What Is The Smallest Value Of Radius R That Intersects These Circles?

From Mathematics Forum:

What is the smallest value of radius r that intersects these circles? If circles with radius r are drawn with all lattice points (points with integer coordinates) as centers, what is the smallest value of r that any line with slope 0.4, slope 2/5 intersects some of these circles.

Answer: r = 0.5

Why Is It So Difficult For Me To Pronounce The Spanish "R" In Promo, But Not For Others Like Tres?

From Languages Forum:

Why is it so difficult for me to pronounce the Spanish "r" in promo, but not for others like tres? I can pronounce the Spanish R correctly for a lot of words, but if you stick a P in front of it, I am baffled. Any tips on why Promo, and other certain consonants, are so hard?

Answer: The difference between your mouth forming a "p" sound and the Spanish "r" sound is considerably greater than shifting from a "t" to an "r". It's sort of like the difference between making a basket from half-court, and making one from the free-throw line. Because your tongue doesn't have as far to go between "t" and "r," the shift is easier and therefore you accomplish it more effectively.

How Can I Arrange The Letters R And L In 64 Different Ways Using 6 At A Time?

From Mathematics Forum:

How can I arrange the letters R and L in 64 different ways using 6 at a time? There are 64 ways to arrange the letters R and L, or any two letters, in 6 letter combinations like: LLLLLL LRLRLR RLLRRL etc.. I need six more. Please help!

Answer: OK this is the pattern: first 32 ... has L as first letter second 32 has R on second letter: first 16 has L second 16 has R third 16 has L fourth 16 has R on third letter: first 8 has L second 8 has R third 8 has L fourth 8 has R fifth 8 has L sixth 8 has R seventh 8 has L eighth 8 has R and thus the pattern so for each sequence of the next letter ... it just takes half the number of the prior set of letters to change ... until ultimately on the Th position ... you alternate between the letters . then you complete your combination .

Why Is My R&D Coefficient In A Production Function Turns Out To Be Statistically Insignificant?

From Economics Forum:

Why is my R&D coefficient in a production function turns out to be statistically insignificant? I am running a production function estimation to determine the elasticity of output with respect to R&D, I am obtaining a dubious result of an insignificant R&D coefficient although, bearing the correct sign. I am seeking an explanation of why this maybe so.

Answer: It depends on the definition of the R$D variable. The interpretation can be education,total factor productivity or technical improvement etc. Random variable can be also helpful.

What Is The Volume Of The Solid Of Revolution Generated By Revolving R About The X-Axis?

From Mathematics Forum:

What is the volume of the solid of revolution generated by revolving R about the x-axis? Let f(x) = e^(-3x/2) Let R be the region between the graph of f and the x-axis on the interval 0 < x < 1. Find the volume V of the solid of revolution generated by revolving R about the x-axis. I've been trying all night to figure this problem out with no luck at all. Please help!

Answer: Use the method of disks. Draw the region R and a typical disk. This disk has a radius of [e^(-3x/2) - 0] and a thickness of DC. It contributes an increment of volume Dav given by dV = πr²dx = π(e^(-3x/2))² dx = π e^(-3x) dx The total volume V is given by 1 ∫ π e^(-3x) dx 0

What Percentage Does H & R Block Charge For A Refund Anticipation Loan?

From United States Forum:

What percentage does h & r block charge for a refund anticipation loan? I need money and am expecting a decent tax return. Does anyone know the approximate amount that H & R block charges for one of its refund anticipation loans? And how much do they charge to do the actual taxes? I know it's a ripoff but I really need the cash so I am considering it.

Answer: DO NOT USE H&R BLOCK FOR A RAUL.....Efile on line yourself using direct deposit to get the refund in 8-14 days. H&R BLOCK along with HS BC BANK are running a scam this year with the Refund Anticipation Loan -- telling consumers that they have been approved for the loan and will receive the money in 1-2 days. However, people that have been getting the loan for the past 3, 5, 8 years are being denied all of a sudden, with the bank stating that their criteria for the loan changes every year. If you fill today 01/29/2009 on line with direct deposit, according to the IRS Refund Cycle Chart, you will see your refund deposited on 02/06/2009 -- just one week. Save yourself $300 and the headache of dealing with H&R Block and the Emerald Card, which is a way for H&R Block to "Hijack" your money, collect interest and cause a delay in your return.

Prove That If R Is A Commutative Ring With Unity, Then The Invertible Elements Form A Group With Respect To Th?

From Mathematics Forum:

Prove that if R is a commutative ring with unity, then the invertible elements form a group with respect to th? Part 1) An element a in a commutative ring R with unity e is said to be invertible if there is an element b in R such that ab=e. Prove that if R is a commutative ring with unity, then the invertible elements form a group with respect to the multiplication of the ring. Part 2) What is the group of invertible elements in ZZ4?

Answer: Write U = set of invertible elements in R. 1) Closure: a and b are in U then there exist a^-1 and b^-1 so that aa^-1 = bb^-1 = 1. Then (ab)(b^-1a^-1) = a(bb^-1)a^-1 = a(1)a^-1 = aa^-1 =1, so that ab is also in U. 2) Clearly U is associative since R is. 3) 1 is clearly in U. 4) Clearly, by the definition of U every element has an inverse. ---------------------------------------------------------------------------------------------------------------------- U(Z/4) = {1,3}. If a is invertible in Z/4 then ab = 1 mod 4 is solvable. So a can't be 2 otherwise A = 1 mod 4 implies 2 divides 1. If a = 1 then 1*1 = 1 mod 4, and if a = 3 then 3*3 = 9 = 1 mod 4. A more general way to do this part is: Using Bezout's theorem/Euclidean algorithm, gcd(a,4) = 1 implies ab = 1 +4d = 1 mod 4. The only numbers with gcd(a,4) =1 are a = 1 and 3.

What Is The Direct Correlation Of R-Value To Sound Dampening?

From Do It Yourself (DIY) Forum:

What is the direct correlation of R-value to sound dampening? Owens Corning Insulating R-19 compared to R-13 would reduce/absorb x% of sound. Typically sound absorption is rated as a coefficient with 1.0 being 100% and .5 being a 50% reduction. What value would R-19 or R-13 provide in reducing sound?

Answer: That's going to be hard to estimate because the R value of Owens Corning insulation is resistance to HEAT/COLD and not sound or vibration.

What Must Be The Value Of R For The Astronauts To Weigh 1/4 Of Their Earth Weight?

From Physics Forum:

What must be the value of r for the astronauts to weigh 1/4 of their earth weight? Suppose the surface (radius = r) of a cylindrical space station is rotating at 23.1 m/s to provide artificial gravity. What must be the value of r for the astronauts to weigh 1/4 of their earth weight?

Answer: Answer --> 217.6 m Given. v = 23.1 m/s a = 2.4525 m/s^2 (25% of 9.81 m/s^2 Earth gravity) Original equation is: a = v^2 / r Solve for r: r = v^2 / a With values: r = (23.1 m/s)^2 / (2.4525 m/s^2) r = (533.61 m^2/s^2) / (2.4525 m/s^2) r = 217.6 m

What Is The Radius R Of The Cone That Will Result In A Surface Area Of 6Π In^2?

From Astronomy & Space Forum:

What is the radius r of the cone that will result in a surface area of 6π in^2? A conical paper cup is to have a height of 4 inches. What is the radius r of the cone that will result in a surface area of 6π in^2?

Answer: 2 π r h = 6π in^2 & r = 4". h = 6 π / (2 πX4) = 3/4 ".

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