Wednesday

October 1, 2014

October 1, 2014

Total # Posts: 10,750

**Discrete Mathematics**

The idea is to reduce the nesting of parentheses which will then give possibilities of simplification. Remember to name the rule of simplification as justification. Start with the left-hand side: (p ^ (~ (~ p V q))) V (p ^ q) de Morgan's law: = (p ^ ( p ^ ~q)) V (p ^ q) ...
*July 26, 2013*

**Discrete Mathematics**

If I make the statement: If it rains then I stay home. I did not say what happens if it does not rain, so we don't get to know. The inverse would be: If it does not rain then I do not stay home. Here it is making a statement which is not derived from the original statement...
*July 26, 2013*

**Discrete Mathematics**

The inverse of If p then q would be If ~p then ~q (i.e. if not p then not q) We have p=(x+2)(x-3)>0, so ~p would be (x+2)(x-3)<0 and since q=x<-2 ∨ x>3 ~q would be x>-2 ∧ x<3 (de Morgan's law). If there is no typo, then we do not find the inverse ...
*July 26, 2013*

**Discrete Mathematics**

"I am not sure what this one is but I will see whether or not I get this right. If x < -2 V x < 3 then (x + 2) (x - 3) < 0 " This translates to If q then p, which is the converse of the original statement if p then q. Remember at the beginning I wrote: ...
*July 26, 2013*

**Discrete Mathematics**

There is no algebraic manipulation to be done, just like the raining and staying home. Let p = (x+2)(x-3) > 0 q = x<-2 ∨ x>3 Then p->q, or "if p then q", would translate to the original statement of If (x+2)(x-3)>0 then x<-2 ∨ x>3. The ...
*July 26, 2013*

**Discrete Mathematics**

The example is to apply mathematical logic to the results of the solution of an algebraic inequality. There is nothing to do algebraically, but to modify the original statement to make the converse, inverse and contrapositive. If the original statement were: "If it rains...
*July 26, 2013*

**Discrete Mathematics**

correction: p: (x+2)(x-3) >0 q: x<-2 ∨ x>3
*July 26, 2013*

**Discrete Mathematics**

Here's a summary drawn from: http://www.jimloy.com/logic/converse.htm statement: if p then q converse: if q then p inverse: if not p then not q contrapositive: if not q then not p For the given example: Statement: ∀x∈R, if(x+2)(x-3) > 0 then x<-2 or x>...
*July 26, 2013*

**Geometry**

Vertically opposite angles are equal. What is x when 4x=56?
*July 26, 2013*

**math :) **

You're welcome!
*July 26, 2013*

**math**

If the box has dimensions which are whole number of cm's, then it can fit 1200 cm³ / 1 cm³ =1200 cubes.
*July 26, 2013*

**mathematics**

You probably mean "All my other digits are the same." "I am five digit number greater than 40,000 but less than 60,000." means that the first digit is either 4 or 5. "My ones digit is 3 more than my ten thousands digit" means that the first and ...
*July 26, 2013*

**Psychology**

(C) is correct.
*July 26, 2013*

**math**

Fabrics are usually rectangular. So the given fabric will be assumed to be a rectangle with length 75" and width 45". Since the maximum dimension of a square cut from the fabric cannot exceed 45", the biggest square will be 45"x45". The corresponding ...
*July 25, 2013*

**Physics**

Let mass of water in Wa = Ma mass of glass = Mg a) mass = Ma+Mg b) mass = Ma + Mg - ρV + ρV = Ma + Mg c) mass = Ma + Mg + ρV - V = Ma + Mg - (ρ-1)V
*July 25, 2013*

**Physics**

a) buoyant force equal total mass, assuming the boat floats. b) From Archimedes principle, the total mass equals the mass of liquid displaced by the boat, so if h=height immersed, then 2*3*h*1000 kg = 4500 kg. Solve for h, and then subtract from 2 m to get the height out of ...
*July 25, 2013*

**Physics**

It was a typo. :) Net difference=1290-180=1110kg=total mass it can lift. Net payload=1110-500=610kg
*July 25, 2013*

**math :( do not post new questions at the end of other posts**

It would be to your advantage not to add on to other posts. Posting this question as a new post will get you a quicker response.
*July 25, 2013*

**math**

Excellent observation. I missed that!
*July 25, 2013*

**math**

Multiply the mass by the acceleration due to gravity, g, where g=9.81 m/s².
*July 25, 2013*

**Math**

They built a total of 42*4=168 chairs. Peter built 50 chairs, (the most), Paul built 49 (most below 50) Mary built 49 (most below 50) So Lent built 150-50-49-49=20 chairs.
*July 25, 2013*

**physics**

Ignoring air-resistance on the sensor. Horizontal acceleration, ah = 2.52 m/s² Horizontal component of force =m*ah Weight of sensor = mg Since the directions of m*ah and mg are orthogonal (at 90°), the vector sum is required for the tension of the cable T=sqrt((mg)^2...
*July 25, 2013*

**physics**

Assume the crate is below the worker, with a cable in-between. Mass of worker, mw = 833/9.81= 84.9 kg mass of crate, mc = 1380/9.81=140.7 kg Total mass = mw+mc= 225.6 kg Tension in cable above worker =(mw+mc)*(g+a) =225.6*(9.81+0.62) =2354 N Tension in cable between worker and...
*July 25, 2013*

**calculus (please help steve)**

Indeed. I have misread the question and just calculated the area. Some work will need to be done on the function F(x,y)=(x^2+y^2)^2/(x^2*y^2) because it is an improper integral as (x,y)->(0,0). The existence of the integral will have to be demonstrated at (0,0), and the ...
*July 25, 2013*

**calculus (please help steve)**

Typo: Y2(x)=-5.5+√(5.5^2-x^2) Subsequent lines are not affected.
*July 25, 2013*

**calculus (please help steve)**

Let C1: x^2+y^2=7x <=> (x+3.5)^2+y^2=3.5^2 C2: x^2+y^2=11y <=> x^2+(y+5.5)^2=5.5^2 We see that C1 has a centre at (-3.5,0), and C2 has a centre at (0,-5.5) Thus (0,0) is one of the intersection points. To find the other intersection point, we equate C1=C2 to get 7x...
*July 25, 2013*

**solid mechanics**

Unit volume expansion, e =εx+εy+εz =(1-2ν)(σx+σy+σz)/E Using σx=40*10^3 N σy=σz=0 E=205 GPa ν=0.3 Volume change =0.2*0.02*0.02*e =0.0008e
*July 25, 2013*

**solid mechanics**

Assuming an isotropic and elastic material, εy=-0.00775/40 σx=80 kN G=40 N/mm^2 (40 kN was probably a typo) Use εy=(σy-ν(σx+σz))/E ....(1) and G=E/[2(1+ν)] ...(2) Solve for ν by substituting E=2G(1+ν) from (2) into (1) &...
*July 25, 2013*

**solid mechanics**

Sorry, typo above: shear stress should have read τ. γ would have been shear strain.
*July 25, 2013*

**solid mechanics**

If I am not mistaken, tangential stress on a plane section at 60° to the longitudinal axis would be the shear stress, γ, and the normal stress on the same plane is the normal stress, σ. σx=250 kN / (0.1²) m² =25 MPa σy=0 α=60° ...
*July 25, 2013*

**Linear Equations in Two Variables**

The answer to this question is any point (x,y) which lies on the lien. To find points that lie on the line, substitute any finite value of x, and evaluate y. Present the answer as a coordinate pair (x,y). For example, let x=1, y=2x-3=2(1)-3=-1 So (1,-1) is a point on the line...
*July 23, 2013*

**To Debela Duguma**

Your question tucked at the end of another post was probably lost. Post the complete question as a new post if you would like help.
*July 23, 2013*

**statistics**

xBar > 50 => {49+61, 49+62, 61+62} => P(xBar>50)=3/7C2=3/28 xBar>60 => {61+62} => P(xBar>60)=1/7C2=1/28
*July 22, 2013*

**physics**

There are lots of assumptions made in this question. In reality, there is a temperature gradient between the outer part of the egg and the (yolk) in the middle, which means that the inner part of the egg is always cooler than the outer part. This gradient diminishes with time...
*July 22, 2013*

**statistic**

a numerical value for a correlation coefficient can never be greater than one or less than minus one.
*July 22, 2013*

**Gen physics**

μmg≥m|a| => |a|≤μg = 0.632g
*July 22, 2013*

**Dynamics**

gradient = rise/run = 0.06 At 1m/s (horizontal distance), the bike and the rider (mass=80 kg) gains potential energy of mgh = 80*9.81*(1m/s * 0.06) = 47.88 W Therefore speed (in the horizontal direction) = 200/47.88 m/s (horiz.) = 4.2474 m/s (horiz.) = 4.2474*(1.0018) m/s (on ...
*July 22, 2013*

**dynamics**

Sum work done and energies. Frictional force = F N Stopping Distance = D = 5 m Speed uphill = v = 6 m/s before braking: KE=(1/2)mv^2 PE=0 W=0 after braking: KE=0 PE=mg*Dsin(θ) W=D*F Equate KE+PE+W before and after braking, and solve for F.
*July 22, 2013*

**Data Structures and Algorithms**

If the question asks for the last digits, you could code and evaluate the recursive formula to get the results. If you would like a check, you are welcome. The sum of the 3 last digits is 20.
*July 22, 2013*

**Physics**

mass of horse = mass of water displaced (Archimedes principle) = 0.027*4.2*6.5 m^3 * 1000 kg/m^3 = 737.1 kg Weight of horse = mg = 737.1 * 9.81 N = 7230 N
*July 21, 2013*

**Calculus**

given f(x)=2√x Therefore f(1)=2*√1=2, which means that (x0,y0)=(1,2) is a point on the curve (given). Find f'(x)=(d/dx)2√x=1/√x the tangent at (1,2) is the line passing through (1,2) with a slope equal to it's slope, namely f'(1). Thus the ...
*July 21, 2013*

**physics**

Some reading will help you understand the subject, and also help you solve other problems faster. Read, for example: http://en.wikipedia.org/wiki/Total_internal_reflection
*July 21, 2013*

**Incomplete**

I hope you realize that incomplete questions are either not answered or will be put on hold until all information is supplied.
*July 21, 2013*

**Physics :)**

You're welcome!
*July 21, 2013*

**Physics**

Equate kinetic and potential (spring) energies: KE=(1/2)mv² PE=(1/2)ks² Solve for k k=mv²/s² N/m (verify that quantities are in consistent units).
*July 21, 2013*

**physics**

The same question has been answered twice before. See http://www.jiskha.com/display.cgi?id=1374277875
*July 21, 2013*

**MATH**

Move the decimal point of both numbers 2 places to the left to get 6.0288 divided by 2. Now divide each digit successively by 2 to get 3.0144.
*July 21, 2013*

**Math :)**

You're welcome!
*July 21, 2013*

**Math**

Divide 57 by 9 to get 6 with remainder of 3 (check: 9*6=54, 54+3=57) So the mixed number is 6 3/9 = 6 1/3
*July 21, 2013*

**math**

Lateral surface of a cylinder Al=2πr*h where h is measured along the axis of the cylinder. When the rectangle is rotated along it's length, then h=length, r=width. When the rectangle is rotated along it's width, then h=width, r=lengh. So you can calculate the ...
*July 21, 2013*

**Math<Please Help>**

Simple way: Multiply the planar area (25m*12m) by the average depth of (1+4)/2=2.5m to get volume= 750 m³. Calculate the area of the trapezoid which is obtained by cutting a vertical section along the length: 25*(1+4)/2. Multiply the above by the width of 12 m to get the ...
*July 21, 2013*

**Math**

Computers actually use binary number systems, since a switch can either be on or off. However, contents of computer memory is more concisely represented by octal and hexadecimal representations because 1. they are easy to convert to and from binary system 2. they are condensed...
*July 21, 2013*

**GCSE Physics**

Energy paid for =30/0.15=200 KWH Number of hours for boiler = 200 KWH / power of boiler The number of hours will not be know until the power of the boiler is known.
*July 20, 2013*

**math**

Q4c: 1/x^2*x*sqrt(x)*sqrt(sqrt(x))=a^c; 1/x^(1/4) = a^c x=a^(-4c) For: log5(5-4x)=log√5(2-x) log5(5-4x)=log5(2-x)² 5-4x=(2-x)² x=±1
*July 20, 2013*

**physics**

Volume of liquid =3.57*10^-4 m^3 =357 ml mass of liquid =357 g mass of aluminium (can) =421-357 =64 g density of aluminium = 2.7 g/ml Volume of aluminium = 64/2.7 cc = 23.7 cc
*July 20, 2013*

**geometry**

I am sorry about the incorrect designations. However, the same process can be used to solve for CP=3, although the result would be different. It seems to me that Steve's method is simpler, so use his method. Using Newton's method to solve for a non-linear equation f(x...
*July 20, 2013*

**geometry**

First draw the square ABCD and indicate a point P inside the square near the side AB about 1/3 from A to B. Label the lengths AP=1, PB=2, PD=3, and each side of the square s. Join BD and mark the length (√2)s. Label ∠APB as α, ∠DPA as β. Consider each ...
*July 20, 2013*

**Statistics**

The following reference may confirm your assumptions. http://cjasn.asnjournals.org/content/3/5/1246.full
*July 19, 2013*

**MAT LAB**

For 9_3, the question is not clear because we do not see the accompanying figure. However, on examining the data, it seems probable that the two "walls" (meaning no strain/movement along that direction) are in the y-direction, which means that εy=0. From the ...
*July 19, 2013*

**MAT LAB**

Note: Equations (A), (B) and (C) may be used to solve problem 9_2_1, namely Lx=L(1+εx),... Watch the signs of the stresses.
*July 19, 2013*

**MAT LAB**

Note that 1/20 is a relatively large strain and the above equations are approximate to first order and may not be accurate for large strains. Use the relations: εx=[σx-ν(σy+σz)]/E ....(A) εy=[σy-ν(&sigmaz;+σx)]/E ....(B) &...
*July 19, 2013*

**MAT LAB**

9_1_1 Recall that for an isotropic material, when σx is applied on a material of modulus of elasticity E, then the strains are: εx=σx/E from which e can be calculated. Since εy=-νσx/E, and similarly εz=-νσx/E, we are able ...
*July 19, 2013*

**Calculus**

This is a project you need to do using Mathematica. I suggest you go ahead and actually learn to use Mathematica to solve the above problems. If you have doubts and would like to check you results, you are welcome to post them for a check here.
*July 19, 2013*

**math**

Yes, 2655 in³.
*July 19, 2013*

**math**

Calculate volume of locker V=L*W*H Calculate volume of books (given) B=1545 in³ Calculate volume left =V-B
*July 19, 2013*

**Math**

The volume to be integrated is bounded by the planes 0≤x≤2 0≤y≤2 z=0 and the surface z=16-x²-2y². Thus the volume is given by the triple integral: V=∫∫∫z dz dx dy Where z is evaluated from 0 to 16-x²-2y², x and y are both evaluated ...
*July 19, 2013*

**math**

The rule for converting from metres to centimetres is that one metre equals 100 centimetres.
*July 18, 2013*

**Solution Set**

{x+y=3 ............(1) {-3x+2y=-19 ...........(2) Solve by elimination. Multiply (1) by 3 and add to (2) in order to eliminate x: 3x+3y=9 ..........3(1) -3x+2y=-19 .......(2) Add together 0x+5y=-19+9=-10 Solve for y: y=-10/5 = -2
*July 18, 2013*

**Calculus**

If you need help with finding the standard forms of the particular solution, check your course notes, your textbook, or the following link: http://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx
*July 18, 2013*

**Calculus-ODE**

Start with solving for the complementary solution to the homogeneous equation 2y"+3y'+y=0, the characteristic equation is 2r²+3r+1=0 which is an algebraic equation which can be factorized into (2r+1)(r+1)=0 or r={-(1/2), -1} The complementary solution is ...
*July 18, 2013*

**math**

Proportions: 100% : 1.75 hours x% : 1 hour x=1*100%/1.75
*July 16, 2013*

**math**

Use time = 1/(1/M+1/R)
*July 16, 2013*

**math**

2=1/(1/6+1/B) => B=1/(1/2-1/6)=3
*July 16, 2013*

**math**

1/(1/20+1/30+1/10) =60/11 minutes
*July 16, 2013*

**math**

1/(1/6+1/5.5+1/2.2) =1.245 DAYS
*July 16, 2013*

**algebra**

√(75) =√(25*3) =√(5²*3) =5√3
*July 16, 2013*

**math**

2³=?
*July 16, 2013*

**gen physics**

The centre of gravity is located at a point such that the product of mass multiplied by the distance to the C.G. is equal, namely: Let x = distance from mA, then 50-x = distance from mB. mA*x = mB(50-x) solve for x, and hence 50-x.
*July 16, 2013*

**gen physics**

apparent ρ=7860-1000=6860 kg/m² Tension in wire =apparent weight =apparent mass*g =(0.154³)*6860*9.81 N =246 N (approx.)
*July 16, 2013*

**physics**

ω2=ω1)+angular acceleration*time or time = (ω2-ω1)/angular acceleration =(0.28-0)/0.021 =40/3 sec.
*July 16, 2013*

**Math**

Please comment on the previous answer before reposting: http://www.jiskha.com/display.cgi?id=1373921871
*July 16, 2013*

**math :)**

You're welcome. :) The method above is correct, but the final result should be 2 7/24 lbs, since 2*24=48, and 55-48=7. Sorry for the oversight.
*July 16, 2013*

**math - addition of fractions**

The question requires us to add three fractions, with different denominators. The first step is to find a common denominator which is the LCM (least common multiple) among 3,4 and 8. Since 4 divides 8, so 4 need not be accounted for. The LCM of 3 and 8 is just the product 24, ...
*July 16, 2013*

**Geomtry**

I have a different interpretation of the problem. If I were to assume "three sides" as one length (parallel to the canal) and the two other sides perpendicular to the canal, then we are only fencing three sides on land, and the fourth side is bounded by the canal. ...
*July 16, 2013*

**math**

240.75 is correct.
*July 16, 2013*

**Math**

From the knowledge of divisibility, we know that 2 is a factor (all even numbers). That reduces 2002=2*1001 Again, the difference of sums of alternate digits equals zero (1+0)-(0+1)=0, so it is divisible by 11. That makes 2002=2*11*91 We should (try to) know all prime ...
*July 16, 2013*

**Math**

She cannot subdivide the equilateral triangle into 2 isosceles triangles. This is the smallest N which is impossible. She can subdivide it into 3 congruent isosceles triangles by joining the centroid with each of the vertices. Each triangle is then 30-30-120 as angles. Each of...
*July 15, 2013*

**Calculus**

The idea is to find the family of lines perpendicular to L:7x+5y-2=0. Out of that, we find the particular line L1 passing through P(-6,-2). The intersection of L and L1 gives the required point (closest to P). Family of lines perpendicular to L passing through P0(x0,y0): L : ...
*July 15, 2013*

**Statistics**

With replacement, the probability of selecting a good apple stays at 60/80=3/4. For a two-step experiment, the probability is the product of individual steps, hence, probability of select a good apple in each pick is (3/4)^2=9/16
*July 15, 2013*

**maths**

Two trains with speeds s and s+5 km/hr. Initial distance=340 km final distance = 30 km Total distance travelled = 340-30=310 km Total speed = s+s+5=2s+5 Time = 2 hrs Form equation equating distance travelled Time*speed=distance, or 2(2s+5)=310 2s+5=155 2s=150 s=75 Speeds of ...
*July 15, 2013*

**French**

"J'ai faim" is the proper expression to say "I am hungry." Just like in English we would not say "I am hunger", it would be incorrect say the equivalent in French. Another notable difference in French from English is about age. We would say &...
*July 15, 2013*

**object oriented programming**

Can you show us your pseudocode as a start?
*July 14, 2013*

**trig**

Parentheses are assumed missing. Implied parentheses are ALWAYS required in numerator and denominator of fractions. (cos^2x+sin^2x)/(cot^2x-csc^2x) This problem can be solved by converting all functions in terms of sine and cosine according to the standard definitions. (cos^2x...
*July 14, 2013*

**Java programming- simulation of rolling dice**

You have made the arrays die1...die4 to do two things: 1. as a counter (accumulator) for the frequency, and 2. as the value of the face. This is an impossible task, and that explains why the total adds up to more than a million. I suggest you make the following changes: 1. Add...
*July 14, 2013*

**Elementary mechanics**

Use the kinematics equation: Vf=Vi+at where Vf=final velocity=i-2j (m/s) Vi=initial velocity, yet unknown a=acceleration=F/m (in vector form) t=time=10 s a=(2i+7j)/5=0.4i + 1.4j Vf=(i-2j)+(0.4i+1.4j)(10) =(i-2j)+(4i+14j) =5i+12j
*July 14, 2013*

**Computers C++**

What are your thoughts?
*July 14, 2013*

**GEOMETRY (SA oftriangular pyramid)**

In the calculations of surface area of a pyramid, the height is not required if the apothem (slant height) is given. The height is required, however, to calculate the volume of a pyramid. In fact, the height h is not consistent, because h should always be less than the slant ...
*July 14, 2013*

**GEOMETRY (SA oftriangular pyramid)**

Lateral surface area =perimeter of base * apothem /2 =3b*s/2 (for a regular pyramid with a triangular base) Area of triangular base with side b =(√3)*b/2*(b/2) =(√3)b²/4
*July 14, 2013*

**math:units conversion**

Convert 6 cm to mm = 60 mm. Now add 60mm to 4 mm to get your answer.
*July 14, 2013*

**Math**

If each team plays with each of the other four teams N times, then the number of games played would be: 4, 8, 12, ... Can you find which of the five numbers does not belong?
*July 13, 2013*

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