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A batter hits a baseball 3 ft above the ground toward the center field fence, which is 10 ft high and 400 ft from home plate. The ball leaves the bat with a speed 115 ft/s at angle 50o above the horizontal.
(a) Denote the ball trajectory, r(t) = hx(t), y(t)i, wth respect to time, t. Assuming that t = 0 corresponds to the instant when the ball leaves the bat, what are x(t) and y(t)?
(b) Is it a home run? (Does the ball clear the fence?)
Suppose you need to know an equation of the tangent plane to a surface S at the point P(2, 1, 3). You don't have an equation for S but you know that the curves. Find an equation of the tangent plane at P.
Give an example of a dictionary for which the current basic feasible solution is optimal and yet the coefficients of the non-basic variables in the z row are not all negative - Derive the dual of the new LP. Verify that an optimal dual solution wil..
Identifying local maximum, local minimum.
a plane flies 435 miles with the wind and 375 against the wind in the same length of time. if the speed of the wind is 10 mph. find the speed of the plane in still air?
Find the probability of making a Type II error.
Deduce that Pne-na converges for any a 0. Prove that the series Pe-nx+cos(nx) is defined, continuous and differentiable (with a continuous derivative) on (a,8) for any a 0.
A third observation is added: w3 together with s3. Assume w3 is different from w1,w2 and s3 from s1,s2. The worker fits a line to the three observations by minimizing the sum of the squared vertical distances between the line and the data points. Wri..
Two specific mathematical examples of concepts that could be taught using Venn diagrams. For each concept explain what the mathematical concept is, how the Venn diagram is used in that concept and how the Venn diagram might be helpful for stude..
Let f and g be the functions given by f(x) = 1 + sin(2x) and g(x) = e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g.
If the measure of the median of an isosceles trapezoid is 5.5, what are the possible integral masure for the bases?
A Cooling evaporator in a fridge case with a design temperature of 5 Deg C. The Air off and Air on the fridge coil varies pending Ambient, Product, Product temperature/Mass etc.
The expression 200 - 16t2 models the height in feet of an object that falls from the initial height of 200 feet t seconds after being dropped. Find the height of the object after 1.25 seconds.
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