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A prime number which is afactor of 20 30 and 105?
Five
What are the factors of 800 in afactor tree?
800 400,2 200,2,2 100,2,2,2 50,2,2,2,2 25,2,2,2,2,2 5,5,2,2,2,2,2
What word means the number like 101001000 and so on It is the result of using only 10 as afactor?
decimal
Is 7 afactor of 63?
Try it. Divide 63 by 7, for example with a calculator - if you get only zeroes after the decimal point, then it is.
Do you have to put it twice when you multiply it byitself?
no you dont because it is afactor of that number. example: what is the factors of 4 and 16 1,2and 4 1,2,48,and 16
Is 24 a multiple or factor of 4?
'24' is a multiple of '4' ( 4 x 6 = 24) However, '4' is a factor of '24'.
What is the convesion afactor?
A conversion factor is a ratio that expresses how one unit is equivalent to another unit. It is used to convert from one unit to another in mathematical calculations, especially in chemistry and physics. For example, the conversion factor between feet and meters is 1 foot = 0.3048 meters.
What is the GCF of 48 and 140?
48=2*24 24 is not a factor of 140 48=3*16 16 is not afactor of 140 48=4*12 12 is not a factor of 140 48=6*8 6and 8 are not factors of 140 48=2*2*2*2*3 140=2*2*5*7 GCF is 2*2=4
What is descimation?
a Descimator is basically nothing but a down sampler or simply one which reduses the signal sampling rate.the basic working of adecimator can be illustrated with an example eg:consider a signal x(n)={1,2,2,3,1,-3,4,2}and we are told to descimate this by afactor of 2 then then output result would be y(n)={1,2,1,4} which clearely shows that u have reduced the number of samples therby reducing the frequency rate so when we descimate by a factor M we should discard M-1 samples
Prove that there is no rational number whose square is 3?
This is the same as proving the square root of 3, which I will write sqrt(3) is irrational. When I prove that, I am proving there is not rational number whose square is 3. So here goes: I put some extra help comments in (extra help) like this. Just ignore them if you don't need them.Let sqrt(3) = a/b where a and b are integers and they are in lowest terms, meaning they have no common factors, WE know if they had common factors we can always find another expression that has no common factors by canceling out the common ones. So a/b does exist.squaring both sides of sqrt(3) = a/b gives us 3 = a2/b2 so a2 = 3b2Now a2 must have its factors as even powers of primes.(because of the exponent 2 on the left and both sides must have the same total power since they are equal). So it musthave 32 as one of its factors. (can't be just 3 since that is 31 which is an odd exponent and when added to the 2 in b2 gives us an odd exponents also) This means a must have 3 as a factor. ( if 32 is a factor then 3 must be also)Now 3b2 has a factor 32 so b2 has afactor 3. But if b2 has a factor 3, then since powers must be even,it has 32 as a factor. This means that b must have 3 as a factor also.So we have shown that both a and b have 3 as a factor. But we statedthat a/b has no commonfactors and we just found one, namely 3. So we have a contradiction, and it follows thatwe cannot express sqrt(3) as a rational fraction.Here is another proof from WikiAnswers.com from someone who asked the same question.The number, , is irrational, ie., it cannot be expressed as a ratio of integers a and b. To prove that this statement is true, let us assume that is rational so that we may write= a/b1.for a and b = any two integers. We must then show that no two such integers can be found. We begin by squaring both sides of eq. 1:3 = a2/b22.or3b2 = a22a.If b is odd, then b2 is odd; in this case, a2 and a are also odd. Similarly, if b is even, then b2, a2, and a are even. Since any choice of even values of a and b leads to a ratio a/b that can be reduced by canceling a common factor of 2, we must assume that a and b are odd, and that the ratio a/b is already reduced to smallest possible terms. With a and b both odd, we may writea = 2m + 13.andb = 2n +1Therefore,(a)^2 + (b)^2 = (2m+1)^2 + (2n+1)^2and(a)^2 - (b)^2 = (2m+1)^2 - (2n+1)^2Also,[(a)^2 + (b)^2] / [(a)^2 - (b)^2] = 2Which leads to:[2(m^2 + n^2) + 2(m + n) + 1] / [2(m^2 - n^2) + 2(m - n)] = 2Which is impossible since numerator is odd but denominator is even.One more proof for you. Sometimes one proof makes more sense to a given person. Also, it is nice to see things proved in a slightly different wayIf √3 is rational, we can express it as a/b, a fraction in its lowest terms this mean the greatest common divisor or gcd of a and b written (a,b) or gcd(a,b) = 1. Also it is important to note that b is not 1, because that would mean √3 is an integer, which we know it is not.Now square both sides as we did in the other proofs.√3 = a/b3 = a²/b²since gcd(a,b) = 1, then gcd(a²,b²) = 1 (This is because if the there are no common factors and you square it, you stilll have no common factors, look at 2/3 for example, gcd (2,3)=1 and 4/9 still has gcd of 1 because is is 2/3 x2/3)But from 3 = a²/b² we can write a² = 3b².we can write this as a²/b² = 3b²/b² (since b2 /b2 =1) This fraction is clearly NOT in its lowest terms (remember, b is not 1) hence the contradiction.and we have that √3 is not rational.
What are some differences between the Wrangler and the Sahara Jeep?
ORIGINAL ANSWER:The Jeep Wrangler in the 2007 model year has three variants: therUnlimited, the Rubicon, and the Sahara. So this means that theWrangler is the Jeep Model, whereas the Sahara is a package optionfor it.**************************************************************ANSWER; LONG VERSION: (Scroll Down for SHORT VERSION in BOLD)First off, there are more "variants" in the 1997 models than thoselisted. In fact, the above answer lies somewhere between misleadingand dead wrong -although they are all Jeep Wranglers, the Rubicon and UnlimitedModels are very different animals.Here's The ScoopThe Rubicon is for serious off-roading. If you are serious aboutfour wheelin' or considering a Rubicon, please read the paragraph atthe end of this post! It contains very important information.The Unlimited is longer, and newer Unlimiteds are 4 Door Vehicles.It was introduced in 2004, and originally was just a bit longer fromnose to tail, with notably more room in the rear cargo area. Then in2007 (or so) the Unlimited got even longer, and grew doors for theback seat passengers. This is a very nice addition to the lineup,but for those interested in off-roading, be advised that the longerwheelbase will adversely affect your break-over angle.ANSWER; SHORT VERSION:The Sahara is a Jeep Wrangler, in its traditional 2 Door formfactor, with a multitude of upgrades.The Sahara package includes 6 cylinder engine, Premium Rims, FogLamps, A/C, CD Player w/better sound system, Leather trimmedsteering wheel, Full Metal Doors with Glass Windows, "SaharaBadging" (decals that say "SAHARA" - 1 on each side of the Jeepbetween front wheel wells and the door hinges), Side Steps, PremiumCloth Seats, Premium Floor Mats, Premium Soft Top, and a few moredepending on year.In recent years, the Sahara edition also includes ElectronicStability Control, Power Windows and Locks, Keyless Entry/Alarm, 7Speaker Infinity Sound System (350 watts), Height-AdjustableDriver's Seat, 18" Rims with Premium Tires, Floor Console, TintedWindows, Cruise Control, Traction Control, Tow Hooks - 2 Front and 1Rear. Also note that in recent years, they have eliminated the 4cylinder engine, and even the base model comes with a 6 cylinderengine.The "Sport" package includes the following: 6 cylinder engine, Alloyrims, Fog Lamps, A/C, CD Player w/better sound system, Leathertrimmed steering wheel, and "Sport Badging" (decals that say "SPORT"- 1 on each side of the Jeep between front wheel wells and the doorhinges). Sport also includes a ton more upgrades in recent years,like Electronic Stability Control, Larger Rims and Better Tires,Cruise Control, etc. It is now just called the "S" package.NOTE:each individual vehicle can have individual upgrades above and beyond anincluded package. Example: I bought a brand new 2002 Wrangler w/the"X" package. The X package included basically everything the Sport package includedexcept for floor mats and fog lamps. But, in addition to having the X package,my Jeep also had an upgraded stereo system and Trac-Lock. Trac-Lock is afeature that automatically locks the rear differential if it sensestoo much slip. It's great. Even when in 2 (rear) wheel drive on wetroads, I had excellent traction.Only Read the following if you are into off-roading, considering aRubicon, or love tech talk.The Rubicon's 4WD system, driveline and axles are designed for off-roading. You will not get better on-road performance from a Rubicon!You will actually get better on-road performance from non-Rubiconmodels. RUBICONS ARE MEANT FOR OFF-ROADING AND DO NOT HAVE TRACTIONCONTROL OR STABILITY CONTROL. THE 4WD SYSTEM IS PART TIME AND MEANTONLY FOR OFF-ROAD USE OR KNEE-DEEP SNOW. You WILL cause prematurewear on the axles, transmission and the transfer case if you engagethe Rubicon's 4WD system on-road and you drive on dry pavement. Evenon wet roads, the full time 4WD systems on the other models willperform better. And hitting that dry patch will make itliterally hop around turns. If you are not holding on tightly, itcould even rip the steering wheel from your grip, and you may wellslam into oncoming traffic. The only advantage whatsoever to begained from the Rubicon in on-road use is from the traction of thetires in deep snow. BUT this advantage can be added to ANY Wranglerby simply getting tires with a more aggressive tread. All Wranglerswill handle the larger size tires found on the Rubicon - 255/75/Rxx(rim size varies from year to year and is not afactor). Beware, however! This is overkill in most situations. Mostof these aggressive tread tires, like the Goodyears on the Rubicon,are Mud Tires. The rubber is made of a harder compound, and, whenyou attempt to stop abruptly on wet pavement, you will slide likeyou are on ice! Trust me! I did it! I put 31" Goodyear MT/R's on myWrangler, and when I went to to stop abruptly on slightly wetasphalt, I slid uphill -only slightly uphill, but I kid you not! Islid UPHILL through a red light and hit some old dude in an Impala.I creamed his car, and damn it, I bent my Warn Rock Crawling Bumper!AGGRESSIVE TREAD / MUD TIRES SUCK ON ROAD!I feel that anyone who buys a Rubicon and does not use it for off-roading should be shot in the knee caps... and then hanged. lol...
Guidance for heat sink selection in semiconductor devices?
Heat-Sink SelectionIn selecting an appropriate heat sink that meets the required thermalcriteria, one needs to examine various parameters that affect not only the heatsink performance itself, but also the overall performance of the system. Thechoice of a particular type of heat sink depends largely to the thermal budgetallowed for the heat sink and external conditions surrounding the heat sink. Itis to be emphasized that there can never be a single value of thermal resistanceassigned to a given heat sink, since the thermal resistance varies with externalcooling conditions. When selecting a heat sink, it is necessary to classify the air flow asnatural, low flow mixed, or high flow forced convection. Natural convectionoccurs when there is no externally induced flow and heat transfer relies solelyon the free buoyant flow of air surrounding the heat sink. Forced convectionoccurs when the flow of air is induced by mechanical means, usually a fan orblower. There is no clear distinction on the flow velocity that separates themixed and forced flow regimes. It is generally accepted in applications thatthe effect of buoyant force on the overall heat transfer diminishes tonegligible level (under 5%) when the induced air flow velocity excess 1 2 m/s(200 to 400 lfm).The next step is to determine the required volume of a heat sink.. Table 2shows approximate ranges of volumetric thermal resistance of a typical heat sinkunder different flow conditions.Flow conditionm/s (lfm)Volumetric Resistancecm3 °C/W (in3 °C/W)natural convection500-800(30-50)1.0 (200)150-250(10-15)2.5 (500)80-150(5-10)5.0 (1000)50-80(3-5)Table 2: Range of volumetricthermal resistanceThe volume of a heat sink for a given low condition can be obtained bydividing the volumetric thermal resistance by the required thermal resistance. Table 2 is to be used only as a guide for estimation purposes in the beginningof the selection process. The actual resistance values may vary outside theabove range depending on many additional parameters, such as actual dimensionsof the heat sink, type of the heat sink, flow configuration, orientation,surface finish, altitude, etc. The smaller values shown above correspond to aheat sink volume of approximately 100 to 200 cm3 (5 to 10 in3)and the larger ones to roughly 1000 cm3(60in3).The above tabulated ranges assume that the design has been optimized for agiven flow condition. Although there are many parameters to be considered inoptimizing a heat sink, one of the most critical parameters is the fin density. In a planar fin heat sink, optimum fin spacing is strongly related to twoparameters: flow velocity and fin length in the direction of the flow. Table 3may be used as a guide for determining the optimum fin spacing of a planar finheat sink in a typical applications.Fin length, mm (in)Flow conditionm/s (lfm)753.01506.02259.030012.0Natural convection6.50.257.50.30100.38130.501.0 (200)4.00.155.00.206.00.247.00.272.5 (500)2.50.103.30.134.00.165.00.205.0 (1000)2.00.082.50.103.00.123.50.14Table 3: Fin spacing (in mm/inches) versus flow and fin lengthThe average performance of a typical heat sink is linearly proportional tothe width of a heat sink in the direction perpendicular to the flow, andapproximately proportional to the square root of the fin length in the directionparallel to the flow. For example, an increase in the width of a heat sink by afactor of two would increase the heat dissipation capability by a factor of two,whereas and increase the heat dissipation capability by a factor of 1.4. Therefore , if the choice is available, it is beneficial to increase the widthof a heat sink rather than the length of the heat sink. Also, the effect ofradiation heat transfer is very important in natural convection, as it can beresponsible of up to 25% of the total heat dissipation. Unless the component isfacing a hotter surface nearby, it is imperative to have the heat sink surfacespainted or anodized to enhance radiation.Heat Sink TypesHeat sinks can be classified in terms of manufacturing methods and theirfinal form shapes. The most common types of air-cooled heat sinks include: Stampings: Copper or aluminum sheet metals are stamped intodesired shapes. they are used in traditional air cooling of electroniccomponents and offer a low cost solution to low density thermal problems. Theyare suitable for high volume production, because advanced tooling with highspeed stamping would lower costs. Additional labor-saving options, such astaps, clips, and interface materials, can be factory applied to help to reducethe board assembly costs.Extrusion: These allow the formation of elaboratetwo-dimensional shapes capable of dissipating large heat loads. They may becut, machined, and options added. A cross-cutting will produceomni-directional, rectangular pin fin heat sinks, and incorporating serratedfins improves the performance by approximately 10 to 20%, but with a slowerextrusion rate. Extrusion limits, such as the fin height-to-gap fin thickness,usually dictate the flexibility in design options. Typical fin height-to-gapaspect ratio of up to 6 and a minimum fin thickness of 1.3mm, are attainablewith a standard extrusion. A 10 to 1 aspect ratio and a fin thickness of 0.8″can be achieved with special die design features. However, as the aspect ratioincreases, the extrusion tolerance is compromised.Bonded/Fabricated Fins: Most air cooled heat sinks areconvection limited, and the overall thermal performance of an air cooled heatsink can often be improved significantly if more surface area can be exposed tothe air stream. These high performance heat sinks utilize thermally conductivealuminum-filled epoxy to bond planar fins onto a grooved extrusion base plate. This process allows for a much greater fin height-to-gap aspect ratio of 20 to40, greatly increasing the cooling capacity without increasing volumerequirements.Castings: Sand, lost core and die casting processes areavailable with or without vacuum assistance, in aluminum or copper/bronze. thistechnology is used in high density pin fin heat sinks which provide maximumperformance when using impingement cooling.Folded Fins: Corrugated sheet metal in either aluminum or copperincreases surface area and, hence, the volumetric performance. The heat sink isthen attached to either a base plate or directly to the heating surface viaepoxying or brazing. It is not suitable for high profile heat sinks on accountof the availability and fin efficiency. Hence, it allows high performance heatsinks to be fabricated for applications.Figure 2 shows the typical range of cost functions for different types ofheat sinks in terms of required thermal resistance.Figure 2: Cost versus required thermalresistanceThe performance of different heat sink types varies dramatically with theair flow through the heat sink. To quantify the effectiveness of differenttypes of heat sinks, the volumetric heat transfer efficiency can be defined aswhere, m is the mass flow rate through the heat sink, c isthe heat capacity of the fluid, andTsa isthe average temperature difference between the heat sink and the ambient air. The heat transfer efficiencies have been measured for a wide range of heat sinkconfigurations, and their ranges are listed in Table 4.Heat sink typen range,%Stamping & flat plates10-18Finned extrusions15-22Impingement flowFan heat sinks25-32Fully ducted extrusions45-58Ducted pin fin,Bonded & folded fins78-90Table 4: Range of heattransfer efficienciesThe improved thermal performance is generally associated with additionalcosts in either material or manufacturing, or both.Thermal Performance GraphPerformance graph typical of those published by heat sink vendors are shownin Fig. 3. The graphs are a composite of two separate curves which have beencombined into a single figure. It is assumed that the device to be cooled isproperly mounted, and the heat sink is in its normally used mounting orientationwith respect to the direction of air flow. The first plot traveling from thelower left to the upper right is the natural convection curve of heat sinktemperature rise, Tsa,versus Q. The natural convection curves also assume that the heat sinkis painted or anodized black. The curve from the upper left to lower right isthe forced convection curve of thermal resistance versus air velocity. Inforced convection,Tsaislinearly proportional toQ, hence Rsa is independent of Q and becomesa function only of the flow velocity. However, the natural convectionphenomenon is non-linear, making it necessary to presentTsa asa function of Q.Figure 3: Typical performance graphsOne can use the performance graphs to identify the heat sink and, for forcedconvection applications, to determine the minimum flow velocity that satisfy thethermal requirements. If the required thermal resistance in a force convectionapplication is 8 °C/W, for example, the above sample thermal resistanceversus flow velocity curve indicates that the velocity needs to be at or greaterthan 2.4 m/s (470 lfm). For natural convection applications, the requiredthermal resistance Rsa can be multiplied by Qtoyield the maximum allowableTsa. The temperature rise of a chosen heat sink must be equal to or less than themaximum allowableTsa atthe same Q.The readers are reminded that the natural convection curves assume anoptional orientation of the heat sink with respect to the gravity. Also, theflow velocity in the forced convection graph represent the approach flowvelocity without accounting for the effect of flow bypass. There have been alimited number of investigations2,3 on the subject of flow bypass. These studies show that flow bypass may reduce the performance of a heat sink byas much as 50% for the same upstream flow velocity. For further consultation onthis subject, readers are referred to the cited references.When a device is substantially smaller than the base plate of a heat sink,there is an additional thermal resistance, called the spreading resistance, thatneeds to be considered I the selection process. Performance graphs generallyassume that the heat is evenly distributed over the entire base area of the heatsink, and therefore, do not account for the additional temperature rise causedby a smaller heat source. This spreading resistance could typically be 5 to 30%of the total heat sink resistance, and can be estimated by using the simpleanalytical expression developed in Reference 4.Another design criterion that needs to be considered in the selection of aheat sink, is the altitude effect. While the air temperature of an indoorenvironment is normally controlled and is not affected by the altitude change,the indoor air pressure does change with the altitude. Since many electronicsystems are installed at an elevated altitude, it is necessary to derate theheat sink performance mainly due to the lower air density caused by the lowerair pressure at higher altitude. Table 5 shows the performance derating factorsfor typical heat sinks at high altitudes. For example, in order to determinethe actual thermal performance of a heat sink at altitudes other than the seallevel, the thermal resistance values read off from the performance graphs shouldbe divided by the derating factor before the values are compared with therequired thermal resistance.Altitudem/ftFactor0, sea level1.00100030000.951500 50000.90200070000.863000 100000.803500120000.75Table 5: Altitude deratingfactorsReferencesAavid Engineering, Inc., EDS #117, InterfaceMaterials, January 1992.R.A. Wirtz, W. Chen, and R. Zhou, Effect of FlowBypass on the Performance of Longitudinal Fin Heat Sinks, ASME Journal ofElectronic Packaging",Vol.~116,pp.~206-211,1994.S. Lee, Optimum Design and Selection of Heat Sinks,Proceedings of 11th IEEE Semi-Therm Symposium, pp. 48-54, 1995.S. Song, S. Lee, and V. Au, Closed Form Equation forThermal Constriction/Spreading Resistances with Variable Resistance BoundaryCondition, Proceedings of the 1994 IEPS Technical Conference, pp. 111-121,1994.RELATED ARTICLESFlash Diffusivity Method: A Survey Of CapabilitiesThe development, specification, and quality control of materials used in electronics packaging and thermal management often require the measurement of thermophysi
