A beam whose centre of gravity divides it into two portions, a and b. is placed inside a smooth sphere; show that, if 0 be its inclination to the horizon in the position of equilibrium and 2a be the angle subtended by the beam at the centre of the sphere, them - a tan 0 tan a. %3D b+a

Q: Show that the graph of the equation r = 2a sin θ, a > 0, is acircle of radius a with center at…

A:

Q: For long cirular cfinder of Re two halves maintained at temprature U1 and Vi respectively, Show that…

A:

Q: find the length of the indicated portion of thecurve.r(t) = (et cos t)i + (et sin t)j + etk, -ln 4…

A: Given, r(t)=etcosti+etsintj+etk length L=∫-ln40r'(t)dt            .......(1) now derivate given…

Q: Given line YZ tangent to OJ at point Y and mzWYZ = 119, what is the measure of arc WXY %3D Y W X.

A: Measurement of arc is the angle subtended by arc at the center of circle.

Q: Let P(cos t, sin t) be a point on the unit circle x2 + y2 = 1 in the first quadrant. Show that t is…

A:

Q: Find the angle 0 E [0, between the planes 2x - y+z= 1 and x + z = -3. Lütfen birini seçin:…

A: Given that the two planes: P1:2x-y+z=1P2:x+z=-3Normal   are,Let,      n^1:    2i-j+k=1n^2:   i+k=-3

Q: A point is rotating with uniform circular motion on a circle of radius r.Find ω if r = 8 cm and v =…

A: Given linear velocity and radius are: Formula used for angular velocity in rad/sec is:

Q: A point is rotating with uniform circular motion on a circle of radius r. Find ? if r = 10 cm and v…

A:

Q: The shape of y = V that has been reflected across the origin. Preview

A: To find:

Q: T. 9. TO = PO 10.Sector of a circle is the region bounded by two radii and their intercepted arc.

A: here we check whether the given statement is true or false.

Q: A beam whose centre of gravity divides it into two portions, a and b. is placed inside a smooth…

A:

Q: The circles r = (3)^1/2 cos u and r = sin u intersect at the point (((3)^1/2)/2, pi/3) . Show that…

A: We have given circles equation r=3cosu and r=sinu For intersection point of these circles…

Q: 11. Evaluate 2 dA, where D is the shaded part inside the semicircle of radius 2 in Figure 26. 2…

A: To Find:  D is the shaded part inside the semicircle of radius 2 From the figure, the restrictions…

Q: A beam whose centre of gravity divides it into two portions, a and s placed inside a smooth sphere;…

A:

Q: In the given figure , the common tangents AB and CD to two circles with centres O and O' intersect…

A:

Q: e) With respect to y = cosx, is there a vertical stretch or compression? f) With respect to y =…

A: To answer parts e and f

Q: Find the length of the hypocycloid defined by the equations x = a cos° (0), y = a sin° (0), 0 < 0 <…

A: Here we have to find the length of the hypocycloid defined by the equation x=acos3(θ) , y=asin3(θ)

Q: A point is roaring with uniform circular motion on a circle of radius r.  Findw if r =7cm and…

A:

Q: A beam whose centre of gravity divides it into two portions, a and b. is placed insıde a smooth…

A: I am attaching image so that you understand each and every step.

Q: Find the length of the indicated portion of the trajectory. rt) = (e 'cos t) i + (e 'sin t) j +3e t…

A: Here I am attaching image so that you understand each and every step.

Q: A beam whose centre of gravity divides it into two portions, a and b. is placed insıde a smooth…

A:

Q: . A beam whose centre of gravity divides it into two portions, a and b. is placed inside a smooth…

A:

Q: A beam whose centre of gravity divides it into two portions, a and b, is placed insıde a smooth…

A:

Q: Consider the curve C parametrized byx = −1 + 6 sin t and y =(1/2)− 6 cos t for −π ≤ t ≤ 7π. What is…

A: First of all, consider the given parametrized equation of curve C. Rearrange the equations to write…

Q: 25. Find the angle 0 that maximizes the area of the isosceles triangle whose legs have length e…

A: Given area from question:

Q: Find the length of one arch of the cycloid 2(t – sin(t)), y = 2(1 – cos(t). х

A:

Q: In circle R with MZQRS = 74 and QR = 17 units find area of sector QRS. Round %3D %3D to the nearest…

A: Given that ∠QRS = 74 degree QR = 17 To find the area of the sector QRS.

Q: Find the length of one arch of the cycloid 8(t – sin(t)), y = 8(1 – cos(t)). %3D

A: Given: x = 8(t -sint(t)) y = 8 (1-cos(t)) To find the length of arc.

Q: dV , where V is the unit sphere.

A:

Q: A point is rotating with uniform circular motion on a circle of radius r. Find v if r 3 inches and w…

A: Given radius and ω are 3 inches and 5 rad/sec, respectively.

Q: following equation aU (1,1). TC with U (0,t)= 0, = 0, and U (x,0)= sin 2. %3D %3D %3D at

A:

Q: BC is a tangent drawn to circle O. OC = 16, BM = 10. Find BC to %3D the nearest tenth. C B to M 16

A: Given: -  BC is a tangent drawn to circle O. OC = 16, BM = 10. To Find BC

Q: Show that the surface area obtained when the arc of the parabola y? = 16az from I = 0 to r = h is…

A: Surface area

Q: 4. Given AB is tangent to OP, AB = 12 and CB = 8. %3D a) Find the area of APAB. b) Find mLAPB (round…

A:

Q: Find the equation of the osculating, normal, and rectifying planes for a (t) ( cos t, – sin t, cos…

A:

Q: The unit circle a + y: =1 can be wrriten in parametric form as x = cos(0) and y= sin0. Find and…

A:

Q: : The area of the surface obtained by rotating the curve y = 2 In a, for 1 < a <e, about the a-axis,…

A: We have to find the integral that given the surface area.

Q: A yo-yo which is 3 inches in diameter spins at a rate of 5000 revolutions per minute. How fast is…

A: Rounds per minute = 5000 To Find:    Speed of the edge of yo-yo spinning in miles per hour…

Q: 1. Draw the curve r² = 2a? cos 20, a > 0 and calculate the area enclosed by this curv

A: This question is about application of integration in polar coordinates

Q: The circles r (V3/2, 7/3). Show that their tangents are perpendicular there. V3 cos 0 and r = sin 0…

A:

Q: Find the length of the portion of the arc given by r(t) = (e 'cos t) i + (e 'sin t) j + 5e ' k, -In…

A:

Q: The shape of a hole pored by a drill is a cone surmounted by cylinder. If the cylinder be of height…

A: Consider the following figure. Given tanα=hr. We know that the volume of the cylinder is…

Q: Consider the curve C parametrized by(x, y) = (5 cos (−12t), 5 sin(−12t)), for −π/2 ≤ t ≤ π/2 What is…

A:

Q: a cosece, y = b cot0, then %3D x? , y? A) ? b? 可 x? y? = 1 ? b? 1 B - a a If x = a sec0,y= b tan 0,…

A: Given:6. x=a cosecθ, y=b cotθ7.x=a secθ,   y= b tanθ

Q: Find the angle in radians between the planes -2x + z = 1 and -ly+ z = 1.

A: See the answer below

Q: Use the figure and the given information to answer the questions that follow. 1. If mPR = 45 and mQS…

A:

Q: Consider the given curve: R(f) = (2 cos f, 12f +3,-2 sin f) Reparametrize the curve using arclength…

A: