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Recent problems solved by 'lwsshak3'

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 Systems-of-equations/733788: Given (x^2+4x+8)divided by (x+k), find the values of k so that the remainder is 20. Please use synthetic division.1 solutions Answer 451098 by lwsshak3(6513)   on 2013-04-18 20:16:37 (Show Source): You can put this solution on YOUR website!Given (x^2+4x+8)divided by (x+k), find the values of k so that the remainder is 20. Please use synthetic division. *** ...-k..|....1........4.............8...... ......................-k.......(-4k+k^2) ..............1....(4-k)....(8-4k+k^2) 8-4k+k^2=20 k^2-4k-12=0 (k-6)(k+2)=0 k=6 or k=-2
 Systems-of-equations/739378: Can someone show me how this is done please .Thanks Write f(x)=-9x^2+18x in standard form.1 solutions Answer 451096 by lwsshak3(6513)   on 2013-04-18 19:57:07 (Show Source): You can put this solution on YOUR website!Write f(x)=-9x^2+18x in standard form. complete the square: This is an equation of a parabola that opens downward. Its standard form: , (h,k)=(x,y) coordinates of the vertex, A is a coefficient that affects the slope or steepness of the curve. For given equation: vertex:(1,9)
 Quadratic-relations-and-conic-sections/739168: Write the equation of the conic section satisfying the given conditions vertices (3,5) and (3,-5) and minor axis of length 41 solutions Answer 451062 by lwsshak3(6513)   on 2013-04-18 15:35:17 (Show Source): You can put this solution on YOUR website!Write the equation of the conic section satisfying the given conditions vertices (3,5) and (3,-5) and minor axis of length 4 *** This is an ellipse with vertical major axis. (y-coordinates of vertices change but x-coordinates do not) Its standard form of equation: , (a>b), (h,k)=(x,y) coordinates of center. For given ellipse: center: (3,0) a=5 (distance from center to vertex on vertical major axis) a^6=25 b=2 (distance from center to end point of minor axis) b^2=4 Equation:
 logarithm/738910: Given that log_8(t) = 2.68, log_8(r) = -0.22, and log_8(z) = -0.45, find the following: log_8((root(9)(r^11))/(t^10z^4))1 solutions Answer 451005 by lwsshak3(6513)   on 2013-04-18 03:56:16 (Show Source): You can put this solution on YOUR website!Given that log_8(t) = 2.68, log_8(r) = -0.22, and log_8(z) = -0.45, find the following: log_8((root(9)(r^11))/(t^10z^4)) ** =0.53-2.42-26.8+1.80 =-26.89
 logarithm/738884: Solve the equation. (Round your answer to four decimal places) e^6x + 6e^3x − 27 = 01 solutions Answer 451003 by lwsshak3(6513)   on 2013-04-18 03:32:30 (Show Source): You can put this solution on YOUR website!Solve the equation. (Round your answer to four decimal places) e^6x + 6e^3x − 27 = 0 take log of both sides 3xlne=ln(2.0166) x=ln(2.0166)/3 x=0.2338
 logarithm/738992: write this as a singe logarithm 1 solutions Answer 451002 by lwsshak3(6513)   on 2013-04-18 03:05:42 (Show Source):
 logarithm/739055: log(3)(x-4)=2-log(3)(x+4) please help me solve this equation. the two on the other side is throwing me off. i just dont get it. 1 solutions Answer 451001 by lwsshak3(6513)   on 2013-04-18 02:42:58 (Show Source): You can put this solution on YOUR website!log(3)(x-4)=2-log(3)(x+4) (x-4)(x+4)=9 x^2-16=9 x^2=25 x=5 or x=-5(reject, (x-4)>0))
 logarithm/739058: This is a story problem. It reads, "you deposit 2500 dollars in an account that pays 3.5% annual interest compounded continuously. What is the balance after eight years?1 solutions Answer 451000 by lwsshak3(6513)   on 2013-04-18 02:19:54 (Show Source): You can put this solution on YOUR website!This is a story problem. It reads, "you deposit 2500 dollars in an account that pays 3.5% annual interest compounded continuously. What is the balance after eight years? ** Formula for continuous compounding: A=Pe^rt, P=initial deposit, r=interest rate, t=years, A=amt after t years For given problem: P=2500 r=.035 t=8 A=2500*e^(.035*8)≈3308 Balance after eight years=\$3308
 Trigonometry-basics/739045: Please help me solve this equation: Direction: Find all solution in the interval [0,2pi) by algebraically: 2sin(^2)*2x+5sin2x-3=01 solutions Answer 450999 by lwsshak3(6513)   on 2013-04-18 02:07:29 (Show Source): You can put this solution on YOUR website!Find all solution in the interval [0,2pi) by algebraically: 2sin(^2)*2x+5sin2x-3=0 *** .. (2sin(2x)-1)=0 sin(2x)=1/2 2x=π/6, 5π/6 (in Q1 and Q2 where sin>0) x=π/12, 5π/12 .. or (sin(2x)+3)=0 sin(2x)=-3(reject, (-1 ≤ sin(2x) ≤ 1)
 Trigonometry-basics/738711: Simplify Cot(x)•sin^2(x)•sec(x)1 solutions Answer 450998 by lwsshak3(6513)   on 2013-04-18 01:42:03 (Show Source): You can put this solution on YOUR website!Simplify Cot(x)•sin^2(x)•sec(x) **
 Trigonometry-basics/738988: Use an Addition or Subtraction Formula to find the exact value of the expression Sin(165)1 solutions Answer 450975 by lwsshak3(6513)   on 2013-04-17 21:24:34 (Show Source): You can put this solution on YOUR website!Use an Addition or Subtraction Formula to find the exact value of the expression Sin(165) *** sin(165)=sin(135+30) =(sin(135)cos(30))+(cos(135)sin(30)) =(√2/2*√3/2)+(-√2/2*1/2) =√6/4-√2/4 =(√6-√2)/4 calculator check: sin(165)≈0.2588.. (√6-√2)/4≈0.2588..
 Trigonometry-basics/738725: Find csc^-1(2) in radians and degrees. How would i do this? 1 solutions Answer 450971 by lwsshak3(6513)   on 2013-04-17 21:01:02 (Show Source): You can put this solution on YOUR website!Find csc^-1(2) in radians and degrees. How would i do this? Another way to read this: x=π/6 or 30º
 Trigonometry-basics/738963: Find the first three x-intercepts of the graph of the given function on the positive x-axis. f(x) = 2 − 4 cos(x +π/3) a. b.2pi c. 1 solutions Answer 450967 by lwsshak3(6513)   on 2013-04-17 20:53:16 (Show Source): You can put this solution on YOUR website!Find the first three x-intercepts of the graph of the given function on the positive x-axis. f(x) = 2 − 4 cos(x +π/3) set f(x)=0 2 − 4 cos(x +π/3)=0 4 cos(x+π/3)=2 cos(x+π/3)=2/4=1/2 x+π/3=π/3, 5π/3, 7π/3 x=0, 4π/3, 2π
 Trigonometry-basics/738948: use the half angle identities to find all solutions in the interval [0,2pi) sin^2x=cos^2(x/2)1 solutions Answer 450965 by lwsshak3(6513)   on 2013-04-17 20:38:42 (Show Source): You can put this solution on YOUR website!use the half angle identities to find all solutions in the interval [0,2pi) sin^2x=cos^2(x/2) *** .. 2cos(x)-1=0 cos(x)=1/2 x=π/3, 5π/3 .. cos(x)+1=0 cos(x)=-1 x=π
 Linear-equations/738807: Solve |2x+4|-6<-101 solutions Answer 450920 by lwsshak3(6513)   on 2013-04-17 15:18:02 (Show Source): You can put this solution on YOUR website!Solve |2x+4|-6<-10 ** two solutions: 2x+4-6<-10 2x<-8 x<-4 .. -(2x+4)-6<-10 -2x-4-6<-10 -2x-10<-10 2x+10>10 2x>0 x>0 .. number line: <===-4).......(0===> solution: (-∞,-4) U (0,∞)
 Trigonometry-basics/738273: State the phase shift of y=cos(theta-pi/3). Then graph the function. The graph that it asks me to use has pi and 2pi as the x coordinates, I'm not sure how to graph on it. 1 solutions Answer 450874 by lwsshak3(6513)   on 2013-04-17 03:43:39 (Show Source): You can put this solution on YOUR website!State the phase shift of y=cos(theta-pi/3). Then graph the function. The graph that it asks me to use has pi and 2pi as the x coordinates, I'm not sure how to graph on it. *** Form of equation for cos: y=Acos(Bx-C), A=amplitude, period=2π/B, phase shift=(C/B) For given equation: y=cos(x-π/3) amplitude=1 B=1 period=2π/B=2π (1/4) period=π/2 phase shift: C/B=π/3/1=π/3 (shift to the right) Graphing: start with coordinates of basic cos curve for one period: (x-axis scale in radians) (0,1), ((π/2),0), (π,-1), (3π/2,(-1)), (2π,0) shift curve (π/3) to the right (0,.5), ((π/3),1), ((5π/6),0), (4π3,-1), (11π/6,(-1)), (7π/3,0)
 Trigonometry-basics/738501: If angle A is acute and tanA is 2/3, them... how do you get the answer of cot(90° − A) =2/3?1 solutions Answer 450869 by lwsshak3(6513)   on 2013-04-17 03:09:37 (Show Source): You can put this solution on YOUR website!If angle A is acute and tanA is 2/3, them... how do you get the answer of cot(90° − A) =2/3 Say, you are working a 30-60 right triangle, for example: let A=30º tan(30º)=1/√3 cot (90-30)=cot(60º)=1/√3 I used 30º for this example, but it will work for any acute angle. This identity also works for sin and cos functions. sin 30º=1/2 cos (90-30)=cos(60º)=1/2
 Trigonometry-basics/738616: Prove sin 2theta = 2tan theta/ 1 + tan^2 theta1 solutions Answer 450868 by lwsshak3(6513)   on 2013-04-17 02:55:51 (Show Source): You can put this solution on YOUR website!Prove sin 2theta = 2tan theta/ 1 + tan^2 theta start with right side: =2sin(x)cos(x)=sin(2x)
 Trigonometry-basics/738583: csc^2theta-cot^2theta/cot(theta)=tan(theta)1 solutions Answer 450866 by lwsshak3(6513)   on 2013-04-17 02:05:05 (Show Source): You can put this solution on YOUR website! Start with left side:
 Trigonometry-basics/738265: What is the exact value of sine of 13pie/12 ?1 solutions Answer 450807 by lwsshak3(6513)   on 2013-04-16 17:40:29 (Show Source): You can put this solution on YOUR website!What is the exact value of sine of 13pie/12 ? ** (in Q3 where sin <0) Use sin half-angle formula to solve: sin(π/12)=sin((π/6)/2) =±√(1-cos(π/6)/2) =-√(1-(√3/2)/2) =-√(2-√3/4) =-√(2-√3)/2 Check with calculator: sin(13π/12)≈-0.2588.. -√(2-√3)/2≈-0.2588..
 Quadratic-relations-and-conic-sections/737544: (y-2.5)^2=4p(x-12) I need the step by step help to get it into y= I do not get this!1 solutions Answer 450723 by lwsshak3(6513)   on 2013-04-16 03:42:50 (Show Source): You can put this solution on YOUR website! I need the step by step help to get it into y= take sqrt of both sides
 Quadratic-relations-and-conic-sections/737563: Parabolas: Write each question in standard form. Identify the vertex, axis of symmetry and direction of opening of the parabola. y=x^2+2x+21 solutions Answer 450722 by lwsshak3(6513)   on 2013-04-16 03:34:04 (Show Source): You can put this solution on YOUR website!Write each question in standard form. Identify the vertex, axis of symmetry and direction of opening of the parabola. y=x^2+2x+2 complete the square: y=(x^2+2x+1)-1+2 This is an equation of a parabola that opens upward. Its standard form of equation: , (h,k)=(x,y) coordinates of the vertex, A is a coefficient that affects the slope or steepness of the curve. .. For given parabola: vertex: (-1,1) axis of symmetry: x=-1 parabola opens upward. see graph below as a visual check:
 Quadratic-relations-and-conic-sections/737564: Hyperbolas: Graph each hyperbola. Identify the verices, foci, and asymptotes X^2/4 - y^2/16 = 11 solutions Answer 450721 by lwsshak3(6513)   on 2013-04-16 03:21:41 (Show Source): You can put this solution on YOUR website!Graph each hyperbola. Identify the verices, foci, and asymptotes This is a hyperbola that has a horizontal transverse axis (x-term listed first ahead of y-term) Its standard form of equation: For given hyperbola: center: (0,0) a^2=4 a=2 vertices: (0±a,0)=(0±2,0)=(-2,0) and (2,0) .. b^2=16 b=4 .. c^2=a^2+b^2=4+16=20 c=√20≈4.47 foci: (0±c,0)=(0±4.47,0)=(-4.47,0) and (4.47,0) .. Asymptotes: (equations of lines that go thru center, y=mx+b, m=slope, b= y-intercept) Slopes of asymptotes of hyperbolas with horizontal transverse axis=±b/a=±4/2=±2 .. Equation of asymptote with negative slope=-2 y=-2x+b b=0 y=-2x .. Equation of asymptote with positive slope=2 y=2x+b b=0 y=2x ... y=±(4x^2-16)^.5 See graph below as a visual check:
 Quadratic-relations-and-conic-sections/737799: How do you find an equation of the parabola with vertex (-3,-4) and focus (-3,-3)? 1 solutions Answer 450719 by lwsshak3(6513)   on 2013-04-16 02:48:14 (Show Source): You can put this solution on YOUR website!How do you find an equation of the parabola with vertex (-3,-4) and focus (-3,-3)? This is a parabola that opens upward: Its basic equation: , (h,k)=(x,y) coordinates of the vertex For given parabola: vertex: (-3,-4) axis of symmetry: x=-3 p=1 (distance from vertex to focus on the axis of symmetry) 4p=4 Equation:
 Quadratic-relations-and-conic-sections/738106: write the standard form of the equation of the parabola with the directrix x=(-1/2) and vertex at (0,0)1 solutions Answer 450717 by lwsshak3(6513)   on 2013-04-16 02:35:30 (Show Source): You can put this solution on YOUR website!write the standard form of the equation of the parabola with the directrix x=(-1/2) and vertex at (0,0) *** Given parabola opens rightward. Its basic equation: y^2=4px axis of symmetry: y=0 p=1/2 (distance from vertex to directrix on the axis of symmetry) 4p=2 equation: y^2=2x
 Age_Word_Problems/738177: when andy was born, sarah, his mother was 25 years old. three years ago his mother was six times as old as andy was then. how old is andy now. show method you used to solve the problem.1 solutions Answer 450716 by lwsshak3(6513)   on 2013-04-16 02:04:13 (Show Source): You can put this solution on YOUR website!when andy was born, sarah, his mother was 25 years old. three years ago his mother was six times as old as andy was then. how old is andy now. show method you used to solve the problem. *** let x=Andy's age now x+25=mother's age now (mother will always be 25 yrs older than Andy) 3 years ago: x-3=Andy's age x+25-3=x+22=mother's age At this time, his mother was six times as old as andy x+22=6(x-3) x+22=6x-18 5x=40 x=8 x+25=33 Andy's age now=8 mother's age now=33
 Linear_Algebra/737927: graph of the function -2(x - 1)^2 = y + 5? 1 solutions Answer 450608 by lwsshak3(6513)   on 2013-04-15 16:25:49 (Show Source): You can put this solution on YOUR website!graph of the function -2(x - 1)^2 = y + 5 This is an equation of a parabola that opens downward: Its standard (vertex) form: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex. A is a coefficient that affects the slope or steepness of the curve. .. For given equation: -2(x - 1)^2 = y + 5 rearrange terms to standard form: A=-2 vertex: (1,5) axis of symmetry: x=1 y-intercept set x=0 y=-2+5=3 see graph below:
 Trigonometry-basics/737549: Use the given information to find cos 2x, sin 2x, and tan 2x. (Enter your answers in exact form.) cos x = sqrt(2)/7 ,3π/2 < x < 2π a)cos 2x b)sin 2x c)tan 2x I know that for cos 2x, the answer will be #/49 but that is really as far as I got1 solutions Answer 450521 by lwsshak3(6513)   on 2013-04-15 04:09:48 (Show Source): You can put this solution on YOUR website!Use the given information to find cos 2x, sin 2x, and tan 2x. (Enter your answers in exact form.) cos x = sqrt(2)/7 ,3π/2 < x < 2π a)cos 2x b)sin 2x c)tan 2x *** let O=opposite side let A=adjacent side let H=hypotenuse .. ...
 Trigonometry-basics/737658: solution of sec2x=1 in the interval of (0,360)1 solutions Answer 450520 by lwsshak3(6513)   on 2013-04-15 03:21:11 (Show Source): You can put this solution on YOUR website!solution of sec2x=1 in the interval of (0,360) sec(2x)=1 2x=0 x=0 note:cos(0º)=1 sec=1/cos=1
 Trigonometry-basics/737716: Rewrite the expression as an algebraic expression in x. Assume x>0 cos(2tan^-1(1/x))1 solutions Answer 450517 by lwsshak3(6513)   on 2013-04-15 02:51:29 (Show Source): You can put this solution on YOUR website!Rewrite the expression as an algebraic expression in x. Assume x>0 let O=opposite side let A=adjacent side H=hypotenuse ... let y=tan^-1(1/x) tan(y)=(1/x)=O/A O=1, A=x