Decide whether the problem can be solved using precalculus or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, explain your reasoning and use a graphical or numerical approach to estimate the solution. Find the distance between the points (1, 1) and (3, 9) along the curve y = x2

Q: Find equations of both lines through the point (2, –3) that are tangent to the parabola y = x2 + x.…

A: We have to find equations of both lines through the point (2 , -3) that are tangent to the parabola…

Q: Find the length of the curve defined by Y = 3x³/2 + 3 from x :3 to x = 9.

A: Question: Find the length of the curve defined by y= 3x^3/2 + 3 From x=3 to x= 9

Q: Find the equations of all lines through the origin that are tangent to the curve y = x - 10x2 – 4x.…

A: Given curve is y=x3-10x2-4x

Q: The slope of the tangent line at any point (x, y) on a curve is 2,. If the point (9, 3) is on the…

A:

Q: ) Find the slope m of the tangent to the curve y = 9 + 5x² – 2x3 at the point where x = a. 10а + 6а?…

A:

Q: The slope of the tangent line to a curve at any point (?,?) on the curve is equal to 3x2y2. Find an…

A:

Q: The curve's equation is given by x* + y4 = x² + y?

A: Here is the solution of the given problem.

Q: The curve has an equation of x = y^3, find the radius of gyration with respect to the x-axis. * 0.89…

A: Given curve is x=y3. We have to find the radius of gyration with respect to the x-axis. Since, no…

Q: Find the exact length of the curve = √(y - 3), 1 ≤ y ≤

A:

Q: given curve about the x-axis. 1. y = 7x, 0 < x <1

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the length of the following curve. y = 2x + 4 on 3-2, 24 (Use calculus.)

A:

Q: The slope of the tangent line at any point (x, y) on a curve is If the point (9, 3) is on the curve,…

A: Given,            The slope of the tangent line at any point x,y on a curve is 2x.            The…

Q: Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the…

A: Given

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: 2) Kaybiang Tunnel located in the Ternate- Nasugbu area is said to be the longest underground tunnel…

A: Given : Length of tunnel is 300 metres and vertical distance is 4.85 metres

Q: Decide whether the problem can be solved using precalculus or whether calculus is required. If the…

A: Suppose f(x) is a continuous function on the closed interval [a,b]. Then the arc length from a to b…

Q: Find the length of the curve with equation x2 (y + 1)3 from the point where æ = 0 to the point where…

A: Since the given curve is  x2=y+13      from point x=0 to x=33. Given curve can be written as x=y+132…

Q: Find the point on the graph of y = x3 such that the tangent at the point is parallel to the line y –…

A: Consider a graph: y=x3……1   Equation of line parallel to the tangent of above equation is:…

Q: Find the shortest distance from x²+3y²=12 to the point (4,2).

A: We have to find the shortest distance from x²+3y²=12 to the point (4,2).…

Q: Find the distance from the point Q to the line ℓ.

A: Given: Q=0, 1, 0, l with equation xyz=111+t-203.

Q: Find the value of x and the length of ST. ST and SR are tangents. 9х- 39 6x

A:

Q: Find the length of the curve defined by y = 3z3/2 - 3 from x = 3 to a = 9. The length is

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Q: Find the point on the curve 4x

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Q: Find the exact length of the curve y3 = 22 from (-1,1) to (8, 4).

A: Use formula of length of curve

Q: 3. Solve for x. 20 7x+2 18 ár+3

A:

Q: Find an equation of the line tangent to the graph of y = at the point (4, 6/2). Answer: y = 이별

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Q: Estimate solutions of the following equation using a Graphical Estimation method. (You need to show…

A:

Q: Find the two values of a for which the line connecting the point,(1,-1) to a point (a,a2) on the…

A:

Q: Find all values of x such that the tangent line to the graph of y = 5x² – 16x + 5 is steeper than…

A:

Q: Use calculus to find the point on the curve y = 3x−1 that is closest to the point (2, 0).

A:

Q: 14. Solve for x. 3x r+4 19 8.

A:

Q: 1) 5x + 1 6x - 5

A: We have to find the value of x

Q: Find the exact length of the curve. + 4х 1 < x < 3 y

A:

Q: Find the length of the curve defined by y = 4x3/2 + 11 from x = 2 to x = 8.

A: We will differentiate the function and use the arc length formula.

Q: Find a value for x so that distance from (x,3,6) to the origin is 9

A:

Q: The slope of the tangent line at any point (x, y) on a curve is 25 If the point (9, 3) is on the…

A: Explained below

Q: For the cruciform in the figure below, the equation is x²y2 - 9x2 – 4y2 = 0, find the equation of…

A: To find the equation of the tangent line for the given curve.

Q: Q4\ Find an equation for the tangent line drawn to the circle (x- 3)2 + (y+ 3)2 = 50 at the point P…

A: Here, the given equation of the circle is (x-3)2+(y+3)2=50. We need to find the equation of the…

Q: The slope of the tangent line at any point (x, y) on a curve is If the point (9, 3) is on the curve,…

A:

Q: Find the distance between the point (1,1) and (3,9) along the curve y=x2

A: Given:The points (1,1) and (3,9) along the curve y=x2To find the distance we need use calculus as…

Q: find the slope of the curve at the point indicated. 19. у %3D 5x — Зх?, X =

A:

Q: Find the length of the curve : y = + from x = 1 to x = 3 - 3 4x

A:

Q: Solve the standard equation of every circle that passes through the points P(1,-1) and Q(3,1) and is…

A: I am attaching image so that you understand each and every step.

Q: The curve has an equation of x = y^3, find the radius of gyration with respect to the x-axis. * O…

A: The curve has an equation x=y3 K=IxA K= Radius of gyrationIx=Moment of inertia/Secon moment of…

Q: Find the equations of all lines through the origin that are tangent to the curve y = x³ – 4x² – 4. -…

A: Topic:- application of derivatives

Q: Find the equations of all lines through the origin that are tangent to the curve y = x³ – 6x2 – 2x.…

A:

Q: Find the exact length of the curve. X=1/3sqrt(y)(y-3), 9 less than or equal to Y less than or equal…

A:

Q: Find the length of the curve x = (1/3)(sqrt y)(y - 3) where 1 is less than or equal to y which is…

A:

Q: go Find the equations of the tangent lines to the graph of y=x²+6 graph of a to 197 +6 that through…

A: To find out the equation of tangent line and also graph it.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.