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Answers by Jon P.

a:  Yes, because each president has only one birthday   b:  No, because there could be more than one person living in a house.  So there can be more than one output, which means it is not a function.   c:  It depends.  If you're only looking at...

The rule for the function says take x and add it to the previous value of the function.  So if you just look at the integers, you have a sequence where the difference between each value and the one before is increasing by 1 at a time.  That's not the same as an arithmetic sequence, because...

This is the series 1 + 2 + 3 + 4 + ... + 10000, or stated in words, the sum of the first 10000 integers.   There's a simple rule for this sum:  n(n+1)/2, where n is the number of integers you're counting.  Try it for the first few values of n and see...

It's not a technical mathematical term, but in this case it probably means "negative".   So you'd have 4 consecutive even numbers:  n, n+2, n+4, n+6.  The statement can be written as follows:   -4(n + n+6) = 6 + -(n+2 +...

You'll need to use two rules:  derivative of a product, and chain rule.   Let's let f(x) = x, and g(x) = ln 2x   Dx f(x) g(x) = f(x) Dx g(x) + g(x) Dx f(x)   Dx g(x) = 1/(2x) Dx 2x = 1/(2x) * 2 = 1/x     (As an aside, notice that...

The remainder of 3 when dividing by 5 means that it has to end with 3 or 8.  But rhe remainder of 2 when dividing by 4 means it has to be an even number, so it has to end with 8, not 3.   Look at the pattern numbers ending in 8 as they are divided by 3:    8 /...

Unless I'm missing something, the two sides of each equation are exactly the same, except that on the left side the denominators are x and y, and on the right side, the denominators are 2 and 3.  Therefore at least one solution is x=2 and y=3.   Another way to solve them is simply...

First, notice that (a + 1/a)2 = 42 = 16.  But also, (a + 1/a)2 = a2 + 2a(1/a) + 1/a2 = a2 + 2 + 1/a2 = a2 +  1/a2 + 2   So a2 + 1/a2 + 2 = 16, so a2 + 1/a2 = 14.   Now, do that again...   (a2 +...

physics question (answer)

Call his takeoff speed v.  This is a vector that points at an angle of 28° above horizontal.    Start by resolving this vector into vertical and horizontal components.  The horizontal component (vx) is v cos 28° and his vertical component (vy) is v sin 28°.   Let's...