If the distance from P(1, 0) to the point T(12) is x, determine the coordinates P(1,0) of the point at the indicated distance: A - x O (-4/5, 3/5) O (4/5, 3/5) O (-4/5, -3/5) O (4/5, -3/5)

Q: 7. Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Given a function of the curve, y=ax4+bx3+cx2+dx+e To find the coefficient a,b,c, and d such that the…

Q: A curve on the xy-plane passes through the point (0, a) for some number a, and has the property that…

A: This problem is based on a variable separable first order ordinary differential equation. We have to…

Q: Find the length of the curve on y=2x^(3/2) from x=0 to x=1

A: Explanation of the solution is given below...

Q: Find the distance between the point (0, 4, -1) and the line defined by r(t) = +t

A:

Q: Find the length of arc of the curve 9y^2=4x^3 from the origin to the point (3,2 squareroot of 3)

A: The arc length of a curve y=f(x) from x=a to x=b is defined by the integral L=∫ab1+dydx2dx.

Q: If the length of the curve y = 3 x7 from the point (0, 0) to the point (xo, f(xo)) is L = 8 , then…

A: Length of curve

Q: 2 Find the distance from the point B = [0 5 0 to the line 1 +t| 0 -3

A: Here we will find the distance between the given point and line,

Q: 20. Find the point on the curve y= /x that is closest to the point (3, 0).

A:

Q: Find the exact length of the curve. x =Vy ( - 3), 1sys 25

A: given: x=13yy-3

Q: Find the distance from the point Q to the line ℓ. Q = (2, 2), ℓ with equation [x y] = [-1 3] + t [1…

A: GIVEN: Q = (2,2)               xy = -13 + t 1-1

Q: Find the exact length of the curve. y= In{1 – x²), o s 1. 0 sxs! 7. I Ju =

A: We will find the exact length of the curve as shown below

Q: If the distance from P(1, 0) to the point T(1 ) is x, determine the coordinates P(1,0) of the point…

A:

Q: Q1. Find the length of the of the curve y -x2 X2 from x = 0 to x = 3.

A: Given curve is, y=13x32-x12 To find the length of the curve from x = 0 to x = 3

Q: Find the exact length of the curve. y = In(1-x), 0sxs 8.

A: Given that: y=ln 1-x2, 0≤x≤18

Q: 1. Find the length of the curve: y = x/2 , x = 0 to x = 4

A:

Q: 9. Find the point (x, y) on the line y = 2x + 3 such that the distance from (x, y) to (1, 1) is as…

A:

Q: Find the length of the curve 3y = 2(x² + 1)2 from x = 0 to x = 3.

A:

Q: Find f (x-y3)d a + xy dy if the contour C looks as follows: It consists of two arcs of radius 1 and…

A:

Q: Find the length of the segment of the curve y = f (x) = e ^ x between the abscissa points x = 0 and…

A:

Q: The length of the curve y = from x = 0 to x 6 is

A:

Q: Find the length of the following curve. 3 y = 2x from x = 0 to x= 1 The length of the curve is

A: Given curve y=2x32 The length of the curve have to be found from x=0 to x=1 The length of curve…

Q: 15. When a line L is tangent to the circle 2 + v = 100 at the point (a, 6), find the equation of…

A:

Q: Find the length of the curve y = In(1 – x), 0sxs.

A: Given: y=ln(1−x2)0≤x≤12

Q: The perpendicular from the origin to the line y = mx + c meets it at the point (-1, 2). Find th…

A:

Q: 2. Find the point on the curve y = VI thats is closest to the point (3,0)

A:

Q: Find the length of the curve y=x^3/2 from (1,1) to (2,2squareroot2)

A:

Q: Find the length of the curve given by S(x) = (a -) defined on the interval (1, 2].

A: Consider the given curve:

Q: Find the length of the following curve. y=4x^3/2 from x=0 to x=5

A: The given curve is y=4x32 from x=0 to x=5. Compute the arc length as follows.

Q: Find the exact length of the curve. y = In(1 - x²), o s x s

A: Solve the problem using definite integral

Q: If the length of the curve y = 4 x7 from the point (0, 0) to the point (Xo, f(xo)) is L= 1 (145)*…

A:

Q: Find the length of the curve. y = (4 - x2/3) 3/2 from x = 1 to x = 8 O 9 O 12 O 18 O 6

A:

Q: find the length of the curve on the given interval: y=1/3(x^2+2)^(3/2), [0, 1]

A:

Q: The tangent line to the graph of y = In(x² – 1) is perpendicular to the line a + y = -1 at the point…

A:

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Equidistant points mean that the distance of two points represented by P1 and P2 is equal to the…

Q: Find the points on the curve y-9x closest to the point (0, 4). ) and (O

A:

Q: The equation of the tangent to the curve y = x – 3x² – 2x + 2 at the point where the curve cuts the…

A: We have to find  the equation of tangent in the form of y=mx+c.

Q: What is the value of c such that the line y=2x+4 is tangent to the parabola y=cx^2.

A: Given that the line y=2x+4 is tangent to the parabola y=cx2. The derivative of y=cx2 is dydx=2cx.…

Q: For what value of c is the curve y = c/(x + 1)tangent to the line through the points (0, 3) and (5,…

A:

Q: Find the length of the curve defined by y = 3 In 3 from x = 8 to x = 9.

A: Use derivative of function and length of curve formula .

Q: The tangent line to the graph of y = In(2x) is perpendicular to a + 4y = 1 at the point where Select…

A:

Q: 5. Find the distance between the point (4, 3, 1) and the line f(t) = (2x - 1, –3y + 1, 2)

A:

Q: Find a number k such that the line y=6x+4 is tangent to the parabola y= x2 + k.

A:

Q: 3) Find the exact length of the curve y = x² – In x for 1< x < 2. 1„2

A:

Q: Find the exact length of the curve. y = In (1 - x2) ,    0≤   x ≤ 1/2

A: Given, y=ln1-x2,0≤x≤12 We know the ars length formula is, L=1+dydx2dx Now we find the derivative by…

Q: Find the exact length of the curve. y = In(1 - x²), o sxs

A: Find dy/dx, then put it in the arc length formula.

Q: Find the value of 'a' for which the tangent to the curve ƒ(x) = (a + 2) x³ − 3ax² + 9ax − 1 never…

A: