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No. While a Chihuahua-Dane cross might be problematic, Chihuahua-Shepherd and Dane-Shepherd crosses are not (Google is your friend). Dogs revert to the standard street mutt in just a couple generations -- if they survive. Survival for small breeds, if let run loose, is suspect. Dogs are neotenized wolves, small dogs much more so than big dogs. Like corn, which cannot survive in the wild, our domestication of the dog has bred a lot of the very traits needed for survival out of them. Toy breeds act like puppies (very young puppies) for their entire life because they essentially are puppies for their entire life.

So, just a plain old spherical cap. The integral you have in the original post is not quite right. It is missing a factor of two: It yields the area of the half of the spherical cap that extends above the x-y plane. Suppose the cap is the part of the sphere with [math]x>R-H[/math]. Let [math]z_+=\sqrt{R^2-(x^2+y^2)}[/math] and [math]z_-=-\,\sqrt{R^2-(x^2+y^2)}[/math]. The spherical cap comprises the two half-spherical caps defined by the functions z+(x,y) and z-(x,y). These two functions obviously have the equal areas over the x-y region of interest: determine one of them and multiply by two. For z+(x,y), the area is [math]A_{z_+}=\int_{R-H}^R \int_{-\sqrt{R^2-x^2}}^{\sqrt{R^2-x^2}} \sqrt{\frac {R^2}{R^2-x^2-y^2}}\; dy\,dx[/math] i.e., your integral in post #1 with limits specified. Note that I switched the integration order. How to solve this: Hint: Define [math]Y=\sqrt{R^2-x^2}[/math] and make the trig substitution [math]y=Y\sin\theta[/math]. You will get a ridiculously simple result. Remember to multiply by 2. An even easier way: This is a surface of revolution. An even easier way: The area [math]dA[/math] of an infinitesimal chunk of a sphere is [math]r^2\sin\theta d\phi\,d\theta[/math] (Mr. Skeptic's post #3).

Understanding Manish is pretty easy. "I'm hungry." Translation: "I'm hungry." When we don't say what we mean, women know exactly what we mean: "I feel like dancing!" Translation: "I'm horny." "So, you had a hard day at work. Would you like a backrub?" Translation: "I'm horny." "Nice dress!" Translation: "Nice cleavage! That makes me so horny!" The difference between Manish and Womanish starts at a young age. Example: A mother of all boys hears "MEOOW! bang crash thump" come from upstairs. She yells at her sons, "What was that?" The boys say "We just threw the cat down the laundry chute. It was cool." A mother of all girls hears "MEOOW! bang crash thump" come from upstairs. She yells at her daughters, "What was that?" The girls say "Nothing." "Nothing" can mean nothing, or everything. "What's wrong, honey?" "Nothing". That nothing might mean "Nothing, really. I had a hard day at work. But if I ask you for a backrub you'll want to have sex and I had too hard a day at work to even think about sex." Or it might mean "Nothing, really. But why do you ask? Is something wrong? Should I be worried? Should something be wrong? Have you been cheating on me?" And of course it might mean "Everything, you dumb dolt. Our relationship is going down the toilet. We really need to talk."

I'm going to be blunt, transgalactic: Do it yourself. You are using as a crutch homework help sites such as this, along with the plethora of other sites where you post the exact same questions. As a consequence, while you might be getting your homework done, you obviously are not learning a blasted thing. How are you going to fare when it comes to exam time? How are you going to fare in upper level courses where there aren't so many people around who can help? How are you going to fare in the real world where the people who can help work for companies that compete with the one for which you work?

mooey, do you mean a true spherical cap (the part of a sphere to one side of the intersection of a plane and a sphere), or some more generic shape? If you are indeed talking about a spherical cap, the answer is quite simple. I don't want to give it to you yet. Mr. Skeptic's equation will work quite well. Another approach: look at it is as a surface of revolution of a circular arc.

Trig substitution. General suggestions: ∫ f(x2+a2) dx -- try x=a tanθ, motivated by identity tan2θ+1 = sec2θ ∫ f(x2-a2) dx -- try x=a secθ, motivated by identity sec2θ-1 = tan2θ ∫ f(a2-x2) dx -- try x=a sinθ, motivated by identity 1-sin2θ = cos2θ

Ding ding ding ding!!! We have a winner! I suspect our female members would disagree.

I disagree. That view pretty much wipes out almost all useful physics. How much useful physics can you do without some observer-dependent quantities? The problem with relativistic mass is not that it is illusory. Velocity and energy are equally frame-dependent but are quite useful and very non-illusory concepts. The chief problem with relativistic mass is that it is synonymous with energy (literally synonymous; m=E/c2). The concept of relativistic mass doesn't add much of value (just use energy) but it certainly does add confusion.

While some non-scientific beliefs do not conflict with science, many do. Example: There is a lot of fake medicine out there. These faux medical techniques can kill people, either outright or by keeping the victims away from the medical techniques that could have cured them. Should scientists refrain from debunking those techniques just because some people believe these non-scientific techniques work? A lot of "religions, ghost hunters, and the supernatural believers" pretend to use science to authenticate their beliefs. They create evidence, ignore falsifying evidence, use every form of logical fallacy, all to justify their beliefs. Lying in the name of one's religion apparently is not a sin. Things like the Creation Museum damage science and society as a whole. Scientists have long learned that such garbage must be addressed. Look at it this way: Suppose some unscrupulous scientist falsifies evidence or creates an out-and-out hoax (e.g., Igor and Grichka Bogdanov, Charles Dawson, Hwang Woo-Suk, ...). Scientific ethics demands that these hoaxes be thoroughly exposed rather than ignored. How does creating fake fossils for pure greed differ in any way from creating false evidence in favor of young earth creationism? Scientific hoaxes, whether religiously motivated or not, must be addressed.

Just because some quantity depends on the observer's reference frame does not mean that that quantity is illusory. It just means it is frame-dependent.

It's called the "solar cycle" for a reason. Some people are wrong. No information exists on this phenomena because it doesn't exist. Look at it this way: A visibly variable sun would invalidate the climatological models that underlie claims of anthropogenic global warming. The large number of scientists who doubt the validity of AGW would have published evidence of a visibly variable sun in every major scientific journal that touches on climatology. There are no such publications. The solar cycle does not change the visible output of the Sun. It does change the invisible output of the Sun, and by quite a bit. The Sun puts out considerably more energy in the radio range during solar max than during solar min. The solar wind also increases significantly during solar max. You do not see radio waves or the solar wind.

Sione, this thread started with a misunderstanding on your part and then a stubborn insistence on your part that it was not a misunderstanding. To reiterate what has already been said, there is no absolute reference for velocity. Read up on Maxwell's equations. Thread moved to pseudoscience and speculation.

It had everything to do with health. The body excretes lead at an extremely low rate. Ingested lead, like mercury, tends to stay in the body and interferes with a number of bodily and mental functions. From http://www.nlm.nih.gov/medlineplus/ency/article/002473.htm (emphasis mine):

I'll make it extremely simple for you. We have extremely good kinematic observations of the sun and moon. We know that, whatever the cause, the Earth and Moon are accelerating toward one another at 2.73 millimeters/sec2. We also know that, whatever the cause, the Earth and the Moon are accelerating toward the Sun at 5.93 millimeters/sec2. These are facts. Gravity explains these facts quite nicely. Electrostatic models do not. If the Earth orbits the Sun solely by electrostatic attraction, one must be positively charged and the other negatively charged. If electrostatics is responsible for the Moon's orbit around the Earth, the Moon must be charged opposite that of the Earth -- the same as the Sun. Yet the Moon accelerates toward, not away from, the Sun, and with pretty much the same acceleration experienced by the Earth.

True simultaneity, and hence a universal "now", does not exist. Please read the links in post #6.

You make some rather extravagant claims. Show the math, and while you're at it, answer the question in post #17.

Arghhh! I was in the midst of writing an (overly long) rebuttal to Velikovsky's claims when my browser went belly up. In retrospect, there is no need. His claims have been fully falsified, repeatedly. His garbage is just that -- garbage. To Peron: Explain how planets can have moons, or humans can place artificial satellites in orbit about our Moon using only electrostatic principles. (Hint: The Sun would spit the Moon out of the solar system.)

The proper definition is [math]W=\oint {\mathbf F}\cdot d{\mathbf l}[/math] The "[math]\cdot[/math]" symbol indicates inner product. For a constant force and a straight line path this simplifies to [math]W={\mathbf F}\cdot {\mathbf d}[/math] Only in the very simple case where the force and displacement are aligned do you get W=F*d. These simplifying cases are used in high school physics because high school physics students (and unfortunately, their teachers) do not have the necessary mathematical background to understand the general formula.

Inability to properly convert Celsius to Fahrenheit notwithstanding, the ISS is not in thermal equilibrium with the ionosphere. Any largish structure in space will not come into thermal equilibrium with the extremely rarified medium that occupies that space. It will instead come into thermal equilibrium with the radiation that courses through that space. An object far from any star will come into thermal equilibrium with the cosmic microwave background radiation, 2.725 Kelvin. An object close to a star (Pluto is close to a star) will come into thermal equilibrium with the radiation emitted by the star.

What you are talking about, gib65, is the anthropic principle. The wiki article on this topic, http://en.wikipedia.org/wiki/Anthropic_principle, is fairly well written and has a lot of references. Google "anthropic principle" and you will find even more. Warning: A lot of what you will find on the 'net on this topic is pure mumbo-jumbo.

Anything with two dots above it means the second time derivative of the thing in question. In this case, the thing in question is some function phi, typically used to indicate some kind of potential energy.

Velikovsky? This garbage was debunked 60 years ago! Every single one of his points is false.

The numbers you quoted from Baez' Relativistic Rocket article simply assume the spacecraft has a constant proper acceleration of 1g. If you read the article further you will see how much fuel is needed to accomplish this voyage, and that is assuming perfect conversion of mass to photons.

The temperature of the stuff that occupies space and the temperature of an object in that space will not be the same. That is why Klaynos has asked "what kind of thermometer". The Earth's atmosphere extends (very tenuously) over 1,000 kilometers (620 miles) above the Earth's surface. 240 kilometers (150 miles) above the Earth is inside the atmosphere. The temperature of the atmosphere is around 1000o C at that altitude. A "large scale" thermometer would never get that warm. The Space Station, for example (http://science.nasa.gov/headlines/y2001/ast21mar_1.htm) heats up to about 250o C while sunlit and drops to about -250o C zero when shaded.

Coffee stains on the tray tables. "How can you trust the airplane maintenance when they can’t wipe the coffee stains off the flip trays?" (Tom Peters, "In Search of Excellence"). Sometimes a seemingly small thing such as coffee stains on the flip trays in an airplane can indeed derail the message. The airplane might well be very safe, or humans might well be causing significant harm to the natural environment, but all it takes is one seemingly unrelated item such as coffee stains or a grossly exaggerated claim of an ongoing mass extinction and the intended message is wiped out. Particularly so since we do not yet know what caused these past mass extinction events or how truly widespread they were. The logical fallacy here is pretending that the average extinction rate we see in the biological record is the same as the instantaneous extinction rate we see now. We do not know what the peak instantaneous extinction rate was during the past mass extinction events.