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Let x(t) be a cubic Bézier curve determined by points p0, p1 , p2 , and p3.
a. Compute the tangent vector x' (t). Determine how x' (0) and x' (1) are related to the control points, and give geometric descriptions of the directions of these tangent vectors. Is it possible to have x' (1) = 0?
b. Compute the second derivative x"(t) and determine how x"(0) and x"(1) are related to the control points. Draw a figure based on Fig. 10, and construct a line segment that points in the direction of x"(0).
Fig. 10
Water is 80°C in copper pipe 10 cm long and 2.6 cm in diameter is surrounded by air at temperature of 10°C. How much heat is lost by convection in one hour
Find a formula for the volume V(t) of the mixture at time t minutes. Find a differential equation that tells the rate of change of the amount of alcohol A(t) at time t minutes.
Determine the expected payoff of the game
A student thinks of a polynomial p(x) of arbitrary degree, and non-negative integer coefficients. How can you determine the student's polynomial by asking for two values of her polynomial
Let R be a region in the first quadrant enclosed by the curves of , , and the vertical lines and . Find the area of the enclosed region. Give your answer correctly rounded to two decimal places.
a card drawn from a standard deck of playing cards. a)what is probability that it is an ace? b)what is probability tu be a face card.
a person deposited $500 in a saving account that pays 5 percent annual interest that is compounded yearly. At the end of 10 years, how much money will be in the savings account?
One professor grades homework by randomly choosing 5 out of 15 homework problems to grade.
you can earn 5% per year compounded annually for the next 4 years, followed by 8% per year compounded quarterly for 5 years. What is the average annual compounded rate of return over the 9 year period? Express your answer with monthly compounding.
What score does a patient at the 75th percentile receive? d. What percentage of patients score between 185 and 199?
You are standing 50 ft away from a building. The angle of elevation to the building is 72 . What is the height of the building?
A farmer wants to set aside a rectangular plot of land to contain 160 square meters. If the width is 19 less than the length, find the dimensions of the plot.
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