The angle between tangent and the radius vector of the curve r 5(1- sin@) at 0= is %3D

Q: Find the length of the latus rectum of the curve rsin²x=cosx

A: The given curve is: rsin2x=cos x

Q: The graph of f(x) = −sin x has infinitely many tangent lines that pass through the origin. Use…

A:

Q: Construct a line tangent to arc UV at point U. L this as line UY. Construct another line tangent to…

A: Solution of the problem as follows

Q: Consider the curve: (=Ce"cos(-4t ),e*sin(-4+),e* Compite the are length functien SH): (with intial…

A: Given the curve :    f = ( e^-t cos (-4t) , e^-t sin (-4t) , e^-t) We have to compute the arc length…

Q: The curve with parametric equationsx = t, y = 1 - cos t, 0 ≤ t ≤ 2πis called a sinusoid. Findthe…

A: The slope of the tangent is:

Q: Consider the curve parametrized by a = e-sin(0) and y = ecos(8) for 0 ≤ 0 < 2π. At what points (x,…

A: The parametrized curve x=e-sinθ and y=ecosθ for 0≤θ&lt;2π.

Q: an airplane is moving horizontally at 150 mph over an observer at a height of 4000ft.how fast is the…

A:

Q: Use Newton’s method to find the coordinates, correct to six decimal places, of the point on the…

A:

Q: Of the infinitely many lines that are tangent to the curve  y = −3 sin(x)  and pass through the…

A: Given :    Of the infinitely many lines, that are tangent to the curve y = −3 sin(x)  and pass…

Q: Tangent are drown from the origin to the curve y = sin x.Prove 2 2 that their points of contact lies…

A: The given curve is  y = sinx To find tangent passes through (0, 0)

Q: Let A be a curve defined by the equations 3 x = 3t2 – 4 and y = sin (-nt). Set up (do not evaluate)…

A: Here, the given parametric curve A is: x=3t2-4, y=sin-32πt Now, to find the arc length of A from…

Q: 3. Use Newtons method to find the coordinates, correct to six decimal places, or the point on the…

A: Given: The given point on the parabola is: y=(x-1)2  Now we can write the given point of the…

Q: Use a tangent line approximation to estimate the value of V9.2. Enter the answer in the box. Round…

A:

Q: Determine the x - y coordinates 5 sin²t of the points where the parametric equation y=2 cost 0≤t≤ 2π…

A: The curve has horizontal tangent where the slope is 0

Q: The curve with parametric equationsx = t, y = 1 - cos t, 0 ≤ t ≤ 2πis called a sinusoid. Findthe…

A:

Q: Use Newton’s method to approximate the indicatedroot of the equation correct to six decimal places.…

A:

Q: A projectile is fired with an initial speedof 500 m / sec at an angle of elevation of 45. What is…

A: Given u=500m/sec and angle=45degree In the above figure u is the projectile initial velocity and H…

Q: Find the equation of the tangent plane to the surface 3 – 12y – sin(r*:) = 0 at the point (2, 1,0).…

A: To find gradient of the function.

Q: What is a di¡erentiable curve’s unit tangent vector? Give an example.

A:

Q: Find the equation of the tangent line to the parametric curve x = 2t2 and y = 7t2 – 2t3 – 1 at the…

A: find the slope of function using the chain rule and then use the equation  of a tangent line to…

Q: Find the tangent line(s) to the parametric curve given by a = t-9t and y =t at (0, 9) %3D %3D

A: We have to find the tangent line

Q: Sketch the regions enclosed by the given curves and find its area. Thank you. y = 4 cos(7x),   y =…

A:

Q: What is Lagrange's theorem?

A: Lagrange theorem is one of the central theorems of abstract algebra. It states that in group theory,…

Q: When a particle is located a distance of x metres from the origin, a force of cos(x) Newtons acts…

A: The given question can be solved as shown in step2.

Q: Determine the real root of the equation r sin(x) + cos(x) = 0 in the interval (2, 3) by using…

A: The equation in form f(x)=0 is called a transcendental equation. If the function is continuous on…

Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

A: Equations of the curve in the given question is: Slope of tangent line is given by dy/dx, hence…

Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

A:

Q: 3. A projectile is fired from ground level with an initial velocity of 35 m/s at an angle of 35°…

A:

Q: Find the slope of the tangent line to polar curve r=5sinθ at the point (5/2,π/6).

A: This question is related to Straight line, we will solve it using given information.

Q: What is the lenght of the arc of the circle r = sin 0 that remains outside of the cardioid r =1- sin…

A: The graph is as follows

Q: Find equations for the a) tangent line and b) normal plane to the curve 1 x=t- cost, y = 3+ sin 2t,…

A: x=t-cost, y=3+sin2t, z=1+cos3t We know that rt=xt, yt, zt dxdt=1+sint, dydt=2cos2t, dzdt=-3sin3t At…

Q: Use Newton’s method to find the coordinates of the inflection point of the curve y = x2 sin x ,…

A:

Q: Consider the parametric cuve given by: X= Int a.) Find slope- intereept equation of line targent to…

A:

Q: Explain how to find the arc length of a function that is a smooth curve on the interval [a, b].

A: Let f(x) be a smooth curve on the interval [a, b]  Smooth curve has continuous derivative. As [a, b]…

Q: Regionenclused by the_curve (r=2 cos20)-

A: Given:     r=2cos2θ

Q: a) Find the equation of tangent line of curve that is given by parametric equations x = 3cost + sint…

A: The slope of the tangent at a point on the curve, y=f(x) is equal to the first derivative of the…

Q: A baseball is hit from a height of 3.2 feet above the ground with an initial velocity of 178 feet…

A:

Q: Find the arc length of the segment of curve y = In(cos x) for 0< x<"/3. DO NOT integrate in your…

A:

Q: Use a tangent line approximation to estimate the value of /4.2. Enter the answer in the box. Round…

A: Consider the given function 4.2

Q: Use a linear approximation to estimate sin 29°

A:

Q: Let C be the curve which uses straight line segments to travel from (0, 0) to (0,1) to (2,0) and…

A: The curve C is the line segments travels from 0, 0 to 0, 1 to 2, 0 and then back to 0, 0. Draw the…

Q: Compute the arc length exactly. Please round your final answer to three decimal places. 1 y = -x -In…

A:

Q: The force on a particle is described by 6x + 1 at a point x along the x-axis. Find the work done in…

A:

Q: Find the derivative dydx of the polar function r=sec(2θ) at θ=π4

A:

Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

A: Given:

Q: Use a tangent line approximation to estimate the value of /9.2. Enter the answer in the box. Round…

A:

Q: Find the arc length (in parametric form) over the interval: 0stsi

A: The arclength can be obtained by using the expression L=∫t1t2dxdt2+dydt2dt. Here, dxdt is the…

Q: Find all the points where r = 4 + 2sin(theta) has verticle and horizontal tangent lines.

A: Find the points on the vertical and horizontal tangent lines.