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Question: A bead is formed by drilling a cylindrical hole of circular cross section and radius a through a sphere of radius r>a, the axis of the hole passing through the center of the sphere.
(a) Write a definite integral expressing the volume of the bead.
(b) Find a formula for the bead by evaluating the definite integral in part (a).
We also discussed rotations of common shapes in the plane using a change-of-base. Walk through one or two examples and discuss how the "usual" basis {(1,0) and (0,1)} can be limiting. Does this suggest why other bases might be better in certain ci..
Suppose the minimum detectable amount is 0.1% and a dinosaur is dated with 40K to be 69 million years old. Is this possible? What is the maximum age of a fossil that we could date using 40K?
Find the equilibrium solution Weq of the DE, and interpret it in ?financial terms.
Draw a different rectangle farm whose perimeter is also 16 centimeters. Label the length of its sides.
A box with a square base has length plus girth of 114 in. (Girth is the distance "around" the box.) What are the two possible lengths of the box, if its volume is 2000 in3?
find both the time and the position of the particle when the particle is further to the left. justify
Find the values of the six trigonometric functions for the angle θ. Find the values of the six trigonometric functions for the angle θ. Assume a = 1, c = 4.
Suppose that every hour there are two new bacteria in a colony for each bacterium that was present the previous hour, and that all bacteria 2 hours old die.
Let A = {1, 2, 3, 4, 5} and R be the relation on the set A whose matrix is attached below. Determine whether R is reflexive, irreflexive, symmetric, asymmetric, antisymmetric, or transitive. For each property, either explain why R has that propert..
a 0.151 kg baseball is pitched with a velocity of 43.1 m/s. ignoring air resistance what is the baseballs momentum after being pitched.
Analyze how the different forces will come together to create a convergence between the interests of stockholders and managers indicating the most likely impact to profitability. Provide support for your response.
The vice president of business services at Prescott College (PC) is worried about the future of her on campus bookstore. The 25 year old college has operated its own bookstore for its entire history, but now finds that it may have to contract out..
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