A = TrVP + h°. a. Find dr/dh for a cone with a lateral surface area of A = 15007. b. Evaluate this derivative when r = 30 andh = 40.

Q: Given y dx – xy? dy where D is described by æ? + y? <1 -

A:

Q: If the curve I=3+ at? y= at + bt has a tangent line y=r-4 at t 1, what is a+b? %3D

A: We have to find a+b

Q: The parametric form of the tangent line to the image of f(t) = (2t², ?,t +2) at t = 1 is L(t) =

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 lengths of the following curves: b. x = cost and y = t + sin t, 0<t<n

A: we have to find the length of the given curve

Q: Ex:57 Find the FisiE of the Juuctiou sin TIt ZL oくtくし - siu -Lくtく

A: Given, The formula for the Fourier series expansion is,

Q: Given the xーxy+y? %3D 9 2. Curve 6. Find the coordinates of the POTnts on the Curve where the…

A:

Q: Ex 3 identify the equarion of a line a) parallei that is é b) perpendicular y= x-2 through ly,-1)

A:

Q: Consider the parametric curve x = Vt , y= 3t –1, for t20. Find the slope of the tangent line to this…

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

Q: Use a calculator to approximate the area of the surface generated when the given curve is revolved…

A: Solve the given

Q: ind the tangent and normal to the curve y =2e at the point where the curve meets the y – axis

A: Find the equation of the tangent

Q: Find where the slopes of the tangent to the curve r=e^(theta/2+1) are horizontal 0 less or = theta…

A:

Q: Find the tangent line to the cycloid (x(t), y(t))= (t – sint, 1– cost) at t = to.

A: Given xt=t-sint, y(t)=1-cost we have to find the tangent line cycloid at t=t0

Q: d'y Consider the curve y = ry+ 1, What is the value of at (0, 1)? dz

A: Given curvey2=xy+1

Q: dy Find for the curve 49 + 6x° = 3 + sin(7x-y). da

A:

Q: Evaluate (3y - esinz)da + (7x+ V +1)dy where C is the unit circle

A:

Q: Find an equation for the tangent plane to the surface 2? – ry? = 0 at the point G, 2, 3)

A:

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

A: Given that:

Q: nd the tangent plane to the equation z = a? – 4y? – 2y at the point ( – 3, 3, – 33)

A: In this question, concept of tangent  is used. Tangent A tangent is the line that runs parallel to…

Q: Differentiate y = arccos(e). dy Answer: da ||

A: We have to differentiate y=arccose4x.

Q: Find the sope to the tangent Iine of the equation ,-y +ear (0,3) Hirt perform impl cit…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find the points on the curve a = t? – 4t + 1, y = t² + 8t – 8 that have: A. a horizontal tangent…

A: Let's find.

Q: Find the length of the subtangent and subnormal of a point of the curve y=b sin (x/a)

A:

Q: In AVWX, the measure of X=90°, XW = 24, WV = 25, and VX = 7. What ratio represents the tangent of…

A: Given triangle is   tan W = ?

Q: Use the arc length formula to find the length of the curve y = 2-3x, -2 is less than or equal to x…

A:

Q: Find . F.dr when F(x,y) = (2x,3y²) and C is only the first quadrant part of a circle of radius 3…

A: Let C be a smooth curve and r→t=xti^+ytj^+ztk^ be the position vector of any point x,y,z on C.…

Q: . SR is tangent to OP and OQ. от QT = 6; TR = 8; PR = 30. PQ ?; ST ?: PS = ? S T R

A: Given that, any SR is tangent to ⊙P and ⊙Q. Also, QT = 6, TR = 8 and PR = 30. Here, ∆RTQ is right…

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

A:

Q: The curve assumed by a heavy chain or cable is: y = C cosh %3D If C = 50 Calculate; The value of…

A:

Q: Find the cylinder surface determined by Curve 4x?+9g? -36=0 and d= ( 1, -1. 32 line.

A:

Q: Given ZY = 25, What is the distance from ZS %3D U W T. S Y

A: Given:

Q: Find the distance from the origin to the point (x, y).

A: Distance between Ax1, y1 and Bx2, y2 is, AB=x2-x12+y2-y12

Q: Use the formula A = 27 dy 1 + dx dx to determine the surface area of the parabolic reflector…

A:

Q: Find the equation of tangent to the circle x + y = 25 at the point (3, –4) %3D 25 ix + O b. y = 7 O…

A:

Q: Find the equation of the tangent to the curv e y = 23 Az-12 at the point where a = 3. Answer:

A:

Q: Find the tangent plane to the equation z 5x? – 2y? – 5y at the point (3, 0, 45).

A: We need to find the tangent plane equation at (3,0,45)

Q: the of the curve d:laaR? Find detined by is čonstant. 870 Curiature a(t) =|1 Cost, 1 sint, o where…

A: A vector is a quantity that has both magnitude and direction. In general vectors are represented as…

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

A:

Q: Eliminate the parameter to find Cartesian equation of the curve: x=2 sint, y = 5 cost, -n <t<n 6. a

A:

Q: DA particle moves along a line with velocity IG ? at tim 4++3

A: To find the distance travelled by the particle for the given time period.

Q: An airplane is flying in the direction 25° west of north at 800 km&gt; h. Find the component form of…

A:

Q: Find the slant height of the cone whose lateral surface area is 22000 m' and radius is 140 m. 22 Use…

A: Lateral surface area=pi r l m^2. Where l is slant height of cone.

Q: An airplane is flying in the direction 25° west of north at 800 km/h. Find the component form of the…

A:

Q: Find the tangent plane to the curve T = [t, t², t³] which pass through point M (2, –, –6) .

A: If the parametric equation of a curve is given by , then the tangent direction is given by . The…

Q: Find xdy + ydx, where C is the arc of the curve C y = et for 0 < x < 5

A:

Q: Find the linear velocity of a point rotating at 30 revolutions per second on a circle ofradius 6…

A: Given that , A point is rotating at 30 revolutions per second on a circle of radius 6 cm. To find…

Q: nd the length of a tangent drawn to a circle of radius 3.2cm from a point which is 5 cm away from…

A:

Q: ind an equation of the tungent line to y= 45in2 X at point (i II

A:

Q: For (z +y)? = z² -f find the points where the tangents are horizontal.

A:

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.