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Let x (t) and y (t) be cubic Bézier curves with control points {p0, p1, p2, p3} and {p3 , p4 , p5 , p6}, respectively, so that x(t) and y(t) are joined at p3. The following questions refer to the curve consisting of x(t) followed by y(t) For simplicity, assume that the curve is in R2.
a. What condition on the control points will guarantee that the curve has C1 continuity at p3 ? Justify your answer.
b. What happens when x' (1) and y' (0) are both the zero vector?
A rectangular piece of paper with perimeter 100cm is to be rolled to form a cylinder. Find the dimensions of the paper that will produce a tube with maximum volume.
Let A be a symmetric and positive definite (SPD) matrix. Is A^-1 ( inverse of matrix A) a SPD matrix? If so, prove it. If not, explain and give an example.
What is the frequency, in millions of Hertz (megahertz), of this radio station? Round your answer to the nearest tenth of a megahertz.
Chi square test
The temperature of a cup of Starbucks coffee at time t (in minutes) is T(t)= 70 + c e^(-kt) . Initially, the temperature of the coffee was 200 degrees F.
your company is thinking about acquiring another corporation. you have two choices-the cost of each choice is 250000.
if the light source is located three feet from the base along the axis of symmetry and the opening is fourteen feet across, how deep should the searchlight be?
Find the equation of the plane which is tangent to the graph of f(x, y) = 4 arctan (xy) at the point (x, y) = (1, 1). Find the equation of the tangent plane to x + y + z = exyz at the point (0, 0, 1).
A spherical weather balloon is being inflated. Beginning at 24 cm, the radius of the balloon is increasing at the rate of 4 cm per second. Express the surface area of the balloon as a function of time (in seconds). If needed you can enter as pi. (..
If α is even, prove that α-1 is also even. Does a corresponding result hold if α is odd? List the left and right cosets of the subgroups in each of the following:
What level of reduction corresponds to the lowest average cost per pound of pollutant? What would be the resulting average cost to the nearest dollar?
A general form of Parseval's Theorem says that if two functions are expanded in a Fourier Series.
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