# Search results

1. ### Story Problem w/ parabolas

If its a perfect parabola, then what's the x coordinate of the maximum height?
2. ### Simple Conic I am sure - Overlooking it

Rewrite the 4 so that you have x^2/something. Do the same thing with the 3
3. ### Alternate ways to show a line is a tangent to a curve

With calculus you can show that the given line and the line tangent to the circle at the single intersection point are one and the same. But all you need to do is prove that there is only one intersection
4. ### Best PreCal Text to Prep for SAT Subject Math IIC Test?

What math will you be taking now? Will you have to start from scratch or just review? I went to sparknotes.com to review and look for tips on 3D geometry and sequences. Its pretty good for things on the test you may not have been exposed to in precalc class, but there probably arent enough...
5. ### Is this true: |x|=+-x?

|x| is either positive or negative, but not both at the same time. When taking the square root of both sides of an equation, you must take cases and usually come up with 2 possible solutions, a positive and negative answer
6. ### Determine the value of this function

Thats exactly what it is! 2 equations with 2 unknowns, except your variables are f(2) and f(1/2). We have no clue what these can be, so you need to substitute or eliminate to solve for f(2). The hard part was noticing the trick of letting x=1/2. After that, its all algebra
7. ### Relation between the gravitional constant and the given equation

Yes, thats the "range equation", assuming no air resistance. Notice that complementary angles result in the same range. As for the original question, you dont need calculus for a parabola. Find the axis of symmetry and plug in to find the y coordinate of the vertex.
8. ### Mod of Sine Equation

There is a relationship between b and the period of the function. Assuming this is a vertical position versus time function, the horizontal shift c is often called a phase shift and tells where equilibrium (y = 0 for a sine function) is in relation to the clock. With no phase shift, the function...

You need to use a sign graph because you dont know if the interval from 0 to 1 is positive or negative. If the question asked x2-x > 0 , your method of "just set them equal" would come up with the same interval. The correct answer is everything but 0 to 1, negative infinity to 0 or 1 to positive...
10. ### Convince a classmate that division is not associative.

Its called indirect proof or proof by contradiction, and its a perfectly legitamate form of proof. Assume to the contrary (division is associative) and work until you reach something that cant be true
11. ### Hi, could anyone help me with a algebra question

Guess factors of 60 to plug in using synthetic division/substitution
12. ### Hilbert Hotel

Along the same lines, its important to remember that there are just as many prime numbers and integers as there are natural numbers. Intuitively, youd think there would be more natural numbers, but the cardinality of all 3 sets is aleph0
13. ### Sine, cosine and tan graphs

Either brush up on the unit circle or do a bunch of memorizing: http://img404.imageshack.us/img404/6708/trigbi7.png [Broken]
14. ### How Do I Derive Equation From a Graph?

You can get a best fit line from a graphing calculator or Excel, seeing as you already have the data in there
15. ### Make x the subject of

Another thing to be careful of is when you take the square root of both sides of an equation. \sqrt{x^2} doesn't equal x, it equals the absolute value of x \sqrt{(-2)^2} = |-2| = 2 If you have: x^2 = 4 and take the square root, you should get x = +/-2 because \sqrt{x^2} = 2 = |x|
16. ### Solving Trigonometric Equations

You can solve it like any other quadratic. What would you do with 2y2 + 3y = 0 ?

In the limit, only the highest degree matters. Because the numerator and denominator have the same degree, the function will have a limit (horizontal asymtote) approaching infinity. Divide the coefficient of the numerator by the coefficient of the denominator and you have all thats left when x...

For #2, when you plug -27 in you get a number over a nonzero. That means the limit equals the value of the function, in this case, 0
19. ### Finding sums and squares

Or you can find the axis of symmetry once you have y = 2x^2 - 40x + 400
20. ### Prime factorization, Exponents

This was taken from a math contest a few months ago. Homework Statement xx*yy=zz find z if: x=28 * 38 y=212 * 36 Homework Equations Theres undoubtably some trick, but I have yet to find it The Attempt at a Solution Dont even think about calculator I showed my math teacher, and...
21. ### One Sided Limits Question

Plug in 2. You get a nonzero number over 0, which means dividing a common factor wont help. The graph is asymtotic at x=2. You can show which infinity the function goes to with a sign graph. Find all important numbers (roots, asymtotes) and evaluate the function in between each number. The graph...
22. ### Minimum value as x varies

You can do this or find the axis of symmetry and vertex. For parabolas, you dont need to use derivatives
23. ### Yes or no, Can you square root a zero

If you make the rather basic assumption that the question was posed over reals in an R^2 Cartesian plane, than imaginary numbers are not up for discussion. Furthermore, the concept of order (less than, greater than) dissolves in the complex number system, which makes delta-epsilon pretty hard to do
24. ### Yes or no, Can you square root a zero

If youre asking about the limit of \sqrt{x}, you can only approach it from the right. Because the limit point is unapproachable from the left, the limit does not exist. Remember, its not a polynomial so you cant just plug it in
25. ### Proof calculation help

You need to replace those 1's with the general form of an odd number. Put all odd numbers in terms of all whole numbers and do the binomial expansion