36. Moving along a parabola A particle moves along the parabola y = x² in the first quadrant in such a way that its x-coordinate (measured in meters) increases at a steady 10 m/sec. How fast is the angle of inclination 0 of the line joining the particle to the origin changing when x = 3 m?

Q: 12) A PARTIUE is movING ALONG A ITYBERBOLA xy =8. AS IT REAUHES tHE POINT (4,2), THE Y-COOR DINATE…

A:

Q: Suppose that the Celsius temperature at the point (x, y) in the xy-plane is T(x, y) = x sin 2y and…

A:

Q: (a) Show that the point (2, 4) lies on the curve 2° +y° – 9xy = 0. Then find the tangent and normal…

A: As given cost for radiators is: Cx=x3-6x2+15x And the revenue for radiators can be calculated as:…

Q: 1. The hiking trail starts at the foot of a steep hill that follows a trajectory described by the…

A: Find your answer below

Q: A point moves around a circle x2 + y2 = 10. When the point is at (1, 3), its x coordinate is…

A:

Q: A bug is moving along the right side of the parabola y = x^2 at a rate such that its distance from…

A: Let (x,y) be a point on the parabola y=x^2. Then (x,y)=(x,x^2).Let, distance from origin= p. Given,…

Q: A particle moves along a hyperbola xy = 12. As it reaches the point (6, 2), the y-coordinate is…

A: Application of differentiation

Q: A particle moves along a hyperbola xy = 12. As it reaches the point (6, 2), the y-coordinate is…

A:

Q: 5. A particle is moving along the curve y = x² + x in such a way that the y-coordinate is increasing…

A: Given:- A particle is moving along the curve y = x² + x in such a way that the y-coordinate is…

Q: 5) The flight path of a missle follows the curve y = 2x -1 in such a way that the y value is 3…

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: A 5-kg mass is attached to a spring whose stiffness constant is 80 N/m. The damping is negligible.…

A:

Q: A ball located at point Q, with an initial angle of 0 = 0, on a spinning wheel with a radius of 1…

A:

Q: 24. At what point(s) on the curve (y - 2)² = x is the tangent line vertical? The tangent line is…

A: The given curve,   y-22=x

Q: A bug is moving along the right side of the parabola y=x^2 at a rate such that its distance from the…

A: Differentiate the above expression with respect to t as follows.

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

A: I have written the important facts in the solution part

Q: What is the value of the slope of the tangent line to the curve 2+4.xy + y² = 13 passing through the…

A:

Q: ind the slope and the equation of the tangent line to the curve. Use the delta method. Explain…

A: To find slope and equation of the tangent line to the curvey=2x2-2x+4 at (1,4)

Q: In 1911, Ernest Rutherford discovered the nucleus of the atom. Experiments leading to this discovery…

A:

Q: 2. A horizontal curve on a two-lane highway (10ft lanes) is designed for 50mi/h with a 6%…

A: Rv=835 R=835+102=840 T=R tan ∆2=840 tan 17.5=264.85 STA PC=482+72-2+64.85=480+07.15…

Q: 2) A particle is moving along the curve whose equation is 1+ Assume that the x-coordinate is…

A:

Q: (The clepsydra, or water clock) A 12 h water clock is to be designed with the dimensions shown in…

A:

Q: 2. A particle moves in a circular orbit x? + y = 16. As it passes through the point (2, 2/3 ), its…

A:

Q: Suppose a particle begins to move from the origin (t = 0) following the curve in space r(t) =…

A: Given position of Particle r(t)={5sint,5cost,12t}

Q: 26. a. Find a curve with a positive derivative through the point (0, 1) whose length integral…

A:

Q: 78. A particle starts at the origin and moves along the curve y = 2x32/3 in the positive x-direction…

A: According to question,Given curve,y = 2 x323,speed dxdt= 3 cmsec,t = 6

Q: 3. (15 points) Find a tangent line to a curve eY In y – y² + e³«-1 = e² – 1 at (1, 1).

A:

Q: A particle moves along a hyperbola xy = 12. As it reaches the point (3, 4), the y-coordinate is…

A:

Q: 44. Find a parametrization of the right branch (x > 0) of the hyperbola 1 - using cosh t and sinh t.…

A: The equation of hyperbola is xa2-yb2=1   The right branch (x>0) of the hyperbola can be…

Q: The temperature at location (x, y)is T (x, y) = 20 + 0.1(x^2 − xy) (degrees Celsius). Beginning at…

A: Consider the provided information, The temperature at location is, Tx,y=20+0.1x2-xy The bug is at a…

Q: 29. Find equations for the lines that are tangent and normal to the curve y = V2 cos x at the point…

A: y=2cosx ,   π4, 1 Differentiating with respect to x, we get dydx=2-sinx=-2sinx Now slope of the…

Q: 2. The temperature at any point (x, y) of a rectangular plate lying in the xy plane is determined by…

A: Given problem:- The temperature at any point (x, y) of a rectangular plate lying in the xy plane is…

Q: 1: A fly walks with a speed of 1 cm/sec in every direction of a piece of paper which is considered…

A:

Q: 1. I A particle moving along a curve in the xy-plane has position (x(1), (1), at time 1> 0, where At…

A: Given: For, t > 0vx = dxdt= 6t-313                      (1)vy =   dydt = te-t…

Q: Find the equation of the tangent line to the parabola y = x^2 - 3 at point p(2,12)

A:

Q: A weight stretches a spring 6 inches in equilibrium. The weight is initially displaced 6 inches…

A: In this question, concept of Differential Equation is used. Differential Equation A differential…

Q: Suppose a projectile is fired at an angle of elevation θ with an initial velocity of v0 ft/sec. In…

A:

Q: Can you help me step by step?

A: Given equation of curve is y=ax2+bx+c which passes through (1, 3) so point (1, 3) will satisfy the…

Q: 13. A point moves along the curve y = x² +2 so that the x-coordinate is increasing at the rate of 3…

A: y=x2+2 since x coordinate is increasing at the rate of 3 units per second.where x and y are…

Q: A point moves around a circle x² + y2 = 25. When the point is at (3, 4), its x coordinate is…

A:

Q: 4)) >〇 impending y= 言 メ= Curve, x=0 and Colculote the orea af the regien between the lines by the…

A:

Q: 2. Find the slope of the line tangent to the cardioid r = 1+ sin 0 at the point defined by 0 = "/3…

A:

Q: IT Find the length of the curve y= in (cos x ), 0 < x < 4

A:

Q: Suppose a particle begins to move from the origin (1 = 0) following the curve in space r(t) =…

A:

Q: 4) If a water wave of length L moves with velocity v in a body of water with depth d, then gL the…

A:

Q: 2 2 2 Find the moment of inertia: x3 + y3 = a3 about x = = 0.

A: Let's find moment of intertia.

Q: 2. A particle moves in a circular orbit x² + y² = 16. As it passes through the point (2, 2/3 ), its…

A:

Q: 6/5 rate of change of f(x, y) at the point (1, 1) in the direction of v is V2 find a.

A:

Q: JA string of length l has a zero initial velocity and a displacement yo(x) as shown. (This ini- tial…

A: Given: A string having the length l having a zero initial velocity and displacement as shown in the…

Q: 1)The potential energy of an object oscillating on a spring stretched a distance x from equilibrium…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: A particle moves along a hyperbola xy = 12. As it reaches the point (6, 2), the y-coordinate is…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.