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A few things we will need:

x(t)=t-\frac{t^3}{3} \Rightarrow \frac{dx}{dt}=1-t^2 \Rightarrow \frac{d^2x}{dt^2}= -2t

y(t)=t^2 \Rightarrow \frac{dy}{dt}=2t \Rightarrow \frac{d^2y}{dt^2}= 2
...

okay, we have

x(t)=t-\frac{t^3}{3} \Rightarrow \frac{dx}{dt}=1-t^2

y(t)=t^2 \Rightarrow \frac{dy}{dt}=2t

z(t)=t+\frac{t^3}{3} \Rightarrow \frac{dz}{dt} = 1 +t^2

1) velocity is just...

The tangent of an angle is defined as the proportion of the opposite side to the adjacent side of a right triangle containing that angle, also called opposite over adjacent. So we can find the height...

I got it. I was thinking of having e raised to both sides and using the cubic formula. I need to think more before I post.

Can you verify that the problem is 5^{x-2}+5^{x^2}=626 ? I'll help you, but as it stands, it's crazy hard.

It's no trouble. I'm in the United States, Texas specifically. If you need anything else, just ask.

2L+2W=48 and L=3W.

Plugging in 3W for L and we get

2(3W)+2W=48 \Rightarrow 8W=48 \Rightarrow W=6

and so L=3W=3(6)=18 .

Hi adriancavinder, you have a lot of the fundamentals down, it refreshing to see someone asking for help on their homework and they've actually attempted the problem.

For the first question, the...

Oh, I didn't even notice that. Thanks jcarson2, stats has never been my strong point. :)

You need to double check your problem, you can't have a hyperbola with vertices (0,4) and (0,0) that passes through point (0, \sqrt{5}) . I think the x value of your third point is a typo, or a...

Okay the first thing you need to notice is that this hyperbola opens up and down. The way I know that is because the vertices and the foci are all on the line x=4 . Now the equation for such a...

First of all, I'm assuming you aren't returning any drawn ball to the bag. The probability against anything happening is simply one minus the probability for it happening. So if p is the probability...

I'm not exactly sure what you mean by "what the conic equation is". I think you mean what type of curve it is, also called the conic section. The reason it's called a conic section is because it's...

Glad I could help. As far as the gobbledeegook, formulas look best on this site when put in math brackets. At they beginning of a formula you type [*math] (without the asterisk) and at the end you...

Hi AdrianCavinder. I'm sorry I don't have the time to fully work this out right now. I have to be at work tomorrow and it's getting late over here. But just at a glance, before you take the...

Nerissa: can you double check you problem. You can't cut and paste, it doesn't display right. The hyperbola question I could kind of guess what you meant, but this one is a little to ambiguous.

I'm assuming that you mean 2x^2 + 4 = 4x +y^2 .
The first thing we need to do is put this in a form we can use. I can tell you from experience that this is an up-down hyperbola, because it is of...

It's been three month's since my first post, so I figured it was time for an update. It's really hard I'm not sure where to begin. I guess what I've been doing to heal is as good a place as any. I...

take the ten weeks and subtract it from the total number of weeks, so 14 is the number of weeks that you have left. So take the number of weeks that you have left, and divide it by 24 weeks. So you...

Let A be the number of pounds of type A coffee used, and let B be the number of pounds of type B coffee used. Since this months blend used three times as many pounds of type B coffee then type A...

Since both containers have the same amount of juice, we'll let x be that amount.

x+54 is the amount in the second container, and x-54 is the amount in the first. If the secon is four times...

"The bare bones about acid effects", "A tooth grinding report on the effects of acid on bones", "A story on the tooth fairy, a skeleton and acid", "A skeletal report on acids"

You're going to get bogged down with figures. This is one of those problems that you really need to be carful with your calculations. A simple mistake on any step will give you a bad solution....

first of all, you can't just cut and paste. If you mean a normal distribution curve with \mu=20, \sigma^2 =3 and \mu=20, \sigma^2 =6 , it's just two normal curves both centered on 20 with the...

First move the -13 to the other side and get x^2-2x=13 .
Since the coefficient of x^2 is one, multiply both sides by 4 and get:
4x^2 - 8x = 52 .
Square the coefficient of the original x ...

This problem is intentionally confusing. The kids and the swimming pool has nothing to do with anything. The fact that the truck broke down 16 miles away means nothing, and the cost per foot of...

Don't know if it's illegal, but I've always heard "the rule of seven". Take half your age and add seven, anything above that is acceptable. So half of 16 is 8, add 7, so 15 is the youngest you should...

Graph 3x=y. Your answer is everything below the line. (not including the line)

Piece of cake. Let x be the number. Since x divided by 10 gives a remainder of 9, then x+1 gives a remainder of zero when divided by 10. So x+1 is a multiple of ten. Similarly, since x ...

First, let me say I completely understand the feeling of disconnection associated with a combat tour. I spent a year looking for IED's in Iraq, I know how far away things can seem. I don't know...

arinteana: We aren't going to do your homework. Show me what you've tried, and tell me what you're stuck on, and I'll help you. Also, don't just cut and paste your problems. The first equation of...

That's exactly right

First of all, (y-k)^2 = 4a(x-h) gives a parabola, but it's sideways. We can still derive it, but the only way it's a function is if y is the domain and x is the range. It's a little weird, but...

Sounds like you got it. If you have any more questions, I haunt the Math & Science and Mathematics sections.

I'm sorry, I don't quite understand where you are lost. The answer, \frac{9 \cdot 8 \cdot 7}{3 \cdot 2 \cdot 1} isn't a factorial.

If you don't understand how we went from \frac{9 \cdot 8...

If you take out the ratio, the largest part would be 25.

The negative integer factors would be: -48 and -1, -24 and -2, -16 and -3, -12 and -4, -8 and -6. I've never heard of negative integral factors.

FYI, a quick Google search showed me that an...

ebaines: You're quicker on the draw today than me. :)

If you mean the binomial coefficient,
{n\choose k} = \frac{n!}{k!(n-k)!}

that's easy enough,

{9\choose 6} = \frac{9!}{6! \cdot 3!}

= \frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4...

If you have two consecutive heads and toss a coin again and it isn't heads, then you will no longer have two consecutive heads. You may get a heads on a subsequent toss, but that would not be three...

While I was typing this I also thought of seeing \equiv is used in modular arithmetic. For example, 9\equiv 15 (\ mod{6}) . Now that I think about it, that is probably the most popular use for it....

does it look like this -----> \equiv . It's a general equivalence relation symbol, that is it's used to indicate an equivalence between the two objects on either side of the relation symbol. The...

Since x+y =z and x+y+z=3000 , we get
x+y+z=z+z=2z=3000 \Rightarrow z=1500
And since x+y= z= 1500 \Rightarrow x=1500-y
So
.12 \cdot x +.13 \cdot y + .14 \cdot z = 400
\Rightarrow .12...

Sexual attraction is necessary, but by no means sufficient, for a relationship. As far as not liking his sense of humor, I think a lot of times we're willing to tolerate more if we're more attracted...

Statistics isn't my specialty, so I apologize in advance if I get the terms wrong.

What you need to do is find out how many children in the study have an alcohol related issue and have one...

Tut: Sorry, I didn't see your answer before my last post. The answer was right, but the way you got there was imprecise. Your solution implies that the rocket was going at a constant velocity of 600...

I got the change in D by taking the derivative of D . Remember, D was simply a function in terms of the height. Perhaps a less confusing way to look at it would be:

D = \sqrt{H^2 +400^2} ...

JudyKayTee: I never said she was anything, just that she might be emotionally abusive. And the issue was not that she didn't want to date him it was that she did want to and then didn't, and then she...

It's possible that this is one of those girls that likes not liking her relationship. She'll say she hates relationships, but instead of not being in a relationship, she'll always be in one...

Show me what you've tried and where you are stuck, and I'll be happy to help you. Also you need to rewrite your equation. Some of the signs didn't show, and I'd need to know exactly what it is you...