Wednesday
July 30, 2014

Posts by MathMate


Total # Posts: 10,590

Probability
5 choose 2 * 15 choose 12 =5C2*15C12 =5!/(2!3!) * 15!/(12!3!) =5*4/2! * 15*14*13/6 =10*455 =4550

Calculus-Series
I assume the expression is (n^3)* (e^(-n^4)) for n=1 to +&inf; You can use the ratio test to show that it converges, namely, show that an+1/an < 1 ∀ k≥1. The integral test will result in a definite integral from 1 to +&inf; which is not an elementary function, but...

Calc Help Please
Implicit differentiation: (d/dx)(2x^2+2x+xy=2) 4x+2+y+xy'=0 y'(x)=-(4x+2+y(x))/x y'(2)=-(4(2)+2+y(2))/2 =-(10-5)/2 =-5/2

Math-probability
8 choose 3 =8C3 =8!/((8-3)!3!) =8*7*6/(1*2*3) =56

physics
Take moments about the centre. On father's side: M=70*0.65=45.5 kg-m On children's side: M=(30+30)*x Equate moments and solve for x.

Elements of Structures MIT 2.02
Please see: http://www.jiskha.com/display.cgi?id=1374949947

Math
3/(3+4)

Geometry
We have P1(6,-2), P2(1,3) Use Slope=(y2-y1)/(x2-x1) to find slope.

Math- probability
F=fever S=sore throat P(F)=80% P(S|F)=30% But P(S|F)=P(S∩F)/P(F) P(S∩F)=P(S|F)*P(F)=30%*80%=0.24

Math (probability)
Conditional probability. P=pool G=garage Probability of a home having a pool given that it has a garage is P(P|G)=P(P∩G)/P(G) =11%/50% =22%

Elements of Structures MIT 2.02
Please clarify what are the "other" questions.

Elements of Structures MIT 2.02
I have quite different values as you have. It would help if you show your work so we can compare notes. My approach would be: Since the beam is composite, there is only one value of 1/r at each cross section x, which is given by M(x)/EI. For a cantilever beam, M(x) is evidentl...

Elements of Structures MIT 2.02
Good luck!

Elements of Structures MIT 2.02
1. I suggest you check your EI. 2. You have not confirmed q(x)=q0*x*L (as you have written). I think you mean q(x)=q0*(x/L) If that's the case, I also get δ=-0.0582 as you did. I think the large δ comes from the erroneous EI. If you use EI=8050π, you'd g...

Elements of Structures MIT 2.02
Did you use Ix=Iy=πd^4/64 ?

Elements of Structures MIT 2.02
I have for the core I0=2.5π*10^-9 and for the sheath I1=3.75π*10^-8 Multiplied by the corresponding E gives me EI0=175π (core) and EI1=7875π (sheath). Total(effective)=8050π

Elements of Structures MIT 2.02
is q(x)=q0*x or is q(x)=q0*x*L (as you had it above?)

Elements of Structures MIT 2.02
Do you get 8050π for the EI of the composite beam? I get 8050π For some reason, I get δ=-0.1164, which is exactly double your number.

Elements of Structures MIT 2.02
I guess I did not read that x=0 at the free end (A), and the fixed end (B) is x=L. Also, do you mean q(x)=q0*x*L? What did you get for EI of the composite beam?

Elements of Structures MIT 2.02
" q(x)=qxL,with q0=2.76kN/m. " Most of the time, x is measured from the fixed end (of a cantilever). Is this the case?

algebra
Good catch! Thank you!

algebra
Initially w=width w+5=length w(w+5)=original area Subsequently: w-2=width 2(w+5)=length (w-2)*2(w+5)=2*original area=w(w+5)=area Therefore 2(w-2)(w+5)=w(w+5) Solve for w: 2(w-2)=w (w cannot be equal to -5) 2w-4=w w=4

math
You may have a typo with the given answers. None of them is correct.

Statistic/Psychology
That's correct! Good job!

Statistic/Psychology
A negative correlation means that the increase of one variable will be accompanied by a decrease of the other variable.

Statistic/Psychology
Exactly!

Statistic/Psychology
Correlation coefficients range from -1 to +1 where the two extremes enable the researcher to make almost perfect "predictions". On the other hand, the closer the correlation coefficient approaches zero, the less reliable would be the indication of the regression line...

Linear Algebra
Let x=number of bracelets y=number of necklaces then x+y=120 10x+12y=1400 Solve for x and y. Quick mental calculation, no paper required: If Rosa bought only necklaces, she would have paid 12*120=$1440. Exchanging a necklace for a bracelet saves her $2, so to pay $1400, she mu...

science
Use conservation of kinetic and potential energies: mgh1+(1/2)m(v1)² = mgh2+(1/2)m(v2)² where m=mass of cyclist and cycle (cancels out) g=acceleration due to gravity (9.81 m/s^2) h1=70m h2=35m v1=38 m/s Solve for v2

Discrete Mathematics :)
You're welcome!

Discrete Mathematics
Number of comparisons for 6 numbers: 5+4+3+2+1=15 You need all 15 comparisons unless you modify the algorithm to keep track of exchanges. There are 4 exchanges in this particular example.

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) as...

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...

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 i...

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: stat...

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 c...

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,...

Discrete Mathematics
correction: p: (x+2)(x-3) >0 q: x<-2 ∨ x>3

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>...

Geometry
Vertically opposite angles are equal. What is x when 4x=56?

math :)
You're welcome!

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

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 la...

Psychology
(C) is correct.

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 a...

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

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 wa...

Physics
It was a typo. :) Net difference=1290-180=1110kg=total mass it can lift. Net payload=1110-500=610kg

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.

math
Excellent observation. I missed that!

math
Multiply the mass by the acceleration due to gravity, g, where g=9.81 m/s².

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.

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+...

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...

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 imp...

calculus (please help steve)
Typo: Y2(x)=-5.5+√(5.5^2-x^2) Subsequent lines are not affected.

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...

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

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) &epsil...

solid mechanics
Sorry, typo above: shear stress should have read τ. γ would have been shear strain.

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° Us...

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 ...

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.

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

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,...

statistic
a numerical value for a correlation coefficient can never be greater than one or less than minus one.

Gen physics
μmg≥m|a| => |a|≤μg = 0.632g

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 ...

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.

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.

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

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 r...

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

Incomplete
I hope you realize that incomplete questions are either not answered or will be put on hold until all information is supplied.

Physics :)
You're welcome!

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).

physics
The same question has been answered twice before. See http://www.jiskha.com/display.cgi?id=1374277875

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.

Math :)
You're welcome!

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

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 latera...

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 ...

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...

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.

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

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

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)...

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 ...

Statistics
The following reference may confirm your assumptions. http://cjasn.asnjournals.org/content/3/5/1246.full

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 ...

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.

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) &eps...

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 t...

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.

math
Yes, 2655 in³.

math
Calculate volume of locker V=L*W*H Calculate volume of books (given) B=1545 in³ Calculate volume left =V-B

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 f...

math
The rule for converting from metres to centimetres is that one metre equals 100 centimetres.

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

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

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