Find the distance from the centre at which the velocity in S. H. M. will be half of the maximum.

Q: find the radius of curvature at any point on parabola y2=4ax

A: Given:  y2 = 4axTo find: The radius of curvature at any point on the given parabola. Formula used:…

Q: Show that the tangent lines at the points where the ellipse x² – xy + y² = 3 cross the x-axis are…

A: Explained below

Q: Find the radius of curvature at any point on parabola y2=4ax

A:

Q: Find the equation of the tangent plane to the graph of G(u, w) = sin (uw) at the point (r, ).

A:

Q: Find the tangent/s as directed to the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x –…

A: The objective is to find the equation of tangent line to the parabola x+2y2+2x-y-3=0 which is…

Q: Find the equation of the tangent plane to the surface at the specified point.

A:

Q: Find the tangent to the folium of Descartes  x  3+ y 3= 6xy  at the point (3,3)

A: Consider the given curve: Here the objective is to find the tangent at point p (3, 3).

Q: Find a parametrization for the curve described below. the line segment with endpoints (4,4) and…

A: Given,  A line segment with endpoints 4, 4  and  6, 1  We have to find the parametrization of the…

Q: * Find the equation of the tangent plane to the surface 9a2²-12xy = 5x2+5 at the ivon Ni Smob point…

A:

Q: The surface of a mountain is modeled by the equation h(x, y) = 5000 − 0.001x2 − 0.004y2. A mountain…

A: Hints:  The given equation is h(x,y)=5000-0.001x2-0.004y2 and the given point is (500,500,3750). To…

Q: Find the equation of the tangent plane to the surface 4 =1 at the point 9. 16 (1,-3,2)

A:

Q: Find an equation of the tangent line to the hyperbola y=3/x at the point (3,1)

A:

Q: find the equation of the tangent plane of this surface

A: In this question, we check the surface is simple and then we find the equation of tangent plane at…

Q: Find an equation of the tangent plane to the given surface at the specified point. 2. (-16, 4, -1)

A:

Q: Find all points on the ellipse x2 - xy + y2 = 1 at which the tangent line is horizontal.

A: The given equation of ellipse is,

Q: Find the point(s) on the surface z = 5xy, at which the tangent plane is horizontal.

A:

Q: For a point moving with uniform circular motion, the distance traveled per unit timeby the point is…

A: "For a point moving with uniform circular motion, the distance traveled per unit timeby the point is…

Q: Find the tangent plane to the equation z = 4x2 + 2y? + 5y at the pc

A: Here we have to find the equation of the tangent plane on the curve z=-4x2+2y2+5y at the point…

Q: gment JK and segment HK are tangents to rcle G. J

A: Given that:

Q: Find the velocity of Zoe relative to the surface of the water.

A: The velocity of Zoe Vz is 3 km/hr to west. Velocity of the current Vc is 15km/hr to north. So, the…

Q: whose x-coordinates are equally ine with parabolic runout conner

A: Given as.     python code :

Q: Find the length of the curve. Round to two decimal places. 23 y = 3 1 ,1 <x < 4 4x'

A:

Q: ind the equations of the tangent line to the ellipse x² + 4y² + z² = 9, x = 2 at the point (2, -1,…

A:

Q: A DVD has a diameter of 4.75 in. and rotates at 360.r/min. What is the linear velocity of a point on…

A:

Q: Find the speed of the cycloid c(t) = (4t − 4 sin t, 4 − 4 cost) atpoints where the tangent line is…

A: Given: c(t)=4t-4sin(t), 4-4cos(t)

Q: Find an equation of the plane tangent to the following surface at the given point. V3 A,1, sin (xyz)…

A:

Q: Find a parametrization for the line through the point (a, b) having slope m.

A: Given that slope = m , this can be written as &lt;1,m&gt; vector. And point= (a,b)

Q: Show that the tangent line at a point P = (x0, y0) on the hyperbola(x/a)2−(y/b)2= 1 has equation Ax…

A: Given equation of hyperbola  x2a2-y2b2=1 and given point is P=xo,yo. Since hyperbola is passing…

Q: Show by implicit differentiation that the tangent to the ellipse at the point (xo, yo) is yoy a? b2

A: Given equation is Differentiating both sides with respect to x, we get

Q: If an airplane is flying at 140 miles per hour East and turns in a smooth curve with a diameter of 3…

A: Given Velocity=140 miles per hour diameter=3 miles Centripital acceleration=v2r

Q: ind the points on the curve zx? + 4y? = 1 that have a horizontal tangent line.

A:

Q: Find the equation of the tangent line to right branch of the hyperbola π π x = sect, y = tant, ≤t≤at…

A: Given :x=secty=tant

Q: A particle travels along the parabola y = ax^2 + x + b. At what point do its abscissa and ordinate…

A: Given: y=ax2+x+b

Q: Find the area of the surface formed by rotating the curve with the equation x ^ (2) - (y ^ (2)) /…

A:

Q: Find an equation of the tangent plane to the surface at the given point. fx, у) %3 х2 - 2ху + у2,…

A:

Q: e, Find at the giren point on eauation Of the tangent live. to the corve. X=46",y=f'+|,(4,0)

A:

Q: Compute for the tangential velocity of a wheel rotating at a speed of 2000 rpm such that the radius…

A: Formula for tangential velocity Vt is: Vt=2πrt  here r is the radius of the wheel and t is the time…

Q: Give the equation of the tangent plane to each of these surfaces at the point indicated.

A:

Q: A drive has a maximum speed of 12,000 revolutions per minute. If a disc has a diameter of 12 cm​,…

A: Given 5000 revolutions per minute

Q: Find an equation of the plane tangent to the following surface at the given point. 1 sin (xyz) =

A:

Q: Find an equation of the tangent plane to the surface at the given point. 5 —х — у, z = 5 - (3, -2,…

A:

Q: Pls help ASAP

A: Solve the following

Q: Show that the square of the length of subtangent at any point on the curve by =(x+a)°.(b÷0) varies…

A: We will prove it as following.

Q: SHOwh above with the center of dilation at point A?

A:

Q: メ y= oL Xとn2

A: Given curve is y=ex , 0≤x≤ln2find the area of the surface

Q: On the surface z =, in what direction is z increasing most rapidly when x =1 and y = 2.

A: A function z=f(x,y) increases most rapidly, at a point (a,b) , in the direction of the gradient…

Q: Find the tangent line to the ellipse x^2+4y^2=8 parallel to the line x+2y=6.

A:

Q: Find the radius R, of curvature to the hyperbola y = x + 3x² – x³ at the point x = 0 given that R =…

A: To find the radius R, of curvature to the given hyperbola at point x = 0.

Q: The 35-kg boy is sliding down the smooth spiral slide such that his z coordinate decreases 2 m per…

A: Solution is in step 2