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Given a vector w, the inner product of R^n is defined by:<x,y>=Summation from i=1 to n (xi,yi,wi)
[a] Using this equation with weight vector w=(1/4,1/2,1/4)^t to define an inner product for R^3 and let x=(1,1,1)^T and y=(-5,1,3)^T
Show that x and y are orthogonal with respect to this inner product. Compute the values of ||x|| and ||y|| with respect to this inner product.
[b]In C[0,1], with inner product defined above, consider the vectors 1 and x. Find the angle theta between 1 and x. Determine the vector projection p of 1 onto x and verify that 1-p is orthogonal to p.
write the slope intercept form of an equation of the line that passes through the given point and is parallel to the
Perform the following division
Katie converts the outside temperature from degrees Fahrenheit to degrees celsius. She uses the formula below to convert the temperature.
A company's costs, in millions of dollars, are given by the equation, C = x2 - 3x - 27, where x is the number of items sold, in thousands. What are the costs when 1,000 items are sold? 1,500 items?
Graphs translations
since 1905 the amount of carbon dioxide has been increasing. total production of co2 from all counntries except us
A rectangular swimming pool is twice as long as it is wide. A small walkway surrounds the pool. The walkway is a constant 2 feet wide and has an area of 196 square feet. Find the dimensions of the pool.
Let X be a finite dimensional linear space. Show that, for every subspace Y of X, Y perp perp = Y (that is, the annihilator of the annihilator of Y is Y)
Evaluating the value.
Create a real world situation which would describe the inequality graph below.
Write an algebraic equation for this problem. Solve the equation for the number of gallons needed (x)
Describe what the function |x - a| = b means in Englilsh terms
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