Saturday
April 19, 2014

Posts by MathMate


Total # Posts: 9,948

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

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 therefor...

math
Proportions: 100% : 1.75 hours x% : 1 hour x=1*100%/1.75

math
Use time = 1/(1/M+1/R)

math
2=1/(1/6+1/B) => B=1/(1/2-1/6)=3

math
1/(1/20+1/30+1/10) =60/11 minutes

math
1/(1/6+1/5.5+1/2.2) =1.245 DAYS

algebra
√(75) =√(25*3) =√(5²*3) =5√3

math
2³=?

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.

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.)

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

Math
Please comment on the previous answer before reposting: http://www.jiskha.com/display.cgi?id=1373921871

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.

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, ...

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. Le...

math
240.75 is correct.

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 factoriz...

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...

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 : 7...

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

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 tr...

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 &q...

object oriented programming
Can you show us your pseudocode as a start?

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...

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...

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

Computers C++
What are your thoughts?

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 h...

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

math:units conversion
Convert 6 cm to mm = 60 mm. Now add 60mm to 4 mm to get your answer.

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?

College Algebra
Start with (x-(-1/6))(x-(-8/9))=0 Multiply by 54 on both sides to get (6x+1)(9x+8)=0

trig
Convert all three functions in terms of sine and cosine, hence simplify.

statistics
Possible typo in bold: "Playing game of chance and pay 300 by rolling a fair die one time if you rome a 2 and receive $1300 if you roll a 4 or six you receive $900 if you ore a 3 5 or one receive nothing. find expected value for this game. based on value is it a good game...

statistics
Binomial distribution: - large population=>probability is (almost) constant - p=0.5 (men) q=(1-0.5) (women) - random independent multiple trials N=9 - 2 possible outcomes at each trial P(7)=C(9,7)*p^7 * q^2 =(9!/(2!7!))*0.5^7*(1-0.5)^2 =0.07 (approximately)

Calculus
See: http://www.jiskha.com/display.cgi?id=1373656357

Linear Equation
Let x=number of gallons of regular sold then 220-x=number of gallons of premium sold Total receipt: 2.20x+2.70(220-x)=519 Solve for x.

Math :)
You're welcome!

Math
x=(5±(√15)*i)/2 If you do not expect complex roots, please check for typos in the original question.

Math
x/(x-2) + (2x)/[4-(x^2)] = 5/(x+2) This calls for finding the common denominator, and then solving for x using the numerators. Do not forget to exclude the asymptotes values of x where the denominator becomes zero. LCM (lowest ommon multiple) of denominators (x-2), (4-x²)...

algebra1 HELP PLEASE Thanks you!!
y=√(64*25)=√(40²)=40 f.p.s.

algebra1 HELP PLEASE Thanks you!!
Not sure if there is a typo in your question, the speed is y(x)=5√(x)=5√(25)=25 This corresponding an equivalent acceleration approximately that of Mars.

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