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Let S be the circle in the plane {(x,y) in R^2: x^2 + y^2 = 1} and f: S --> R be a continuous map. Show that there exists (x,y) on S such that f(x,y) = f(-x,-y).
Estimate rate of changes.
Derivative of the natural logarithm by using the fundamental theorem of calculus - Evaluate the derivative of y = ln x. This solution below is not complete.
A glass manufacturer finds that one in every 1000 items produced is warped . What is the probability that in a random sample of 5000 glass items there will be
The number of surfer's special burritos served was sampled during a dinner period 5:00 p.m. - 8:30 p.m. at a taco shop on a weekday. Below is the sample:
Which of the following can be solved by using a system of equations? Laura and Mark went to the movies and spent $29 on movie tickets and snacks. Mark paid $10 more than Laura. How much did each spend?
Problem solving on single mean
performs the study for this product, the results predict the market will be good. Given the results of the study, what is the probability that the market will be good?
Suppose that you select 2 cards without replacement from an ordinary deck of playing cards. If the first card that you select is a king, what is the probability that the second card that you select is a heart?
Linear Fractional Transformation, Consider the transformation w = (i - z) / (i + z). The upper half plane Im z > 0 maps to the disk |w|
Center of Mass of 3D Pyramid, Finding the center of mass of a square-based 3D pyramid is usually done in calculus, but our professor wants us to work it out in algebra.
An automobile manufacturer produces 7 models, each available in 6 different exterior colors, with 4 different upholstery fabrics and 5 interior colors. How many varieties of automobiles are available?
Economics : Equations, Quantity and Profit, A company manufacturers and sells a product. The estimated demand and cost functions are as below
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