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# Recent problems solved by 'lwsshak3'

lwsshak3 answered: 6517 problems
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 Quadratic-relations-and-conic-sections/710284: Please state the coordinates of the vertex. 12y+x^2-4x=-16 1 solutions Answer 436987 by lwsshak3(6519)   on 2013-02-04 19:41:47 (Show Source): You can put this solution on YOUR website!Please state the coordinates of the vertex. 12y+x^2-4x=-16 x^2-4x=-12y-16 complete the square: (x^2-4x+4)=-12y-16+4 (x-2)^2=-12y-12 (x-2)^2=-12(y+1) This is an equation of a parabola that opens down. Its standard form: (x-h)^2=-4p(y-k)^2, (h,k)=(x,y) coordinates of the vertex For given equation:12y+x^2-4x=-16 vertex: (2,-1)
 Graphs/710262: What are 2x-3y-1=3 and 3x-4y-2=3 in y=mx+b format? 1 solutions Answer 436982 by lwsshak3(6519)   on 2013-02-04 19:22:38 (Show Source): You can put this solution on YOUR website!What are 2x-3y-1=3 and 3x-4y-2=3 in y=mx+b format? ** 2x-3y-1=3 3y=2x-4 y=2x/3-4/3 .. 3x-4y-2=3 4y=3x-5 y=3x/4-5/3
 Graphs/710282: The line through (8,-2) perpendicular to the line y=7-2x What an equation of the line described1 solutions Answer 436976 by lwsshak3(6519)   on 2013-02-04 19:15:11 (Show Source): You can put this solution on YOUR website!The line through (8,-2) perpendicular to the line y=7-2x Write an equation of the line described ** Equation of a line: y=mx+b, m=slope, b=y-intercept y=7-2x y=-2x+7 m=-2 slope of the perpendicular line=1/2 (negative reciprocal) y=x/2+b solve for b using coordinates of given point on the line (8,-2) -2=8/2+b b=-6 Equation of the perpendicular line:y=x/2-6
 Graphs/710373: what is the equation of a line that is parallel to the line y=-3x-4 and passes through the point (-4,6)1 solutions Answer 436975 by lwsshak3(6519)   on 2013-02-04 19:06:23 (Show Source): You can put this solution on YOUR website!what is the equation of a line that is parallel to the line y=-3x-4 and passes through the point (-4,6) ** equation of a line: y=mx+bd, m=slope, b=y-intercept y=-3x-4 m=-3 a parallel line will have the same slope y=-3x+b solve for b using coordinates of given point (-4,6) 6=-3*-4+b b=-12+6=-6 Equation of parallel line: y=-3x-6
 Trigonometry-basics/708989: (1+sinx)[1+sin(-x)]=11 solutions Answer 436717 by lwsshak3(6519)   on 2013-02-03 02:18:09 (Show Source): You can put this solution on YOUR website!(1+sinx)[1+sin(-x)]=1 sin(-x)=-sin(x) (1+sinx)[1-sin(x)]=1 1-sin^2(x)=1 sin^2x=0 x=0
 Trigonometry-basics/709119: find the exact value of each expression 21) cot [inverse sin negative root 2 over 3]1 solutions Answer 436715 by lwsshak3(6519)   on 2013-02-03 02:13:37 (Show Source): You can put this solution on YOUR website!find the exact value of each expression 21) cot [inverse sin negative root 2 over 3] Inverse sin(-√2/3) means you are working with a right triangle where: opposite side=-√2 hypotenuse=3 therefore, adjacent side=√(3^2-(√2)^2)=√(9-2)=√7 cot=adjacent side/opposite side=-√(2/7)
 Trigonometry-basics/709526: find the exact value of each expression. 35) sec(inverse sin 5/13 minus inverse tan 3/4) inverse sin means sin^-1 inverse tan means tan^-11 solutions Answer 436714 by lwsshak3(6519)   on 2013-02-03 01:55:05 (Show Source): You can put this solution on YOUR website!find the exact value of each expression. 35) sec(inverse sin 5/13 minus inverse tan 3/4) ** Since the inverses are not special angles, you can only get approximate angles using a calculator. Using calculator set to radians: sin^-1(5/13)≈0.3948 radians tan^-1(3/4)≈0.6435 radians sin^-1(5/13)-tan^-1(3/4) 0.3948-0.6435≈-0.2487 radians cos(0.2487)≈0.9692 sec(0.2487)≈1.0317 (reciprocal of cos)
 Trigonometry-basics/709549: Refer to the graph of y = tan(x) to find the exact values of x in the interval (-π/2, 3π/2) that satisfy the equation. (Enter your answers from smallest to largest.) 3 tan(x)=-3 i got -3 and 8pi/3 and its wrong i do not know where i went wrong 1 solutions Answer 436713 by lwsshak3(6519)   on 2013-02-03 01:27:08 (Show Source): You can put this solution on YOUR website!Refer to the graph of y = tan(x) to find the exact values of x in the interval (-π/2, 3π/2) that satisfy the equation. (Enter your answers from smallest to largest.) 3 tan(x)=-3 ** 3 tan(x)=-3 tanx=-1 x=-π/4 and 3π/4 (in quadrants II and IV where tan<0)
 Rational-functions/709594: Graph the rational function and show all asymptotes, zeros and intercepts R(x) = 3x^2-12/x^2-x-20 1 solutions Answer 436712 by lwsshak3(6519)   on 2013-02-03 01:18:40 (Show Source): You can put this solution on YOUR website!Graph the rational function and show all asymptotes, zeros and intercepts R(x) = (3x^2-12)/(x^2-x-20) .. Horizontal Asymptotes:HA When degree of numerator and denominator the same, divide the lead coefficient of the numerator by the lead coefficient of the denominator: HA: 3/1=3 .. Vertical Asymptotes: VA Set denominator=0, then solve for x-values which make the function undefined. x^2-x-20 (x-5)(x+4) VA: x=5 and x=-4 .. Zeros:(x-intercepts) set y=0 3x^2-12=0 x^2=4 x=±2 .. y-intercept set x=0 (3x^2-12)/(x^2-x-20) -12/-20=3/5=.6 .. number line: <...+...-4....-....-2...+....2....-....5....+....> .. see graph below:
 Trigonometry-basics/708636: Question: solve 3cos(theta)-1 = 4cos(theta) ... Tried to use algebra to solve but my answers were insufficient. 3cos(theta)=4cos(theta)+1 Would I multiply the signs together like ... 12cos(theta)=1 Cos(theta)=1/12 ???? ...Or would I add them like so ... ? 7cos(theta)=1 Cos(theta)=1/7 This also has to do with the unit circle and finding the roots .... Fyi The answer is pi... And I don't understand quite how to get there 1 solutions Answer 436283 by lwsshak3(6519)   on 2013-01-31 14:49:58 (Show Source): You can put this solution on YOUR website!Question: solve 3cos(theta)-1 = 4cos(theta) 3cosx-1=4cosx 4cosx-3cosx=-1 cosx=-1 x=π
 Quadratic-relations-and-conic-sections/708016: Write an equation for an ellipse with major axis of length 10 and foci at (5,2) and (-1,2).1 solutions Answer 436209 by lwsshak3(6519)   on 2013-01-31 03:05:52 (Show Source): You can put this solution on YOUR website!Write an equation for an ellipse with major axis of length 10 and foci at (5,2) and (-1,2). Foci data shows given ellipse has a horizontal major axis. (x changes but y does not) Its standard form:, a>b, (h,k)=(x,y) coordinates of center For given ellipse: y-coordinate of center=2 x-coordinate=midpoint between (-1 and 5)=2 center: (2,2) given length of horizontal major axis=10=2a a=5 a^2=25 Foci 2c=6 (-1 to 5) c=3 c^2=9 c^2=a^2-b^2 b^2=a^2-c^2=25-9=16 b=√16=4 Equation of given ellipse:
 Quadratic-relations-and-conic-sections/707950: Find equation of ellipse having vertices (10,0) and (-10,0) and minor axis (0,9) and (0,-9)1 solutions Answer 436208 by lwsshak3(6519)   on 2013-01-31 02:46:30 (Show Source): You can put this solution on YOUR website!Find equation of ellipse having vertices (10,0) and (-10,0) and minor axis (0,9) and (0,-9) Data shows given ellipse has a horizontal major axis: Its standard form: , a>b, (h,k)=(x,y) coordinates of center For given ellipse: center: (0,0) length of horizontal major axis=20=2a a=10 a^2=100 length of minor axis=18=2b b=9 b^2=81 Equation of given ellipse:
 Quadratic-relations-and-conic-sections/708076: find the vertices and foci X^2/81+Y^2/25=11 solutions Answer 436205 by lwsshak3(6519)   on 2013-01-31 02:29:24 (Show Source): You can put this solution on YOUR website!find the vertices and foci X^2/81+Y^2/25=1 This is an equation of an ellipse with horizontal major axis. Its standard form: , a>b, (h,k)=(x,y) coordinates of center For given equation: center:(0,0) a^2=81 a=9 b^2=25 b=5 vertices: (0±a,0)=(0±9,0)=(-9,0) and (9,0) c^2=a^2-b^2=81-25==56 c=√56≈7.5 foci: (0±c,0)=(0±7.5,0)=(-7.5,0) and (7.5,0)
 Quadratic-relations-and-conic-sections/708176: what is focus and directix of parabola y^2=4(y-1)1 solutions Answer 436203 by lwsshak3(6519)   on 2013-01-31 02:15:48 (Show Source): You can put this solution on YOUR website!what is focus and directix of parabola y^2=4(y-1) I think you meant to write the equation as y^2=4(x-1) This is an equation of a parabola that opens right. Its standard form: (y-k)^2=4p(x-h), (h,k)=(x,y) coordinates of the vertex For given parabola: vertex: (1,0) axis of symmetry: y=0 or x-axis 4p=4 p=1 focus: (2,0) (p-distance right of vertex on the axis of symmetry) directrix: x=0 or y-axis (p-distance left of vertex on the axis of symmetry)
 Quadratic-relations-and-conic-sections/708672: what is the vertex of y=-x2+5x-101 solutions Answer 436202 by lwsshak3(6519)   on 2013-01-31 02:01:39 (Show Source): You can put this solution on YOUR website!what is the vertex of y=-x^2+5x-10 complete the square y=-(x^2-5x+25/4)+25/4-10 y=-(x-5/2)^2-15/4 This is an equation of a parabola that opens down. Its standard form: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex. vertex of given parabola:(5/2,-15/4)
 Quadratic-relations-and-conic-sections/708198: identify the center, the length of major axis, and the length of the minor axis for the following ellipse. -16y+52=-2x^2-8x-y^21 solutions Answer 436200 by lwsshak3(6519)   on 2013-01-31 01:50:57 (Show Source): You can put this solution on YOUR website!identify the center, the length of major axis, and the length of the minor axis for the following ellipse. -16y+52=-2x^2-8x-y^2 rearrange terms 2x^2+8x+y^2-16y=-52 complete the square 2(x^2+4x+4)+(y^2-16y+64)=-52+8+64 2(x+2)^2+(y-8)^2=20 This is an equation of an ellipse with vertical major axis. Its standard form:, a>b, (h,k)=(x,y) coordinates of center For given ellipse: center: (-2,8) length of vertical major axis=2a=2√20≈8.94 length of minor axis=2b=2√10≈6.32
 Trigonometry-basics/708693: Two planes start from Los Angeles International Airport and fly in opposite directions. The second plane starts 1/2 hour after the first plane, but its speed is 80 kilometers per hour faster. Find the airspeed of each plane if 2 hours after the first plane departs the planes are 3200 kilometers apart. Make a system to solve.1 solutions Answer 436199 by lwsshak3(6519)   on 2013-01-31 01:24:06 (Show Source): You can put this solution on YOUR website!Two planes start from Los Angeles International Airport and fly in opposite directions. The second plane starts 1/2 hour after the first plane, but its speed is 80 kilometers per hour faster. Find the airspeed of each plane if 2 hours after the first plane departs the planes are 3200 kilometers apart. Make a system to solve. ** let x=speed of the first plane x+80=speed of the second plane distance=speed*travel time travel time of first plane=2 hrs travel time of second plane=1.5 hrs .. 2x+1.5(x+80)=3200 2x+1.5x+120=3200 3.5x=3080 x=880 x+80=960 speed of the first plane=880 km/hr speed of the second plane=960 km/hr
 Quadratic-relations-and-conic-sections/708598: Find an equation of the hyperbola with the center at the origin. Foci: (0,+-8); asympotes: y=+-4x. I understood all the other questions with that concept but this stumped me.1 solutions Answer 436195 by lwsshak3(6519)   on 2013-01-31 00:44:01 (Show Source): You can put this solution on YOUR website!Find an equation of the hyperbola with the center at the origin. Foci: (0,+-8); asymptotes: y=+-4x. ** FOR SOME UNKNOWN REASON THE COMPLETE SOLUTION WILL NOT POST Foci data show given hyperbola has a vertical transverse axis. Standard form of equation:
 Exponential-and-logarithmic-functions/707922: What is the answer for this: Simplify. 1.ln pi + ln h + 2ln 8 - ln 3 2. 2/3 logb x - 4 logb y + logb z 1 solutions Answer 436155 by lwsshak3(6519)   on 2013-01-30 20:29:49 (Show Source): You can put this solution on YOUR website!What is the answer for this: Simplify. 1.ln pi + ln h + 2ln 8 - ln 3 ln[(πh8^2)/3] .. 2. 2/3 logb x - 4 logb y + logb z logb[(x^(2/3)z)/y^4]
 Exponential-and-logarithmic-functions/708220: Find the inverse of this function: f(x)=log(2x)+3 Here's what I've done. I'm not sure what to do next: x-3=log (2y) log (x-3)= log (2y)1 solutions Answer 436147 by lwsshak3(6519)   on 2013-01-30 20:24:52 (Show Source): You can put this solution on YOUR website!Find the inverse of this function: f(x)=log(2x)+3 interchange x and y x=log(2y)+3 log(2y)=x-3 convert to exponential form: base(10) raised to log of number(x-3)=number(2y) 10^(x-3)=2y y^-1=10^(x-3)/2
 Numbers_Word_Problems/708560: the difference between two numbers is 16.five times the smaller number is equal to 8 less than twice the larger number.find the numbers ?1 solutions Answer 436140 by lwsshak3(6519)   on 2013-01-30 20:08:57 (Show Source): You can put this solution on YOUR website!the difference between two numbers is 16.five times the smaller number is equal to 8 less than twice the larger number.find the numbers ? ** let x=larger of two numbers x-16=smaller of two numbers .. 5(x-16)=2x-8 5x-80=2x-8 3x=72 x=24 x-16=8 larger of two numbers=24 smaller of two numbers=8
 Travel_Word_Problems/708548: a boat traveled downstream a distance of 45 mi ad then came right back. if the speed of the stream was 12 mph and the total trip took 5 hours, find the average speed of the boat relative to the water1 solutions Answer 436137 by lwsshak3(6519)   on 2013-01-30 19:59:35 (Show Source): You can put this solution on YOUR website!a boat traveled downstream a distance of 45 mi ad then came right back. if the speed of the stream was 12 mph and the total trip took 5 hours, find the average speed of the boat relative to the water ** let x= speed of boat in still water x+12= speed of boat in downstream x-12= speed of boat in upstream .. travel time=distance/speed 45/(x+12)+45/(x-12)=5 45(x-12)+45(x+12)=5(x+12)(x-12) 45(x-12+x+12)=5(x^2-144) 90x=5x^2-720 5x^2-90x-720=0 x^2-18x-144=0 (x+6)(x-24)=0 x=-6 (reject, x>0) x=24 average speed of the boat relative to the water: speed of boat twice the speed of the water
 Linear-equations/708545: What is the slope of a line that is parallel to y = 21 solutions Answer 436133 by lwsshak3(6519)   on 2013-01-30 19:41:38 (Show Source): You can put this solution on YOUR website!What is the slope of a line that is parallel to y = 2 slope of a line that is parallel to y = 2 is a horizontal line with slope=0
 Rational-functions/708498: 1.Find the horizontal asymptote of the graph of y =-4x^6+6x+3/8x^6+9x+3. a.y = 1 b.y = one over two c.y = 0 d.There is no horizontal asymptote. 2.What is the graph of the rational function: y =x^2-7x+12/x^2-1 ? 1 solutions Answer 436132 by lwsshak3(6519)   on 2013-01-30 19:37:30 (Show Source): You can put this solution on YOUR website!Find the horizontal asymptote of the graph of y =-4x^6+6x+3/8x^6+9x+3 To find the horizontal asymptote of a rational function when the degree of the numerator and denominator are of the same value, divide the lead coefficient of numerator by the lead coefficient of denominator. The resultant quotient is the horizontal asymptote. In this case: -4/8=-1/2 ans b, y=-1/2
 Rational-functions/708492: Describe the vertical asymptote(s) and hole(s) for the graph of y =x-5/x^2+4x+3. a.asymptotes: x = 3, 1 and no holes. b.asymptote: x = 3 and hole: x = 5 c.asymptotes: x = 3, 1 and hole: x = 5 d.asymptote: x = 5 and hole: x = 31 solutions Answer 436119 by lwsshak3(6519)   on 2013-01-30 18:58:07 (Show Source): You can put this solution on YOUR website!Describe the vertical asymptote(s) and hole(s) for the graph of y =x-5/x^2+4x+3. To find vertical asymptotes, set denominator=0, then solve for x values that make the function undefined. x^2+4x+3=0 (x+3)(x+1)=0 x=-3 or x=-1 asymptotes: x=-3 and x=-1 There are no holes in the graph ans: a
 Trigonometry-basics/707795: Solve the following equation; domain 0x360; if necessary, round off angles to nearest whole degree. Write the degree measurements in ascending order. 3cotx = sqrt31 solutions Answer 435944 by lwsshak3(6519)   on 2013-01-29 20:09:58 (Show Source): You can put this solution on YOUR website!Solve the following equation; domain 0x360; if necessary, round off angles to nearest whole degree. Write the degree measurements in ascending order. 3cotx = sqrt3 cotx=√3/3 x= 240Ί, 60Ί (in quadrants III and I where cot>0)
 Trigonometry-basics/707769: I need to know how to solve f(x)=x^2cos2x and to determine whether the function is even, odd, or neither.1 solutions Answer 435943 by lwsshak3(6519)   on 2013-01-29 20:05:05 (Show Source): You can put this solution on YOUR website!I need to know how to solve f(x)=x^2cos2x and to determine whether the function is even, odd, or neither. ** Function is even if f(-x)=f(x) Function is odd if f(-x)=-f(x) ** f(x)=x^2cos2x cos(-2x)=cos2x (cos is an even function) f(-x)=(-x)^2cos(-2x)=x^2cos2x=f)x) Therefore, f(x) is an even function. .. To solve such equations, x must be determined and expressed in radians,
 Trigonometry-basics/707894: A tire for a car is 28 inches in diameter. If the car is traveling at a speed of 90 mi/hr, find the number of revolutions the tire makes per minute. (Round your answer to the nearest hundredth.)1 solutions Answer 435937 by lwsshak3(6519)   on 2013-01-29 19:47:06 (Show Source): You can put this solution on YOUR website!A tire for a car is 28 inches in diameter. If the car is traveling at a speed of 90 mi/hr, find the number of revolutions the tire makes per minute. (Round your answer to the nearest hundredth.) ** 90 mi/hr*5280 ft/mi*12 inches/ft*60 min/hr mi,hr,ft, cancel out 90*5280/12*60=600 in/min circumference of wheel=π*diameter=π*28=87.965 inches (600in/min)/(87.965 in/rev) 600/87.965≈6.821 rev/min number of revolutions the tire makes per minute=6.821
 Trigonometry-basics/707924: what is the minimum value of the function f(x)= 3+4sin(x+2)1 solutions Answer 435921 by lwsshak3(6519)   on 2013-01-29 19:05:05 (Show Source): You can put this solution on YOUR website!what is the minimum value of the function f(x)= 3+4sin(x+2) Equation of a sin function: y=Asin(Bx-C), A=amplitude, 2π/B=period, phase shift=C/B For given function: 3+4sin(x+2) Amplitude=4 minimum value=-4+3=-1 (Bump the minimum value 4, 3 units up)
 logarithm/707933: how do you write this equation in exponential form log[2]1=01 solutions Answer 435916 by lwsshak3(6519)   on 2013-01-29 18:47:53 (Show Source): You can put this solution on YOUR website!how do you write this equation in exponential form log[2]1=0 This reads log 1, base 2=0 exponential form: base(2) raised to log of number(0)=number(1) 2^0=1
 test/707588: [(Sqrt2) secx-2](2sinx+1)=0 Find all solutions for this equation with the interval [0, 2pi)1 solutions Answer 435751 by lwsshak3(6519)   on 2013-01-29 02:33:32 (Show Source): You can put this solution on YOUR website![(Sqrt2) secx-2](2sinx+1)=0 Find all solutions for this equation with the interval [0, 2pi) ** √2secx-2=0 √2secx=2 secx=2/√2 cosx=√2/2 x=π/4, 7π/4 ( In quadrants I and IV where sec and cos>0)