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Determine whether the given set and operations form a vector space. Give reasons.
Let V be the vector space of all functions f: R->R. Determine whether the following subsets of V form subspaces.
Check that even though =1, the angle theta_i between u and e_i tends to pi/2 as n goes to infinity.
Suppose L_1 is the line through the origin in the direction of a_1, and L_2 is the line through b in the direction of a_2.
The components of v=250i+310j represent the respective number of gallons of regular and premium gas sold.
Express the vector with initial point P and terminal point Q in component form. Show work.
Find the velocity and position vectors of a particle that has the given acceleration and the given inital velocity and positions.
Find the equation of the line passing through a point B, with position vector b relative to an origin O, which is perpendicular to and intersects.
When set at the standard position, Autopitch can throw hard balls toward a batter at an average speed of 60 mph.
If all edges of Kn (a complete graph) have been coloured red and blue, how do we show that either the red graph or the blue graph is connected?
For which values of k are the following vectors u and v orthogonal? Let u,v be orthogonal unit vectors. Prove that d(u,v) = 2^(1/2)
Let V be the vector space of all functions F : R ? R. Determine whether the following subsets of V form subspaces of V.
The subspace of P3 consisting of those polynomials in P3 whose graphs pass through the origin.
Use the triangle of forces to find the magnitudes of the tension in the rope and the normal reaction from the ramp, to the nearest newton.
If you make approximately 15 long-distance calls per month, each averaging 30 minutes, which plan should you select?
Show that this anti-symmetry property is preserved under an arbitrary coordinate transformation.
Formulate a mathematical program that can be used to determine where the "hub" should be located in the plane.
An aircraft of top speed 340 km per hour sets a course to the north-east but, owing to the prevailing wind, its actual speed relative to the ground.
Let M and N be differentiable manifolds. Let alpha: M -> N be a local diffeomorphism. Prove that if N is orientable, then M is orientable.
An extension ladder adjusts in length from 10 ft to 16 ft. Suppose you've leaned your ladder against your house.
Determine the measure of a central angle and the measure of a vertex angle of the polygon.
What is/are the equation/s required to calculate dimensions and construction of a frustum shaped plate in its flat form before rolling into cone shape?
Three buildings are connected together as one. One section is 9'2", another is 45'8" x 16'3" and the last one is 18'9" x 15'8".
Select and discuss two examples of real life objects that incorporate the parabolic shape. Explain why the parabolic shape was used for the objects.
Lines l and m are parallel and are cut by the transversal shown. Determine the measures of angles 1 through 7.