59 or -(9x+8)/(x-10)=11 (9x+8)/(x-10)=-11 9x+8=-11x+110 20x=102 x=5.1

Trigonometry-basics/647906: Suppose 90degrees < theta < 180degrees. Determine with reasons whether each of the following is positive or negative. A. tan(theta + 180degrees) B. cot (theta/2) C. sec (-theta) 1 solutions Answer 406490 by lwsshak3(6527)   on 2012-09-08 21:56:35 (Show Source): You can put this solution on YOUR website! Suppose 90degrees < theta < 180degrees. Determine with reasons whether each of the following is positive or negative. .. A. tan(theta + 180degrees): negative This moves the standard position of theta from quadrant II to quadrant IV where tan<0 .. B. cot (theta/2): negative Theta remains in quadrant II where cot<0 .. C. sec (-theta): positive Theta is in quadrant IV where sec>0 (note: angle not in given domain)

absolute-value/647934: |8x|+56> or equal to 40 1 solutions Answer 406481 by lwsshak3(6527)   on 2012-09-08 21:33:03 (Show Source): You can put this solution on YOUR website! |8x|+56> or equal to 40 solve for 2 conditions .. 8x+56≥40 8x≥-16 x≥-2 or -8x+56≥40 -8x≥-16 x≤2 divide by -8 and reverse inequality sign solution: [-2,2]

Linear-equations/647810: Solve each compound inequality and graph its solution. 8b+9<7b+3<8b-10 1 solutions Answer 406431 by lwsshak3(6527)   on 2012-09-08 18:20:48 (Show Source): You can put this solution on YOUR website! Solve each compound inequality and graph its solution. 8b+9<7b+3<8b-10 ** 8b+9<7b+3 b<-6 .. 7b+3<8b-10 -b<-13 b>13 number line <.......-13<==>-6.............> solution: (-13, -6)

Quadratic-relations-and-conic-sections/647763: Graph a parabola: Give the vertex,axis,range and domain. I am lost as to how to set these problems up. It has been 20 years since I was in school. Here is the problem: f(x)=x^2+10x+23 1 solutions Answer 406428 by lwsshak3(6527)   on 2012-09-08 18:09:49 (Show Source): You can put this solution on YOUR website! Graph a parabola: Give the vertex,axis,range and domain. I am lost as to how to set these problems up. It has been 20 years since I was in school. Here is the problem: f(x)=x^2+10x+23 This is an equation of a parabola that opens upwards. (sign of lead coefficient>0) Its standard form: (y=(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex. Complete the square: f(x)=(x^2+10x+25)+23-25 f(x)=(x+5)^2-2 vertex: (-5,-2) axis of symmetry: x=-5 Range: (-2,∞) Domain: (-∞,∞) see graph below: