Please see the attached file for full problem description. 1. Let Complex 3-space C^3 be equipped with the standard inner product and let W be the subspace of C^3 that is spanned by u_1= (1, 0, 1) and u_2= (1/3, 1/3, -1/3). Project the vector v= (1, i, i) onto W. Show work. Help: : is the
Sec^2B/tanB = (cot^2B- tan^2B)/(cotB-tanB)
** Please see the attached file for the full problem description ** Prove that if u and v are given non-zero vectors in the arbitrary inner-product space V, and are such that <u,v>=0, then {u,v} is a linearly independent subset of V. Show work.
Please see the attached file for the fully formatted problem. 1. Write the vector equation of the line in R^3 which passes through the two points P: (1,-1,3) and Q: (2,-1,-1). Show work. Help: R^3: is Euclidean 3-space
Please see the attached file for full problem description. 1.Let u=(1,-1,3) and v=(2,-1,-1) be vectors in Euclidean 3-space R^3. Find a vector orthogonal to the plane of (subspace spanned by) the vectors u and v. Show work. Help: R^3: is Euclidean 3-space
For the curve: r = ( 2abt, a^2 log t, b^2t^2 ), show that: κ = - τ = 2abt/(a^2 + 2b^2t^2)^2 where κ = curvature of the curve τ = torsion of the curve.
In Metric. Three college students are trapped in deep snow in northern Canada. To survive they must build an igloo using snow large enough for all of them to fit and small enough to not exceed their strength and stamina. Luckily one of them is a math major and quickly formulates the dimensions of the blocks they need to cu
Prove (using angle,ray,line,plane axioms)That the sum of the measures of any set of adjacent angles about a point, whose sides and interiors cover the entire plane is 360.
Calculate AREA of Shape 1 then calculate the area of Re-arranged Shape 1. Did you get the same result? Why are they different? Please see the attached document.
You have a brick of parallelepiped shape. You need to measure its diagonal (a distance between two opposite vertexes remote to the maximum). You have in your disposition a ruler and a rectangular edge of the plane surface (of the table, for example). What should you do to measure the diagonal if 1. You have also a pencil to ma
Suppose <ABC and<CBD form a linear pair, <CBD and <DBE form a linear pair, and m<CBD=30. A. Draw a figure representing these angles. B. Write a paragraph proof showing that <ABC=<DBE.
Given a,b,and c, find three angles A, B and C?
Consider a triangle with sides a, b and c and angles A, B and C. Prove the following version of the Law of Cosines : b^2 = a^2 + c^2 - 2ac cosA
A zero dimensional goat is attached by a rope to a point on the perimeter of a circular field (two dimensional). How long should the rope be (in terms of the radius of the field) so the goat can reach and graze exactly half of the grass of the field?
Find the measure of an interior angle of a regular octagon.
How many lines would you need to add to a pentagonal prism anchored to the ground to make it rigid?
For a gun where the departure angle 'Beta' and the distance "D" in meters that the projectile travels are related by D=1250sin2Beta. Find which departure angles can be used to hit a target 800 meters away.
Joe and Jill set sail from the same point, with Joe sailing in the direction of S4 degree east and Jill sailing in the direction S9 degree west. After 4 hr, Jill 2 mi due west of Joe. How far had Jill sailed?
Find the vale of x if arc AB = 62 degrees and arc CD = 32 degrees (on a semicircle). AD is the diameter of the circle. x = arc BC
When measuring angles using a protractor, how do you decide whether to use the top scale or the botton scale?
Please explain how to find the apothem, especially in regards to 45-45-90 and 30-60-90 triangles.
What is this symbol and what does it mean? See attachment.
Prove true or false, if false give a counter example. If each point in the point set M is a limit point of M, then M is connected.
How much earth would be needed to fill a hole 25 ft long 6ft wide and 2ft deep?
Solve the following ratios: x/4=3/2 3/a=1/6
Is it possible for the volume and surface area of a cube to be equal? Explain.
Assume that AC < w, A-B-C, and D is a point on AC line segment. Let h be a ray with endpoint C such that h meets BD line interior. Prove that h meets AD line.
Prove that the interior of any proper angle is a convex set.
Given: Segment RW and segment SX bisect each other at point V Prove: Line RS is parallel to line XW
I need an equation or equations to help me find out how many pounds of sand I will need to fill my fish tank and so I can determine how much it will cost me. The tank measures 71 inches in length and 18 inches in width. I want to know how much sand I will need for a 3, 4, 5, and 6 inch base.