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The last digit of 2 is 2.
The last digit of 22 is 2+2.
The last digit of 222 is 2+2+2.
The last digit of 2222 is _________.
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ABCD and A′BC′D are both rectangles with side lengths AD=A′D=2,AB=A′B=6. Find the area of shaded region (to 2 decimal places).
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The following is a conversation between Gabriel and Heather:
Gabriel: "I am thinking of two distinct single-digit numbers. Can you guess the sum of these two numbers?"
Heather: "No. Can you give me a clue?"
Gabriel: "The last digit of the product of the two numbers is your house number."
Heather: "Now I know the sum of the two numbers."
So, what is the sum of the two numbers?
Note: It is possible that the product of the two numbers is a single-digit.
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What is the diameter of the semicircle in the diagram below?
Note: The diagram is not drawn to scale.
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A bead slides under the pull of gravity, g, down a frictionless wire segment in the shape of the curve y=e−x, where x is the horizontal direction and y is the vertical direction. The bead starts from rest at (x,y)=(0,1).
The time it takes for the particle to travel between x=a and x=b can be expressed as
ta,b=2g1∫ab1+ReSx1+PeQxdx,
where P,Q,R, and S are integers.
Determine P+Q+R+S.
Note: The constant e is Euler's number.
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