Recent content by cyby

Information you need to know when you're graphing rational functions include... asymptotes and roots. Do you know where your horizontal asymptotes are? What about the vertical asymptotes? Beware, because your graphing calculator may or may not show asymptotes properly! What about the roots...

Why did you do 2*pi*r^2 for the area of the second segment?

The first thing you absolutely need to do is to figure out what 11^-1 mod 20 is.

Displacement is not distance traveled. Review the definition of what displacement is...

The difference is that you're limiting the *domain* of g to be positive. This said nothing about the function must evaluate to. What this is essentially saying is that g(1) is ok, but g(0.5) isn't, because 0.5 is < 1. Everything else looks good.

No. What you said was that x has to be \geq 1 , not g. There is a difference - can you tell me what the difference is?

No. If each side is 1.5cm, then the Volume would be (1.5)^3 = 3.375cm^3, not 2cm^3. The cube root of 2 is actually 1.2599..., which is about 1.26.

The original information will actually give you the density of gold, which is 19.3g/cm^3. Knowing that the density stays the same, you just need to apply the density formula to find the volume, and then cube root that to find the length of each side. If D = m/V, then V = m/D. Knowing that the...

Whereever you saw x, you needed to replace with 1/x. So all you really have is instead of 2*x + 5, you have 2*(1/x) + 5. If h(x) = 1/x + 5, and f(x) = 2x + 5 then you will actually have f(h(x)) = 2(1/x + 5) + 5 = 2/x + 15.

First of all, you do mean f(h(x)), and not fh(x), which to me looks like f(x)*h(x). Under that assumption... f(h(x)) = 2/x + 5. So, you have y = 2/x + 5.. To find the inverse, you usually just switch x and y, and solve appropriately. I'll start with the first step: x = 2/y + 5 Can you...

Oh, well, technically speaking, if your inequality was \leq , then you should include the endpoints in the interval. If your inequality was < , then you should exclude the endpoints. So what you're really working with is [2pi/3, 4pi/3].

If that is the only interval, then indeed it is! In these types of problems, you can always divide the set into intervals and find test points...

Since you have the roots - why don't you pick values between [0, 2pi/3), (2pi/3, 4pi/3), and (4pi/3, 2pi] to check? One or more of these intervals will give you your desired answer.

Keep in mind, x = x^1, so you can apply the power rule for this.

Clearly, is there is a 0.002 chance of it being stolen - then that is the probability they have to pay out $20,000. So the expected loss is (20,000)*(0.002) = $40. Take that away from the $300 they would make otherwise... and the expected profit is $260, as desired. As for the second problem...