Se) Define moments, skewness, and kurtosis. Mention their applications.

Q: Ez fand Pi) Pow = * in Tesm of Po, Pg

A: For a function fx, it is known that  fx=∑kAkPkx                        (i) Where Pk is the Legendre…

Q: Define the moment-ratios ß1 and B2.

A: To define the moment-ratios.

Q: ).Derive the expression for torsion formula of a circular bar?

A: Torsion formula, the geometrical property of a bar's cross section which is involved in the axis of…

Q: (d) Compute curl F.

A:

Q: In conclusion, state the relationship between the mass of the spherical object and the distances…

A: Keeping the distance relative to the ramp constant, it is observed that the knockback distance of…

Q: A particle of mass M is moving in a straight line under constant force of magnitude F and a kv?,…

A:

Q: Exercise 8. Show that the sum of the angles of a geodesic triangle on a surface of positive…

A: We will use the Gauss–Bonnet theorem to prove the given statement.

Q: If two loads are applied to a cantilever beam as shown in the accompanying drawing, the bending…

A: Given information: Given that the random variables X­1 and X2 are independent random variables with…

Q: Find a formula for the distance from the point P(x, y, z) to the yz-plane.

A:

Q: 4. A car is on a driveway that is inclined 20° to the horizontal. If the car weighs 3225 lb, find…

A:

Q: Derive the expression for torsion formula of a circular bar?

A: Torsion of a circular bar ⇒ A member or shaft is said to be under pure torsion when it is subjected…

Q: Find the length of the spiral r=

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: When is An angle in the xy-plane is said to be in standard position?

A: An angle is in standard position if its vertex is located at the origin and one ray is on the…

Q: Derive the frenet frame, curvature and torison o the binormal indicatrix of hypocycloid?

A: We need to Derive the fernet frame, curvature and torsion o the binormal indicatrix of hypocycloid.

Q: EsLimate the integra Sind dy usng Composile trapezodal nule with pate

A:

Q: )2. Find the paramehic from the cuve check whether the cure is a repulor cuve. Alo reparzmetije the…

A: We have to find the parametric form of the curve

Q: The centroid of an obtuse triangle is outside the triangle. true or false?

A: solution ======== The centroid is the concurrent point of the three medians in a triangle. It is the…

Q: If C is the line segment that first connects point 2 to point i, and then the spring piece that…

A: Consider two regions C1 and C2 then these can be defined as follows, Thus, C=C1UC2 The conjugate…

Q: A constant force of 5N (as pictured) does work and displaces the block 4 m.

A: Given,  a constant force of 5N does work and diplaces the block 4m.

Q: Et eNcise the fo is linemr OTDE which of eii> +* - 1ogx dy

A: Given some differential equation. We need to find which of the following is linear differential…

Q: 2r find the moment with respect to the wavic of the area hounded by the parabola v - Av-172 and v

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Q: 2) Find the length of the spiral: r = 0² from 0 = 0 to 0 = V5?

A:

Q: A 20-lb force is applied to the control rod AB as shown. Knowing that the length of the rod is 9 in.…

A:

Q: Distinguish briefly the Skewness and kurtosis

A: Skewness is a measure of symmetry where symmetry means equal proportion to the left and right to the…

Q: of the fillowng Cuve. Aearly ntereepts on the axes O point of Inflechion

A:

Q: Write a formula for the curvature K(t) in terms of ( r' (t) and r" 0) )? And prove it?

A: The curvature Kt is given by Kt=r't×r''tr't3 Now prove this formula in the following.

Q: ) convert the eylindrieal pt (3, 7%,-2) to rectomgular ) conrert the nectamgular ) to cylindrical

A:

Q: Find the amount of force required for a winch to pull a 2700-lb car up a ramp that is inclined at 25…

A:

Q: obtain the value of b. regaring e conomethies and the forme 4= bo t bi Xi Y=bot bixitei

A: For the given linear regression line and its estimate: Y = b0 + b1Xi + ei y^ = b0 + b1 Xi We need to…

Q: The cable AB carries a tension of 400 N. Determine the moment about O (positive if counterclockwise,…

A:

Q: Two tangent segments are drawn to sphere Q from external point E. Where A and B are the points of…

A: Given, E is an external point, and A and B are the points of tangency on sphere Q. The tangent of a…

Q: If the magnitude of the resultant force is to be 9 kN directed along the positivex axis determine…

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Q: A cross section of this oblique cylinder with circular bass formed by a horizontal plane…

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Q: Use De moivrés theorem to ealculate the sauare Toot Of It,

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Q: Will a truck that is 12 feet wide carrying a load that reaches 11 feet above the ground clear the…

A: Here we use the basic equation of the ellipse.

Q: Encuentre el punto sobre la curva y= vx más cercano al punto (3,3)

A: Definition used -    Distance between two points (x1,y1) and (x2,y2)                 S…

Q: Find the angle of tilt θ with the horizontal so that the contact force at B will be equal to 0.76…

A: Draw the free body diagram of the block.

Q: Will a truck that is 16 feet wide carrying a load that reaches 11 feet above the ground clear the…

A: Here we have to uae the concept of conic section.

Q: Possible units of the moment M, are

A: Moment= Force ×  perpendicular distance

Q: Water is pumped into a sphere at a constant rate as seen on the figure.

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

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Q: Determine whether each of the following statements is true or false, and explain why Simpson’s rule…

A: Given statement is  Simpson’s rule usually gives a better approximation than the trapezoidal rule.

Q: Show that the Gauas and mean curvatures on , X = (u + v,u –- v,uv) at u = 1, v = 1 are K = 116 and H…

A: Given, X=u+v,u-v,uv u=1,v=1 , k=116 and H=182 We know that, E=xu,xuF=xu,xvG=xv,xv So, we need to…

Q: Find a formula for the distance from the point P(x, y, z) to the xz-plane

A: The distance between two points x1,y1z1 and x2,y2z2: d=x2-x12+y2-y12+z2-z12 The distance from the…

Q: find the volune of the selid generated by revolving regron bounded by the graphts of dhe ģiven…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: A flat, very thin table has a circular hole with radius 1 and a circular hole with radius 2. The…

A:

Q: "ind the orthogonal compliment to S = span{

A: Here we have to find the,

Q: Which is the complete formula used to find the radius of curvature?

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.