(a) A particle is moving in the vertical plane and the height of the particle is given by y(t)=t^3-15t^2+72t+20 m. Find the values of the position and acceleration when the velocity is zero.

Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: We have  y=ax2+bx+c        at (2,28)           and               y=4x

Q: A miniature quadcopter flies in a curve line from one point to another. Suppose that the path of the…

A: We have to find arc length L= ∫ab1+dydx2dx

Q: 5. Find an equation of the line tangent to the curve y = 3x² 1 and parallel to the line 2x – y + 3 =…

A: Explained below

Q: Find the line tangent to the curve x + y3 = 4 at the point (3/3, –1).

A:

Q: The slope of the tangent line to the parabola y = 2a2 + 2a + 6 at the point ( – 2, 10) is: The…

A:

Q: Find the orthogonal trajectories for the family of curves 6x² + y² -9ax=0.

A:

Q: Find the parabola y= ax2+bx+c that passes through (2,1) and be tangent to the line y=2x + 4 at (1,6)

A:

Q: A heat-seeking particle is located at the point (2, 3) on a flat metal plate whose temperature at a…

A:

Q: How do you find the equation of the tangent line to the parabola for y = x2 − 3x − 1 at x = 4.

A: The equation of the given parabola is y=x2-3x-1. We have to find the equation of the tangent line to…

Q: i) Find the orthogonal trajectories of the family of curves: y : 1+ x?

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems

Q: A miniature quadcopter flies in a curve line from one point to another. Suppose that the path of the…

A:

Q: Find the equations of all tangent lines to the curve x² + 4y2 = 8 that pass through the %3D point…

A: The curve x2+4y2=8 that pass through the point (-4, 0). We have to find the equation of all tangent…

Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 6x – 3, at which the slope of the tangent…

A:

Q: y = x – 2 + Ce* X-

A:

Q: Find the error propagated from the function y = 3x* if an error of 0.06 occurs in the independent…

A:

Q: Find the error propagated from the function y = x³ if an error of 0.05 occurs in the independent…

A: For a function y=f(x) If  error in y is ∆y when error in calculating x is ∆x dydx=∆y∆x

Q: 12. The line y = 8x + b is tangent to the curve y = 2x². Determine the point of tangency and the…

A:

Q: Find the orthogonal trajectories of the curve x^(2) + y^(2) = c^(2)

A:

Q: When we are standing at the point (1,-3), the function f(x, y) = 3x²y+xy is increasing most rapidly…

A: We have to find the direction of  rapid increase of the function using gradient of the function.

Q: Find equations of the tangent lines to the curve 2y² + xy – 3x² 8 at the point or points where x =…

A: The curve 2y2+xy-3x2=8 at the point where x=0

Q: The point on the curve y=vx+2 which is closest to the point (5,2) is

A:

Q: Find the tangent lines. To the cubic y=x³-2x+3 parallel to the line 10x-y=3

A:

Q: 1 A point is moving along the graph of the functiony = dy 9x2 + 6 such that dt = 3 centimeters per…

A:

Q: Find the equation of line tangent of y=x4-2x2+1 at (2,9)

A:

Q: the equation of the tange

A: Given that: The equation of the curve x2 + 4y2 = 8. The equation of the line x + 2y = 8.

Q: 8. Find the slope of the tangent of the curve x² + y² = 10 at the point (1, -3).

A:

Q: 4. Find the orthogonal trajectories of the family of parabola described by the equation (y– 3) = Cx.…

A: The solution of the problem is given in the next step.

Q: At what point on the parabola y =  3 x2+ 2x is the tangent line parallel to the line y = 10x −2? Use…

A: First prinicipal : dydx=limh→0f(x+h)-f(x)h

Q: 8. Find the point on the curve y = √2x 3 from the point (1, 4)-

A:

Q: The cubic y = ax3 + bx2 + cx + d that passes through the points (-1, -10) and (1, -4) and tangent to…

A:

Q: Find the error propagated from the function y = x³ if an error of 0.06 occurs in the independent…

A:

Q: 2. y = V4-x , x=0 and y=0 about the y- axis

A: Given that y=4-x2, x=0 and y=0 about the y-axis

Q: The slope of the tangent line to the parabola y = 3r2 + 6x + 2 at the point ( – 2, 2) is: The…

A:

Q: B. Find the length of the curve y = x² from x 0 tox = 4.

A:

Q: 2. Find the length of the curve y=- 1 from 1<x<2. 8 4x?

A:

Q: (3) Find an equation of the tangent line to the curve y = 2x² + 3 that is parallel to the line %3D…

A:

Q: The line that is normal to the curve x + 3xy - 4y² = 0 at (3,3) intersects the curve at what other…

A: Given: x2+3xy-4y2=0 at (3,3)

Q: Find the equation of the line tangent to the curve y =8/x2+4 at the point (2, 1).

A:

Q: 2. Find the equation of the tangent line to the curve y = x³+ 2x² – x at the point (-2, 7).

A:

Q: Obtain the particular solution for: 2y" +2y=2sinx y(0)=0, y'(0) =1 By using method of variation…

A:

Q: 9. Find an equation of the line tangent to the curve y = 2x - 7x2 + 10 at the point (3, 1). y = 12

A: Given that, the curve is y = 2x2 - 7x2 + 10  To find the tangent line to curve at point (3,1)   To…

Q: A miniature quadcopter flies in a curve line from one point to another. Suppose that the path of the…

A: The given path as y=fx is y=2.15+2.09x−0.41x2 for 0≤x≤3.6. The arc length is calculated by…

Q: Find the length of the curve for 12x = 4y³ + 3y-¹ where 1 ≤ y ≤ 3 Enter your answer in exact form.…

A:

Q: A heat-seeking particle is located at the point (2,3) on a flat metal plate whose temperature at a…

A:

Q: Find equations of both tangent lines to the graph of the ellipse x2/4 + y2/9 = 1 that pass through…

A: We have given equation of curve x24+y29=1 and point 4,0 We will find slope of tangent at any point…

Q: Find a cubic function y = ax3 + bx2 + Cx + d whose graph has horizontal tangents at the points (-2,…

A:

Q: Find the cubic function y = ax³ + bx² + cx + d where its graph has horizontal tangent line at (-2,6)…

A: solve the given problem.

Q: At what point on the parabola y=3x^2+2x is the tangent line parallel to the line y=10x-2? Use first…

A: We have to find the point.

Q: 2. Find the equation of the line that is tangent to the curve y 3 + 3y = x 2 at the point (2, 1).

A: Find the equation of the line that is tangent to the curve y3 + 3y = x2 at the point (2,1).

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.