Solve: The posistion of a particle moving along a coordinate line is s=sqrt(5+4t), with s in meters and t in seconds. Find the particle's velocity at t=1 sec. A) 2/3 m/sec B) 4/3 m/sec C) -1/3 m/sec D) 1/6 m/sec

55,856 results
  1. AP Calculus

    A particle is moving along a horizontal straight line. The graph of the position function (the distance to the right of a fixed point as a function of time) is shown below. Answer the following questions only on the interval (0,8). 1. When is the particle

  2. math

    Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x' (t) is its velocity, and x'' (t) is its acceleration. x(t) = t3 − 12t2 + 21t − 9, 0 ≤ t ≤ 10 Find the open t-intervals on which the particle is

  3. uniten

    3. At t = 0 , a particle leaves the origin with a velocity of 9.0 m/s in the positive y direction and moves in the xy plane with constant accelaration of ( 2.0i - 4.0j ) m/s2 . At the instant the x coordinate of the particle is 15 m , what is the speed of

  4. calculus

    A particle is moving along the curve below. y = sqrt(x) As the particle passes through the point (4,2), its x-coordinate increases at a rate of 4 cm/s. How fast is the distance from the particle to the origin changing at this instant?

  5. Calculus

    A particle moves on a vertical line so that its coordinate at time t is 3 y = t − 12t+ 3, t≥ 0 . When is the particle moving upward and when is it moving downward? Find the distance that the particle travels in the first 3 seconds. I got that t=2 and

  6. Calculus

    A particle is moving along the curve whose equation is (xy^3)/(1+y^2)= 8/5. Assume the x-coordinate is increasing at the rate of 6 units/second when the particle is at the point (1,2). At what rate is the y-coordinate of the point changing at that instant?

  7. Calculus

    Solve: The posistion of a particle moving along a coordinate line is s=sqrt(5+4t), with s in meters and t in seconds. Find the particle's velocity at t=1 sec. A) 2/3 m/sec B) 4/3 m/sec C) -1/3 m/sec D) 1/6 m/sec Thank you!

  8. Calculus

    The velocity function is v(t)=t^2-4t+3 for a particle moving along a line. Find the displacement of the particle during the time interval [-1,6]

  9. Math:)

    A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates 5pi/12 radians? a.

  10. AP CALC. AB

    1.The position of a particle moving on the line y = 2 is given by x(t)= 2t^3-13t^2+22t-5 where t is time in seconds. When is the particle at rest? a. t =0.268, 2.500, and 3.732 b. t = 0, 1.153, and 3.180 c. t = 1.153, 2.167 and 3.180 d. t = 2.167 e. t =

  11. physics

    three point particles are fixed in place in an xy plane. Particle A has mass mA = 3 g, particle B has mass 2.00mA, and particle C has mass 3.00mA. A fourth particle D, with mass 4.00mA, is to be placed near the other three particles. What (a) x coordinate

  12. calculus

    A particle is moving along the curve y= 3sqrt3x+1. As the particle passes through the point (5,12), its x-coordinate increases at a rate of 3 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  13. Calculus

    The velocity function is v(t)=t^2-5t+6 for a particle moving along a line. Find the displacement of the particle during the time interval [-3,6].

  14. physics

    The position of a particle moving along an x axis is given by x = 15t2 - 2.0t3, where x is in meters and t is in seconds. (a) Determine the position, velocity, and acceleration of the particle at t = 3.0 s. x = m v = m/s a = m/s2 (b) What is the maximum

  15. Physics

    A particle starts from the origin at t = 0 and moves along the positive x axis. A graph of the velocity of the particle as a function of the time is shown in the figure; the v-axis scale is set by vs = 7.0 m/s. (a) What is the coordinate of the particle at

  16. Calculus HELP

    A particle is moving along the curve y=5 sqrt (2x+6). As the particle passes through the point (5,20 , its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  17. Math/Physics

    The velocity v of a particle moving in the xy plane is given by v = (6.0t - 4.0t2) i + 4.0 j, with v in meters per second and t (> 0) is in seconds. What is the acceleration when t = 3.0 seconds? When is the acceleration zero? When is the velocity zero?

  18. physics

    Two dimensions. In the figure, three point particles are fixed in place in an xy plane. Particle A has mass mA = 4 g, particle B has mass 2.00mA, and particle C has mass 3.00mA. A fourth particle D, with mass 4.00mA, is to be placed near the other three

  19. Calculus

    The position of a particle moving on a horizontal line is given by s(t)=2t^3-15t^2+24t-5, where s is measured in feet and t in seconds. a: What is the initial position of the particle? b: What is the average velocity of the particle on the interval

  20. science

    the velocity of a particle is given by v=[16t^2i+4t^3j +(5t+2)k]m/s, where t is in seconds. If the particle is at the origin when t=0, determine the magnitude of the particle's acceleration when t=2s. What is the x,y,z coordinate position of the particle

  21. calculus

    the position of a particle moving along a coordinate line is s=√(1+4t) , with s in metres and t in seconds. Find the particle's velocity and acceleration at t=6 sec

  22. AP Calculus

    The position of a particle moving on the x-axis at time t>0 seconds is: x(t)= e^t - t^1/2. a) Find the average velocity of the particel over the interval [1,3]. b) In what direction and how fast is the particle moving at t= 1 seconds? c) For what values of

  23. physics

    The position vector r of a particle moving in the xy plane is r=2ti+2sin[(pi/4)t]j , with is in meters and t in seconds. (a) Calculate the x and y components of the particle's position at , and 4.0 s and sketch the particle's path in the plane for the

  24. physics

    A particle rotates counterclockwise in a circle of radius 6.5 m with a constant angular speed of 7.4 rad/s. At t = 0, the particle has an x coordinate of 3.3 m and y > 0 . A) Determine the x coordinate of the particle at t = 0.716 s. Answer in units of m (

  25. Calc

    A particle is moving along the curve y= 4 sqrt{2 x + 2}. As the particle passes through the point (1, 8), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  26. math

    For 4.95 seconds , a particle moves in a straight line according to the position function: s(t) = e^t(5-t)-5 . a. when id the particle at rest ? when is particle moving forward ? b. Find the total distance traveled by the particle in intervals [0,1]

  27. Calculus

    A particle moves on a vertical line. Its position, s, in metres at t seconds is given by s(t) = t^3 - 9t^2 + 24t, t>0/ I found the velocity and acceleration functions. s'(t) = 3t^2 - 18t + 24 s''(t) = 6t-18 b) When is the particle moving up? down? c) Find

  28. Calculus

    In the next questions, a particle is moving along a horizontal line according to the formula: s=2t^4-4t^3+2t^2-1 a) the particle is moving right when A. 0 is less than t is less than 1/2 B. t is greater than 0 C. t is greater than 1 D. 0 is less than t is

  29. physics

    A particle is moving along a straight line and its position is given by the relation x=(t3- 6t2- 15t+40) m FIND a) The time at which velocity is Zero, b) Position and displacement of the particle at that point. c) Acceleration for the particle at that

  30. Physics

    A particle is moving along a straight line and its position is given by the relation x=( t3-6t2-15t+40)mm. Find:- (a). The time at which velocity is zero. (b). Position & displacement of the particle at that point. (c). Acceleration for the particle at

  31. math

    For 4.95 seconds , a particle moves in a straight line according to the position function: s(t) = e^t(5-t)-5 . a. when id the particle at rest ? when is particle moving forward ? b. Find the total distance traveled by the particle in intervals [0,1]

  32. Calculus

    A particle is moving along the curve y = 3sqrt5x+1. As the particle passes through the point (3,12), its x-coordinate increases at a rate of 4 units per second. Find the rate of change of the distance from the particle to the origin at this instant. I've

  33. Calculus

    How would I solve this: -A particle moves along a line so that, at time t, its position is s(t)=8 sin2t. a) For what values of t does the particle change direction? b) What is the particle's maximum velocity?

  34. math

    The acceleration of a particle at a time t moving along the x-axis is give by: a(t) = 4e^(2t). At the instant when t=0, the particle is at the point x=2, moving with velocity v(t)=-2. Find the position of the particle at t=1/2 if you could show me how to

  35. DIFF. CALCULUS

    A particle is moving along the parabola 4y = (x + 2)^2 in such a way that its x-coordinate is increasing at a constant rate of 2 units per second. How fast is the particle's distance to the point (-2, 0) changing at the moment that the particle is at the

  36. calculus

    A particle is moving along the curve y=5sqrt(3x+1). As the particle passes through the point (5,20) its x-coordinate increases at a rate of 3 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  37. calc

    A particle moves along the curve below. y = sqrt(8 + x^3) As it reaches the point (2, 4), the y-coordinate is increasing at a rate of 5 cm/s. How fast is the x-coordinate of the point changing at that instant?

  38. Inequality

    When I solve the inquality 2x^2 - 6 < 0, I get x < + or - sqrt(3) So how do I write the solution? Is it (+sqrt(3),-sqrt(3)) or (-infinity, sqrt(3))? Why? Thanks. So would this work? abs x < ( sqrt 3 ) or - sqrt 3

  39. Calculus

    Please look at my work below: Solve the initial-value problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/- Sqrt(4^2-4(1)(6)))/2(1) r=(16 +/- Sqrt(-8)) r=8 +/- Sqrt(2)*i, alpha=8, Beta=Sqrt(2) y(0)=2, e^(8*0)*(c1*cos(0)+c2*sin(0))=c2=2

  40. physics

    An alpha particle, the nucleus of a helium atom, is at rest at the origin of a Cartesian coordinate system. A proton is moving with a velocity of v towards the alpha particle from the positive x axis direction. If the proton is initially far enough away to

  41. secant line, tangent line

    f(x) = sqrt(x-1), 1

  42. Calculus

    A particle travels along the x-axis so that its velocity is given by v(t)=cos3x for 0

  43. Maths

    A particle is moving along the curve y=4sqrt(4x+1) . As the particle passes through the point (2,12), its x-coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  44. MATH

    For each set of numbers, draw your own number line on a piece of paper, taking care to plot each pair of irrational numbers. Then write a statement comparing the position of the two given numbers on a number line. Also write an inequality comparing the two

  45. Math Help please!!

    Could someone show me how to solve these problems step by step.... I am confused on how to fully break this down to simpliest terms sqrt 3 * sqrt 15= sqrt 6 * sqrt 8 = sqrt 20 * sqrt 5 = since both terms are sqrt , you can combine them. sqrt 3* sqrt 15=

  46. physics

    If velocity v of particle moving in straight line is related with distance travelled S as v=2(1+S)^1/2. What will the acceleration of the particle?

  47. Calc

    A particle moves along the x-axis in such a way that it's position in time t for t is greator or equal to 0 is given by x= 1/3t^3 - 3t^2 +8 A) show that at time t= 0 the particle is moving to the right. B) find all values of t for which the particle is

  48. physics # 1

    1. If a particle moves in a plane so that its position is described by the function x = Acosùt, and y = Asinùt, it is a.) moving with varying speed along a circle b.) moving with constant speed along a circle c.) moving with constant acceleration along a

  49. Calculus: need clarification to where the #'s go

    A particle is moving along the curve y= 2 \sqrt{4 x + 4}. As the particle passes through the point (3, 8), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  50. Calc

    A particle is moving along the curve y= 3 \sqrt{3 x + 4}. As the particle passes through the point (4, 12), its x-coordinate increases at a rate of 4 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  51. Physics

    A particle is moving along the x-axis subject to the potential energy function U(x) = a(1/x) + bx2 + cx – d, where a = 6.00 J m, b = 26.0 J/m2, c = 3.00 J/m, and d = 26.0 J. Determine the x-component of the net force on the particle at the coordinate x =

  52. Math

    A particle is moving along the curve y = 4x^2 + 1 in such a way that the y coordinate is increasing at a rate of ½ units per second. At what rate is the x coordinate changing at the instant x = 2?

  53. math

    The velocity function is v(t) = t^2 - 6 t + 8 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-1,6].

  54. Calculus

    The displacement (in meters) of a particle moving in a straight line is given by s=2t^3 where is measured in seconds. Find the average velocity of the particle over the time interval [10,13]. the average velocity is 798 What is the instantaneous velocity

  55. calulus

    a particle is moving along the cure y=sqrt x. as the particle passes through the point (4,2), its x-coordinate increase at a rate of 3 cm/s. how fast is the distancefrom the particle to the origin changing at this instant?

  56. Math

    A particle is moving along the curve y= 2 \sqrt{4 x + 4}. As the particle passes through the point (3, 8), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  57. Calculus 1

    A particle is moving along the curve y= 4 \sqrt{3 x + 1}. As the particle passes through the point (1, 8), its x-coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  58. physics

    A particle of charge Q is fixed at the origin of an xy coordinate system. At t = 0 a particle (m = 0.690 g, q = 4.75 µC) is located on the x axis at x = 20.0 cm, moving with a speed of 50.0 m/s in the positive y direction. For what value of Q will the

  59. math

    A particle is traveling along a one-dimensional path (such as a number line). The position of the particle is governed by the time function x(t) ƒ­ 3t 4 ƒ{16t3 ƒy18t 2 ƒy 2 , where t is in minutes and 0 „T t „T 5 . Answer the following questions.

  60. Calculus, Related Rates

    A particle at point A is 50 mm away from a second particle at point B. The first particle is moving toward point B at a constant rate and the second particle is moving at a right angle to the line AB at a rate that is 1/3 of the rate of the first particle.

  61. Calculus-particle motion

    1. A particle is moving on the x-axis (or any number line) Its position x(t), or distance from the origin, at the time t is given by x(t)=4t^3-16t^2+15t. t is greater than or equal to 0 a.) Where is the particle when it is at rest? b.) During what time

  62. calculus

    Me again. One last question! Again, just needed my answer verified with any explanation or walk-through. The position of a particle moving along a coordinate line is s=√(3+6t) with s in meters and t in seconds. find the particle's acceleration at t=1

  63. Calculus

    A particle is moving along the curve . As the particle passes through the point , its -coordinate increases at a rate of units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  64. Calculus

    A particle is moving along the curve y = 2 √{3 x + 7}. As the particle passes through the point (3, 8), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  65. Calculus

    A particle is moving along the curve . As the particle passes through the point , its -coordinate increases at a rate of units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  66. Calculus

    A particle is moving along the curve y = 2 √{3 x + 7}. As the particle passes through the point (3, 8), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  67. calculus

    A particle is moving along the curve y=4((3x+1)^.5). As the particle passes through the point (5,16) its -coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  68. Calculus

    A particle is moving along the curve y = 2 √{3 x + 7}. As the particle passes through the point (3, 8), its x-coordinate increases at a rate of 4 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  69. Calculus

    A particle is moving along the curve . As the particle passes through the point , its -coordinate increases at a rate of units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  70. Calculus (Need Help) - Rectilinear Motion

    Rectilinear Motion: *Need help with these three!* Directions: The position function of a particle moving on a coordinate line is given by the following eq'ns, where s is in feet and t is in sec. Describe the motion of the particle for any time. Make a

  71. calculus

    A particle moves along the curve y=square sqrt 1+x^3. As it reaches the point (2,3), the y-coordinate is increasing ata a rate of 4cm/s. How fast is the x-coordinate of the point changing at that instant?

  72. physics

    A particle is moving along a straight line and its position is given by the relation x=( t3-6t2-15t+40)mm. Find:- (a). The time at which velocity is zero. (b). Position & displacement of the particle at that point. (c). Acceleration for the particle at

  73. Calculus

    A particle moves along a line so that its posistion at any t is greater than or equal to 0 is given by the function s(t)= t^3-8t+1, where s is measured in feet and t is measured in seconds. a) find the displacement during the first three seconds b) Find

  74. Algebra

    Solve for s: h=(square root of 3)times s/2 and solve for h V= (pi)r squared h / 3 Solve for s: h=(square root of 3)times s/2 Multiply both sides by 2. 2h = (sqrt 3)*s*2/2 which cancels the 2 on the right. 2h = (sqrt 3)*s Now divide the right side by

  75. calculus

    Find the equation of the line tangent to the graph of the given function at the point with the indicated x-coordinate. f(x)=(4 sqrt(x)+7)/(sqrt(x)+2); text( ) x=4

  76. some algebra help (radicals)

    I hope I am writing this down right.. I am trying to do some practice questions to learn 10^5 (sqrt)2y - 4^5 (sqrt)2y I am trying to figure out how to solve this They gave us some answers to choose from, but I am clueless on how to solve this 6y ^5 (sqrt)2

  77. Math

    Context: The function v(t) represents the velocity of a particle moving along a horizontal line at any time, t, greater than or equal to zero. If the velocity is positive, the particle moves to the right. If the velocity is negative, the particle is moving

  78. calculus

    velocity of a particle- the displacement s (in meters) of a particle moving in a straight line is given by the equation of motion s=4t^3+6t+2, where t is measured in seconds. Find the velocity of the particle s at times t=a t=1 t=2 t=3

  79. Algebra 2: Radicals URGENT!!

    Could some kind, saintly soul help me solve this problem? Simplify: 8w sqrt(48w^5) - x^2 sqrt(3xw^2) . . =8w(√16)(√3)(√w^4)(√w) - x^2(√3)(√x)(√w^2) =32w^3(√3w) - wx^2(√3x) not much of a "simplification" really 8w sqrt(16*3w^5) - x^2 w

  80. Math/Calculus

    Solve the initial-value problem. Am I using the wrong value for beta here, 2sqrt(2) or am I making a mistake somewhere else? Thanks. y''+4y'+6y=0, y(0)=2, y'(0)=4 r^2+4r+6=0, r=(-4 +/- sqrt(16-4(1)(6))/2 r=-2 +/- sqrt(2)*i , alpha = -2, beta = 2(sqrt(2))

  81. ALGEBRA 1

    Solve the following I am not sure if I did this correct (n-5)^2= 20 n-5=+/- 20 n=5+/- sqrt 20 Thanks yes on the final answer. On the second line, you forgot to type sqrt before 20. You can reduce it some....sqrt20= sqrt(4*5)= 2 sqrt5 Thanks Bobpursley

  82. physics

    A force acting on a particle moving in the xy plane is given by Fx = (2yi +x^2j)N, where x and y are in meters. The particle moves from the origin to a final position having coordinates x=5.00m and y=5.00m, as in Fig. Calculate the work done by F along (a)

  83. Calc

    A particle moves along the x-axis in such a way that it's position in time t for t is greator or equal to 0 is given by x= 1/3t^3 - 3t^2 +8 A) show that at time t= 0 the particle is moving to the right. B) find all values of t for which the particle is

  84. physics! please help!!

    A particle rotates counterclockwise in a circle of radius 6.5 m with a constant angular speed of 7.4 rad/s. At t = 0, the particle has an x coordinate of 3.3 m and y > 0 . A) Determine the x coordinate of the particle at t = 0.716 s. Answer in units of m (

  85. Physics

    At t=0 a particle leaves the origin with a velocity of 5.0 m/s in the positive y direction, its acceleration is given by a=3i-2j m/s^2 At the instant the particle reaches its maximum y coordinate, how far is it from the origin? I'm not sure how to do a

  86. ALGEBRA 1

    Solve by whatever Method 1. X^2 +8X = -16 X^2 +8X +16 = -16 +16 (X +4)^2 =0 X+4 =+/- SQRT 0 X=-4+/- 0 X=-4, X=4 2. 3x^2-2x-5=0 X=-b+/- sqrt (b)^2-4ac 2a a=3 ,b=-4,c=-5 X=-(-2)+/- Sqrt (-2)^2-4(3)(-5) 2(3) X=2+/sqrt64 = 2+/-8 6 X= 2+8=10/6=1 2/3,

  87. calculus

    The velocity function is v(t) = - t^2 + 4 t - 3 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-2,6].

  88. physics

    Somebody please shows me how to solve for b) and c)step by step. I found a)=2.27s but stuck there. A 1.49-kg particle initially at rest and at the origin of an x-y coordinate system is subjected to a time-dependent force of F(t) = (4.00ti − 8.00j) Nwith

  89. calculus

    the displacement (in meter) of a particle moving in a straight line is given by the equation of motion s=5t^3+4t+2, where t is measured in seconds. Find the velocity of the particle at t=3.

  90. Math

    The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s = 4/t^2, where t is measured in seconds. Find the velocity of the particle at times t = a, t = 1, t = 2, and t = 3.

  91. math

    The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s = 6/t2, where t is measured in seconds. Find the velocity of the particle at times t = a, t = 1, t = 2, and t = 3.

  92. math

    The displacement (in meters) of a particle moving in a straight line is given by s = 4 t^3 where t is measured in seconds. Find the average velocity of the particle over the time interval [ 7 , 9]. Find the (instantaneous) velocity of the particle when t =

  93. physics

    Particle moving under influence of a constant force is given by V =√|4-2X| where X is magnitude of displacement of the particle At t=0 initially the particle is noticed to be moving towards east.The distance travelled by the particle in first 5seconds

  94. science

    a particle 100g attach with a horizontal spring moving s.h.m.with amplitude 5cm .when this particle is passes through mid point a small particle placed on it then both moving s.h.m.with amplitude 4cm.find the mass of small particle .

  95. Physics

    A particle leaves its orgin with a velocity of 4 i m/s and a constant acceleration of (-2i + .5j) m/s^2. At the time the particle reaches its maximum X corrdinate a) what is its velocity? b) what is its position vector? I'm not sure which equations i

  96. Geometry

    Points X and Z are on a number line, and point Y partitions line XZ into two parts so that the ratio of the length of line segment XY to the length of line segment YZ is 3:5. The coordinate of X is 0.4, and the coordinate of Y is 2.7. What is the

  97. Calculus - Second Order Differential Equations

    Posted by COFFEE on Monday, July 9, 2007 at 9:10pm. download mp3 free instrumental remix Solve the initial-value problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/- Sqrt(4^2-4(1)(6)))/2(1) r=(16 +/- Sqrt(-8)) r=8 +/- Sqrt(2)*i,

  98. math

    solve 2x^2+3x+8=0 and express the solutions in a+bi form. Let's use the quadratic formula to solve for x and express those solutions in a+bi form. x = [-b + or - sqrt(b^2 - 4ac)]/2a Note: sqrt = square root. a = 2, b = 3, and c = 8 from your problem.

  99. physics

    A 4.0 kg particle is moving along the x axis to the left with a velocity of v= -12.0 m/s. Suddenly, between times t =0 and t = 4.0 x a net force = 3t^2 – 12t is applied to the particle, where F is in N and t is in s. Calculate the velocity of the

  100. Surds

    Solve in the exact form. (sqrt of 4x+1)+(sqrt of x+1)=2 Someone showed me to do this next: Square both sides..so.. 4x+1+2((sqrt of 4x+1)•(sqrt of x+1))=4 I do not understand where the 2 come from ..and why do we need to multiply the sqrt of 4x+1 and sqrt

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