Reference no: EM131071935
Solve the problem.
1) Find a curve through the point (0, 3) whose length integral, 0 ≤ x ≤ 1, is L =
0∫1√(1+4x2) dx.
Set up an integral for the area of the surface generated by revolving the given curve about the indicated axis.
2) xy = 3, 1 ≤ y ≤ 2; y-axis
Solve the problem.
3) A vertical right circular cylindrical tank measures 24 ft high and 12 ft in diameter. It is full of oil weighing 60 lb/ft3. How much work does it take to pump the oil to the level of the top of the tank? Give your answer to the nearest ft · lb.
4) A rectangular sea aquarium observation window is 12 ft wide and 4 ft high. What is the force on this window if the upper edge is 3 ft below the surface of the water? The density of seawater is 64 lb/ft3.
Find the fluid force exerted against the vertically submerged flat surface depicted in the diagram. Assume arbitrary units, and call the weight-density of the fluid w.
5)
Find the center of mass of a thin plate covering the given region with the given density function.
6) The region enclosed by the parabolas y = 50 - x2 and y = x2, with density δ(x) = x2
Find the centroid of the thin plate bounded by the graphs of the given functions. Use δ = 1 and M = area of the region covered by the plate.
7) g(x) = x2 and f(x) = x + 12
Find the length of the curve.
8) y = (16 - x2/3)3/2 from x = 1 to x = 64
Find the area of the surface generated by revolving the curve about the indicated axis.
9) x = 3√(4 - y), 0 ≤ y ≤ 15/4; y-axis
Find the mass of a thin plate of constant density covering the given region.
10) The region between the x-axis and the curve y = 2csc2x, π/4 ≤ x ≤ 3π/4.
|
What is the domain of h
: Let h(x) = 1/ {abs(x-1) - 2 }2. What is the domain of h and What is the domain of h(h(x))
|
|
Correlation between the number of hours
: The following table contains data for 6 baseball teams. Is there a correlation between the number of hours spent in the batting cages and the number of wins produced?
|
|
What is arena bargaining
: The first step in determining compensation costs is to determine the value of the pension benefits.
|
|
What proportion of american employees
: What proportion of American employees spends fewer than 15 minutes per day commuting?
|
|
What is the force on this window
: A rectangular sea aquarium observation window is 12 ft wide and 4 ft high. What is the force on this window if the upper edge is 3 ft below the surface of the water? The density of seawater is 64 lb/ft3
|
|
What creation myths read about eating habits of civilization
: What do the various creation myths read this week demonstrate to historians about eating habits of early civilizations?
|
|
Quality-assurance department
: At the Warren Road MacBurger, the quality-assurance department sampled 50 customers and found that the mean waiting time was 2.75 minutes. At the .05 significance level, can we conclude that the mean waiting time is less than 3 minutes?
|
|
Define a correlation and provide an example
: 1. Define a correlation and provide an example 2. Define causality? 3. Explain if correlation causes causality.
|
|
Estimate the average age of the students
: The president of a large university wishes to estimate the average age of the students presently enrolled. From past studies, the variance is known to be 4 years. A sample of 49 students is selected and the mean is found to be 23.2.
|