## Answers by Jon P.

I assume that the function is supposed to be:  y = (x8)sin x.  Is that correct?   If so, then what I would do is start by taking the log of both sides:   ln y = sin x ln x8 = (sin x) * (8 ln x) = 8 (sin x)(ln x)   Now differentiate both sides. ...

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...

Solving these problems is generally just a matter of stepping through the facts and seeing what they lead to.   First of all, they say that each side of the square is 6 cm.  The perimeter of a square is 4 times the length of a side, because there are 4 sides and they are all the...

Notice that the denominator, 25, is 1/4 of 100, or in other words you can multiply the denominator by 4 to get 100.   So multiply the fraction by 4/4, which is equal to 1.  That way you don't change the value of the fraction, but you multiply both the numerator and the denominator...

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...

Each team has 5 other teams to play, so if they play each team twice, that means that each team plays 10 games.   Since there are 6 teams, that looks like it might mean 60 games.  HOWEVER, when team A plays team B and it gets counted as one of team A's games, team B is playing...

Each number is 200 more than the one before it.  So the next number is 3865 + 200 = 4065.

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...

It looks to me that you did it right, and when I graph the equation I see the vertex where you say it should be.    Try graphing again -- maybe your graph wasn't right.

The y-axis is the line at which x = 0.  So substitute 0 for x in the equation:   y = 0 - 3 = -3.   So when x = 0, y = -3.  So the graph crosses the y-axis at the point (0, -3).

There are several things you can gather from the question:   - Since both started at the same time, and they met at the same time (obviously!  that's what "meet" means!), that means that the time they traveled was the same.  Call that t. - Since distance = speed...

You do this one coordinate at a time -- x, followed by y, followed by z.   The x-coordinate of the first point is 3, and the the x-coordinate of the second point is -2.  That's a difference of -5.  3/5 of that is -3, which means that 3/5 of the way from the first point's x-coordinate...

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 +...

Also...   1. They created the Electoral College for election of the President.  That meant that the voters do not vote directly for President.  They vote for a group of "electors" in each state who then vote for President.  Usually the Electoral College elects...

Start by defining variables to represent the amounts of each of the solutions that are going to be mixed.   So let x = the amount of the 60% solution, and y = the amount of the 30% solution.   First of all, you know that x + y = 300, because after they are mixed you...