A curve is traced by a point P(x,y) which moves such that its distance from the point A(-1,1) is three times the distance from the point B(2,-1)
Homework Answers
sqrt((x-2)^2+(y+1)^2)=3sqrt((x+1)^2 +(y-1)^2)
square both sides, expand the polynomial, collect terms, and you ahve the equation.
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A curve is traced by a point P(x,y) which moves such that its distance from the point A(-1,1) is three times the distance from the point B(2,-1)
2. A particle moves in the x-y plane. Its coordinates are given as functions of time...
2. A particle moves in the x-y plane. Its coordinates are given as functions of time t(2 0) b x(t)-R(at-sina)t), )Sketch the trajectory of the particle. This is the trajectory of a point on the rim of a wheel y(t)-R(1-cosω t), where R and ω are constants. (a) (3 that is rolling at a constant speed on a horizontal surface. The curve traced out by such a point as it moves through space is called a cycloid. (b) (5 Find...
A particle moves along the curve y = x^3/2 such that its distance from the origin, measured along...
A particle moves along the curve y = x^3/2 such that its distance from the origin, measured along the curve, is given by s = t^3 . Determine the acceleration in vector form when t = 2 seconds. The units are inches and seconds.
1. The point P(4. 8) lies on the curve y-(6-x), Suppose Q is the point (x,1 + (6-x)'). a. Find th...
can
you answer two of the questions in the phot please.
1. The point P(4. 8) lies on the curve y-(6-x), Suppose Q is the point (x,1 + (6-x)'). a. Find the slope of the secant line PO for the following values of x. 3. 3.99 4. 3.999 6. 4.1 7. 4.01 8. 4.001 the curve at P b. Use your results from part a to make a guess of the slope of the line tangent to c. Use your...
y 1/(1-x) 5. The point P(2,-1) lies on the curve C If Q is the point...
y 1/(1-x) 5. The point P(2,-1) lies on the curve C If Q is the point (x,1/(1-x), use your calculator to find the slope of the secant line PQ a. (correct to six decimal places) for the following values of x: 1.5 (ii) 1.9 (i) 1.99 (iv) 1.999 (v) 2.5 (vi) 2.1 (vii) 2.01 (vii) 2.001 Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(2,-1) i. b. Using...
Show that the radius of curvature x^(2/3) + y^(2/3) = a^(2/3) at P(x, y) is three times the distance from the origin to the tangent line T.
Show that the radius of curvature x^(2/3) + y^(2/3) = a^(2/3) at P(x, y) is three times the distance from the origin to the tangent line T.
Find a formula for the distance from the point P{x,y,z) to each of the following planes....
Find a formula for the distance from the point P{x,y,z) to each of the following planes. a. Find the distance from P(x,y,z) to the xy-plane. b. Find the distance from P(x,y,z) to the yz-plane. c. Find the distance from P(x,y,z) to the xz-plane. a. Choose the correct formula for the distance from the point P(x,y,z) to the xy-plane. O A. Iz OB. Mx2 + y2 OC. Vz OD. x² + y² + 2? b. Choose the correct formula for the...
Find the directional derivative of the function f(x,y,z) = z4−x3y2 at P(1,-1,1) in the direction of...
Find the directional derivative of the function f(x,y,z) = z4−x3y2 at P(1,-1,1) in the direction of the vector from P(1,-1,1) to the point Q(2,1,0). What is the maximum rate of change of f at the point P(1,-1,1) and in which direction
6.14(a) Prove that the brachistochrone curve (6.26) is indeed a cycloid, that is, the curve traced...
6.14(a) Prove that the brachistochrone curve (6.26) is indeed a cycloid, that is, the curve traced by a point on the circumference of a wheel of radius a rolling along the underside of the x axis. (b) Although the cycloid repeats itself indefinitely in a succession of loops, only one loop is relevant to the brachistochrone problem. Sketch a single loop for three different values of a (all with the same starting point 1) and convince yourself that for any...
7. (14,5) A particular parametric curve is given by x=1-3, y = 21 +3 for -2...
7. (14,5) A particular parametric curve is given by x=1-3, y = 21 +3 for -2 515 3. Sketch the curve using arrows to indicate the direction in which the curve is traced as increases. Then eliminate the parameter / to find a Cartesian equation of the curve. 8. (10,4) Find the equation of the plane through the point (-5, 4, 2) and with normal vector-31 +4j - k. Give your answer in both the vector equation of a plane...
2.1.13 (a) Find the slope of the curve y=x°-11x at the given point P(1. - 10)...
2.1.13 (a) Find the slope of the curve y=x°-11x at the given point P(1. - 10) by finding the limiting value of the slope of the secants through P. (b) Find an equation of the tangent line to the curve at P(1. - 10). (a) The slope of the curve at P(1. - 10) is
2. A particle moves in the x-y plane. Its coordinates are given as functions of time t(2 0) b x(t)-R(at-sina)t), )Sketch the trajectory of the particle. This is the trajectory of a point on the rim of a wheel y(t)-R(1-cosω t), where R and ω are constants. (a) (3 that is rolling at a constant speed on a horizontal surface. The curve traced out by such a point as it moves through space is called a cycloid. (b) (5 Find...
can
you answer two of the questions in the phot please.
1. The point P(4. 8) lies on the curve y-(6-x), Suppose Q is the point (x,1 + (6-x)'). a. Find the slope of the secant line PO for the following values of x. 3. 3.99 4. 3.999 6. 4.1 7. 4.01 8. 4.001 the curve at P b. Use your results from part a to make a guess of the slope of the line tangent to c. Use your...
y 1/(1-x) 5. The point P(2,-1) lies on the curve C If Q is the point (x,1/(1-x), use your calculator to find the slope of the secant line PQ a. (correct to six decimal places) for the following values of x: 1.5 (ii) 1.9 (i) 1.99 (iv) 1.999 (v) 2.5 (vi) 2.1 (vii) 2.01 (vii) 2.001 Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(2,-1) i. b. Using...
Find a formula for the distance from the point P{x,y,z) to each of the following planes. a. Find the distance from P(x,y,z) to the xy-plane. b. Find the distance from P(x,y,z) to the yz-plane. c. Find the distance from P(x,y,z) to the xz-plane. a. Choose the correct formula for the distance from the point P(x,y,z) to the xy-plane. O A. Iz OB. Mx2 + y2 OC. Vz OD. x² + y² + 2? b. Choose the correct formula for the...
6.14(a) Prove that the brachistochrone curve (6.26) is indeed a cycloid, that is, the curve traced by a point on the circumference of a wheel of radius a rolling along the underside of the x axis. (b) Although the cycloid repeats itself indefinitely in a succession of loops, only one loop is relevant to the brachistochrone problem. Sketch a single loop for three different values of a (all with the same starting point 1) and convince yourself that for any...
7. (14,5) A particular parametric curve is given by x=1-3, y = 21 +3 for -2 515 3. Sketch the curve using arrows to indicate the direction in which the curve is traced as increases. Then eliminate the parameter / to find a Cartesian equation of the curve. 8. (10,4) Find the equation of the plane through the point (-5, 4, 2) and with normal vector-31 +4j - k. Give your answer in both the vector equation of a plane...
2.1.13 (a) Find the slope of the curve y=x°-11x at the given point P(1. - 10) by finding the limiting value of the slope of the secants through P. (b) Find an equation of the tangent line to the curve at P(1. - 10). (a) The slope of the curve at P(1. - 10) is
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