Monday
May 25, 2015

Posts by MathMate


Total # Posts: 11,295

Math
Yes, your next step is to solve for x which represents Oliver's share.
August 19, 2013

MaTh
Correct! Good job! :)
August 19, 2013

Math
yes.
August 19, 2013

French
Just a little elaboration: If "this" stands for a masculin noun, such as a basket (un panier), or a bag (un sac), you could say Y a-t-il des oeufs dans celui-ci? If it stands for a feminine object, such as a pocket (une poche), or a plate (asiette), then we would use...
August 18, 2013

math
If it has 2 AND 3 in the prime factorization, it means that the number must be divisible by 2 AND by 3, which means that it is divisible by 6. The number(s) between 50 and 59 that are divisable by 6 would be 54. The prime factorization of 54 is 54 =6*9 =2*3*3*3 =2133 You can ...
August 15, 2013

MATH
What did you get? You would be well to do the 4x4. If you have difficulties, start with a 1 by 1, then 2 by 2 and then 3 by 3 grid. You will find a pattern that you can use later. Once done, do an n × n grid and check if the answer for n × n works for n=4.
August 15, 2013

math
Mass = mass density * volume where mass density = 23.4 g/cm³ volume = 75 cm³
August 15, 2013

Discrete Mathematics-Elementary graph theory
A cycle graph is like a polygons with vertices along the circumference. A complete graph is one where EACH vertex is connect to EVERY OTHER vertex (except itself). Using these definitions, are you able to answer the question?
August 8, 2013

Discrete Mathematics-Elementary graph theory
No it does not matter. You can even use a wavy line. However, we usually use a straight line unless we would like to avoid certain crossing of lines.
August 8, 2013

Discrete Mathematics
By definition, a tree is a connected acyaclic graph. One of the sufficient properties of a tree is that the number of edges equals the number of vertices minus one. Note: number of edges = (sum of degrees of all vertices)/2.
August 6, 2013

Discrete Mathematics
An Eulerian path is a path which passes through ALL edges exactly once. This can happen if the graph has either 0 or 2 vertices with odd degrees. So even an incomplete graph (with degree 0 at one or more vertices) can have an Eulerian path.
August 6, 2013

Discrete Mathematics
The number of edges =(sum of degrees of all vertices)/2
August 6, 2013

Discrete Mathematics
See your next post to find out how to calculate the number of edges. Hence deduce if such a graph can exist or not.
August 6, 2013

Math- Probablility
C=Casper D=Denver Conditional probability: P(C)=0.4 P(D)=0.3 P(C∪D)=0.27 Probability of having been to Casper given she has gone to Denver =P(C|D)=P(C∪D)/P(D) =0.27/P(0.3) =0.9
July 29, 2013

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
July 29, 2013

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...
July 29, 2013

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
July 28, 2013

Math-probability
8 choose 3 =8C3 =8!/((8-3)!3!) =8*7*6/(1*2*3) =56
July 28, 2013

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.
July 28, 2013

Elements of Structures MIT 2.02
Please see: http://www.jiskha.com/display.cgi?id=1374949947
July 27, 2013

Math
3/(3+4)
July 27, 2013

Geometry
We have P1(6,-2), P2(1,3) Use Slope=(y2-y1)/(x2-x1) to find slope.
July 27, 2013

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
July 27, 2013

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%
July 27, 2013

Elements of Structures MIT 2.02
Please clarify what are the "other" questions.
July 27, 2013

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 ...
July 27, 2013

Elements of Structures MIT 2.02
Good luck!
July 27, 2013

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 ...
July 27, 2013

Elements of Structures MIT 2.02
Did you use Ix=Iy=πd^4/64 ?
July 27, 2013

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
July 27, 2013

Elements of Structures MIT 2.02
is q(x)=q0*x or is q(x)=q0*x*L (as you had it above?)
July 27, 2013

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.
July 27, 2013

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?
July 27, 2013

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?
July 27, 2013

algebra
Good catch! Thank you!
July 27, 2013

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
July 27, 2013

math
You may have a typo with the given answers. None of them is correct.
July 27, 2013

Statistic/Psychology
That's correct! Good job!
July 26, 2013

Statistic/Psychology
A negative correlation means that the increase of one variable will be accompanied by a decrease of the other variable.
July 26, 2013

Statistic/Psychology
Exactly!
July 26, 2013

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...
July 26, 2013

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 ...
July 26, 2013

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
July 26, 2013

Discrete Mathematics :)
You're welcome!
July 26, 2013

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.
July 26, 2013

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

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