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Question 1.
(a) For the region bounded by the curve y = 1/25 xe-5x and the positive x-axis, what is the total mass if the density is S per unit area?
(b) What is the x-coordinate of the center of mass?
Question 2.
How do the curves represented by the following two sets of parametric equations differ from each other in terms of extent and dynamics Illustrate with sketches. In both cases - ∞ < t < ∞
x = et/2 x = 3sin(t)
y = 4 - et y = -5 + 9 cos2(t)
(a) Justify the claim that the graph of r = sinθ + cosθ is that of a circle.
At noon, Ship A is 120 km west of ship B. Ship A is sailing north at 40 km/hr and ship B is sailing west at 30 km/hr. How fast is the distance between the ships cit 2M.
What is the probability that student passes?
The height and radius of a right circular can are measured as 60 m and 45 m, respectively, with possible errors of 0.1 m. Use differentials to estimate the maximum possible error in the total surface area.
raph is approximately the distance y in feet a person walks in x hours. What does the slope line represent?
How many applicants did not have sales experience? How many had sales experience, a college degree but not a real estate license? How many had only a real estate license? How many applicants did not have a real estate license?
Find an example, of the BMI between man/woman and estimate a best fit line graphically. Develop an approximate linear model using the point slope form, the slope-intercept form or the standard form line.
A rectangular swimming pool 16 m by 11 m is being filled at the rate of 0.4 m3/min. How fast is the height h of the water rising?
A. At what rate are sales changing in the year 2002? B. What happens to sales in the "long run" (that is, as t )?
A semicircular plate rests on the x-axis, between x = -2 and x = 2. Assuming that the density of the plate varies with a continuous mass-density function given by ρ(y) = (1+y) gram / square cm, find the total mass of the plate.
As the particle passes through the point (π/4, square root 2π) it's x-coordinate is increasing at square root 8 cm/s. How fast is the distance between the origin and the particle changing at this instant?
thermostats are subjected to rigorous testing before they are shipped to air conditioning technicians around the world.
During the first part of a trip, a canoeist travels 97 miles at a certain speed. The canoeist travels 3 miles on the second part of the trip at a speed 5mph slower. The total time for the trip is 2 hrs. What was the speed on each part of the trip?
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