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Prove that a tree with Delta(T)=k (Delta means maximum degree) has at least k vertices of degree 1.understand how you count the degree of the vertices
Vectors and Gradients : Direction of Most Rapid Increase; Critical Points
Example of a quadratic model.A copy of the original data (with reference) and brief discussion of why you chose it.
Vector Spaces and Linear Combinations.Let V be the space of all functions from R to R. It was stated in the discussion
Vector Spaces and Scalar Multiplication.Let V be the space of all functions from R to R. It was stated in the discussion session
Vector Cross Product and Arc length.Find the arc length of the curve given
Vector Fields : Divergence and Curl.Calculate the divergence and curl of the vector field F(x,y,z) = 2xi + 3yj +4zk.
Vector Spaces and Projection Mappings.Let V be a vector space of all real continuous function on closed interval [ -1, 1].
Prove that U is a Subspace of V and is Contained in W. What is presented below has many missing parts as the full question could not be copied properly.
Solving: Multidimensional Arrays and Vectors. A certain professor has a file containing a table of student grades
Gradient Vector and Tangentl Line.If g(x,y)= x-y^2, find the gradient vector (3,-1) and use it to find the tangent line to the level curve g(x,y)= 2 at the poi
Divergence and Curl of a Vector Field.Compute the divergence and curl of v.
Mathematics - Proof of Midpoint Theorem using Vectors.The midpoint of a side of a triangle in R^3 is the point that bisects that side (i.e., that divides it in
Vectors: Resultant Vector.Two students are using ropes to pull on a heavy object, as shown in the diagram below.
Equation of a plane.Specify the area of the triangle defined by p1, p2, and p3.
Linearly dependent set of three vectors. What is an example of a linearly dependent set of three vectors with the property that any single vector
Linear combination of the given vectors. Suppose {v_1, v_2, v_3} is linearly independent set of vectors in R^n.
Translation and reflection. A student claims that anything that can be accomplished by a translation can be accomplished by a reflection
Find a unit vector n perpendicular to the plane through the points P(1, 3, -2), Q(2, 4, 5), and R(-3, -2, 2).
Component form of the vector.Find the component form of the vector v that has an initial point at (1,-2,2) and a terminal point
Normal and binormal vectors to a curve and normal plane. If C is the curve given parametrically by R(t)=cost(i)+sint(j)+2t(k) find
Write a plane equation for plane passing through P (1,2,3) and perpendicular to n = .
Projecting a vector.Let C^3 be equipped with the standard inner product and Let W be the subspace of C^3 that is spanned
Find the volume of the parallelpipe with adjacent edges a,b,and c.Determine if the vectors a and b are parallel, perpendicular or neither.
The surface integral of the normal component of curl F over the open hemispherical surface (x^2)+(y^2)+(z^2)=4 above the xy plane