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Question: A metal plate, with constant density 2 gm/cm2, has a shape bounded by the curve y = x2 and the x-axis, with 0 ≤ x ≤ 1 and x, y in cm.
(a) Find the total mass of the plate.
(b) Sketch the plate, and decide, on the basis of the shape, whether is less than or greater than 1/2.
(c) Find x¯.
If we flip a coin twice, is the event of having an odd number of heads independent of the event that the first flip comes up heads?
A triangular plate with height 3 ft and a base of 4 ft is submerged vertically in water so that the top is 1 ft below the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Give your answer correc..
Search the internet to find two graphs to critique: one you evaluate to be a good graphical representation of the information presented and the other to be a poor graphical representation of the information presented.
A lodge borrows $120,000 for 10 months at an annual interest rate of 9.2%. What is the simple interest due on the loan?
Let p be a prime, let K be a number not divisible by p, and let b be a number that has a kth root modulo p. Find a formula for the number of kth roots of b modulo p and prove that your formula is correct. (hint. your formula should only depend on ..
What is the chance that the next 100 customers will pay an average of more than $128 (including the shipping & handling charges)?
Conditional probability: suppose that if θ = 1, then y has a normal distribution with mean 1 and standard deviation σ, and if θ = 2, then y has a normal distribution with mean 2 and standard deviation σ. Also, suppose P r(θ = 1) = 0.5 and P r(θ = ..
Use the numerical derivative operation to find the rate of change of f(x) at the given value of x. Give your answer accurate to four decimal places.
From the top of a 165 ft lighthouse, the angle of depression to a ship in the ocean is 23°. How far is the ship from the base of the lighthouse?
We want to study the movement of an ant on a grid over m time steps. Think of each time step as another iteration of a loop. The grid is (2n+1)(2n+1) in size centered at (0; 0). Each grid point can be colored white or black. Initially all grid poi..
Question 1: For small-business owners, it's not worth the time or effort to secure intellectual property rights (Canadian and International). Question 2: Explain why you agree or disagree with this statement using supporting facts, information an..
A low stone wall 27 inches high is 64 inches away from a building. What is the length of the shortest pole that passes over the fence and reaches the building?
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