# Posts by MathMate

Total # Posts: 11,744

**Surveying**

We have a parabola, and the crown is 6 inches over a 30-foot width, i.e. 15' on each side of the crown. The elevation of the crown is 612.58, and on each side of the road the elevation is 612.58-0.5'=612.08. Taking x=0 at the crown, the equation of a parabola with the ...

*February 5, 2016*

**Calculus**

s(t)=t²-6t+5 is the position vector. For example, at time=0 hour, s(0)=5, so the person is 5 miles north of LA, etc. Velocity is the derivative of position with respect to time, namely, v(t)=s'(t)=2t-6 At time t=0, v(t)=-6, meaning he was cycling towards LA. ...

*February 3, 2016*

**physics**

So rocket never got propulsion after launch, becomes a projectile. u=92.0 m/s, θ=33° horizontal velocity (constant) ux=u cos(θ) Time to reach wall (in seconds) t1=26.0/ux seconds vertical initial velocity uy=u sin(θ) vertical height at time t sy(t)=uy*t-(...

*February 3, 2016*

**Physics**

To find the resultant, resolve forces into x (due east) and y (due north) components and add. Use a diagram to help you understand the angles.

*February 3, 2016*

**physic**

The largest value of A+B is when they act in the same direction, and the resultant is the sum of the magnitudes. The smallest value of A+B is when they act in opposite directions, and the resultant is the difference of the magnitudes.

*February 3, 2016*

**Physics**

Without the diagram, we're as lost as you are! Is the force F acting up the plane, or down the plane? Is the force F acting horizontally or along the plane?

*February 3, 2016*

**physics**

X-component=200*cos(60)+120cos(210) (positive due east) Y-component=200*sin(60)+120sin(210) (positive due north)

*February 3, 2016*

**Physics**

Air speed=195 m/s (westerly) Air velocity = 195 m/s (West=positive) wind speed = 53 m/s (easterly) wind velocity = -53 m/s Ground velocity = air velocity + wind velocity = 195-53 = 142 m/s Distance = +276 km = +276000 m Time required = Distance/velocity = 276000/142 s = 1944 s...

*February 3, 2016*

**Physics**

1 W/m² is defined as 120 dB. For every 10 dB higher, power is multiplied by 10 times. Inversely, for every 10 db lower, power is reduced (divided) by 10 times. For example, 100 db = (120-20) dB=1W/m²*10^-2 75 dB = (120-45) dB = 1W/m²*10^(-4.5)=10^(-4.5) W/m²...

*February 3, 2016*

**math**

Similarly, for the westward leg, 1 degree of longitude is approximately 111 km*cos(50°)=71.3 km Since plane was at 70°W, and flew westwards, the longitude would increase. Use an accurate value of radius of the earth, R, to replace the 111 km. Formula is R*π/180.

*February 3, 2016*

**Physics**

Use KE=(1/2)mv^2 GPE=mgh where m=mass of plane v=velocity h=height of plane assuming reference plane is ground level. g=9.81 m/s² Use consistent units.

*February 2, 2016*

**Physics please i really need help**

For the reaction time, distance = velocity * time = 23.7*0.427 = 10.12 m For the braking time, v²-u^sup2;=2aS v=0, u=23.7 m/s, a=-9 m/s^2, S=(v²-u^sup2;)/(2a) =-23.7^sup2/(2*(-9)) =32.21 m Stopping distance is the sum of the two distances.

*February 1, 2016*

**Physics**

Speed = circumference / time Circumference = 2πr = 2*π*5.8*10^10 m = 1.16π*10^11 m Time = 88days * 24h/day * 60min/h * 60sec/min =7603200 s Speed = distance /time = 1.16π*10^11 / 7603200 = 47930 m/s = 47.93 km/s

*February 1, 2016*

**physics**

Assuming that the wood block is fixed and stationary. (a) acceleration, a = (final vel. - initial vel) / time = (v-u)/t = (0-16 m/s) / 0.5 = -32 m/s² (b) average force = mass * acceleration = 0.020 kg * 32 m/s² = 0.64 newton (c) Distance, S = ut+(1/2)at² = 16*0....

*February 1, 2016*

**To Soso**

See http://www.jiskha.com/display.cgi?id=1454378710 Hope you realize the problem when you post the same problem too many times, ... and not checking answers before reposts!

*February 1, 2016*

**Geometry**

For the chord AB k=mXB 2k=mAX We will construct diameter CD such that X lies on CD. Now CX=9+7=16 cm, XD=9-7=2 cm Using the theorem of intersecting chords (AB and CD), we have 16*2=k(2k) Solve for k.

*January 29, 2016*

**Math**

Agree with Damon. The only 4 digit number for which 1. all digits are odd, 2. sum of last two digits equal 16 3. divisible by 13 are 7397, 9997, 7579 each of which does not satisfy the requirements 4. digits being distinct, 5. number is less than 3000. However, if the ...

*January 19, 2016*

**math**

Solve step by step. Given a 3-digit number. 1. If it is divisible by 5, it must end with a 0 or a 5. 2. If the number is odd, the last digit must be 5. 3. if product of digits is 15, the product of the two remaining digits must be 15/5=3, namely either 1,3 or 3,1. I.e. the ...

*January 17, 2016*

**physical science**

momentum=60000kg m/s mass = 2000 kg use relationship momentum=mass * velocity which can be solved for velocity: velocity=momentum/mass

*January 17, 2016*

**FRENCH ! (:**

Accents on any keyboard can be done as shown in the following link, for example, & e a c u t e ; stands for é (skip the spaces between & and ;) http://www.starr.net/is/type/htmlcodes.html Other comments: yesterday is hier (not heir). la police et l'ambulance _____ ...

*January 14, 2016*

**Math**

When we're dealing with consecutive numbers representing the sides of a triangle, the average of the perimeter (i.e. perimeter/3) is the middle number. Hence find the other two numbers.

*January 11, 2016*

**Behavioral Stat. Lab**

Where proprietary software is involved, you have a much better help from your instructor because not everyone here has access to minitab.

*January 11, 2016*

**Math**

Student needs to learn the position value of decimal numbers, and that a carry should not shift the digits to the right.

*January 11, 2016*

**Phiysics**

use final velocity = initial velocity + acceleration * time Note: deceleration is a negative acceleration.

*January 11, 2016*

**math - typo?**

Do you mean: "You need 210 snowballs to make the perfect snow fort you make 15 snowballs in an hour but 10 melt every 15 minutes how long will it take you to make the perfect amount?" Checking your question before you post helps you get your answer fast.

*January 10, 2016*

**Math**

If AB is the longest side, then O cannot divide AC and BD in the ratio 1:2 since mAB>mDC. We will use A(BOC) to represent the area of triangle BOC, and so on. Draw a diagram of the trapezoid ABCD with AB//DC and AB>DC. The diagonals AC and BD meet at O. If the division ...

*January 10, 2016*

**science**

In the case of a hydraulic lift, the pressure is (almost) identical, so that Force/area is a constant, where area is the area of the respective piston.

*January 10, 2016*

**Science**

The keyword here is energy reserves. All except one provide energy, but under different conditions. Discover about all four at the link: http://www.livestrong.com/article/281655-functions-of-lipids-carbohydrates-nucleic-acids-proteins/

*January 10, 2016*

**Science**

Ethyl alcohol has a formula of C2H5OH. C8H18 is octane. In any case, you would work out the number of moles of alcohol in 16.5 mL. (note: 16.5 mL*0.789=13.02g) Each mole of alcohol gives out 2 moles of CO2. (Write out the combustion equation). So by proportion, you will get ...

*January 10, 2016*

**MAth 10 (probability**

Make a table for the two spins X| 1 2 3 4 --------- 1| 2 3 4 5 2| 3 4 5 6 3| 4 5 6 7 4| 5 6 7 8 Out of the 16 possible outcomes, count how many satisfy the given condition, and divide this number by the number of possible outcomes.

*January 10, 2016*

**Math**

We'll first find the limit, and I'll let you continue with the derivative. Let Y=Lim x->∞ (2^x+5^x)^(1/x) =Lim x->∞ ((5*2/5)^x+5^x)^(1/x) =Lim x->∞ ((5^x)(2/5)^x+5^x)^(1/x) [law of exponents] =Lim x->∞ ((5^x)((2/5)^x+1)^(1/x) [...

*January 9, 2016*

**Chemistry-Dr.Bob**

Correction: the answer is more appropriately given as 1.54 J/(g-°C) as all the original information is given to 3 significant figures.

*January 9, 2016*

**Chemistry-Dr.Bob**

Use ΣmcΔT=0. For metal, mcΔT=100*c*(29-90)=6100c For water, mcΔT=250*4.184*(29-20)=9414 Applying ΣΔT=0 => 100*c*(29-90)=250*4.184*(29-20) Solving for c gives 1.543 J-g-1-°C-1 as you had it.

*January 9, 2016*

**math**

It depends on the given information. If base radius (r) and height (h) are given, then angle of cone is given as 2tan-1r/h.

*January 9, 2016*

**math**

the parabola y=x² has it's vertex at (0,0). Tangent to parabola has slope dy/dx=2x, at point (±x, x²). For tangents to pass through (0,-25), we have the slope joining (0,-25) and (x,x²) equal to 2x. Slope=(y2-y1)/(x2-x1) => (x^2-(-25))/(x-0)=dy/dx=2x ...

*January 9, 2016*

**French**

There is not enough context to give an answer without making assumptions. However, if we assume this is an itinerary for Élaine, the second date (8 days later) could be assumed to be the return (to San Diego) from Marseille, which is reasonable for a tourist. Assuming ...

*January 9, 2016*

**physics**

It would appear as homework dumping if you don't show your work. Also, if you make an effort to solve the first one, there is a chance you can apply what you learned to solve the other ones, or at least get a good kick-start. I suggest you review class material, attempt ...

*January 9, 2016*

**Maths**

The best way to include a picture is to upload the picture to an image server and post the link. It is not always possible, but give it a try and teachers are likely to help you get it done if there are difficulties.

*January 9, 2016*

**Math**

At the beginning, there are 22*760=16720 food days. After 2 days, there are 20*760=15200 food days left. If this should last only 19 days, it will feed 15200/19=80 persons. You can therefore figure out how many more people came (in addition to the original 76).

*January 9, 2016*

**math**

Since we are given the hypotenuse and one leg, we can find the other leg using Pythagoras theorem. The area is then the product of the two legs divided by two. Height (of the other leg) =√(3.7²-1.2²)=3.5 Base (given)=1.2 m So you have all information to find ...

*January 9, 2016*

**emmanuel**

in a class of ,26 offer mathmatic and 28 offer physics if 8 student do not offer any of the two subject This means that there are 60-8=52 students take at least one subject. Since total number of subjects taken is 26 and 28=54, we know that 54-52=2 students take both. I'll...

*January 7, 2016*

**Math**

******** ******** ******** ********

*January 7, 2016*

**Geometry**

Sum of exterior angles of any polygon is 360°. So if we add up all five exterior angles of the pentagon, we have 2(3x)+2(2x+22)+x+41=360° Solve for x.

*January 7, 2016*

**Statistics**

Start with Googling "history of aids" and read up the first 5 or 10 articles. Otherwise, try http://www.avert.org/professionals/history-hiv-aids/overview and http://www.amfar.org/thirty-years-of-hiv/aids-snapshots-of-an-epidemic/

*January 6, 2016*

**Kercy**

Most of the time the floating is due to deterioration/decay of the body tissues and gases (CH4, H2S, and CO2) are produced, hence reducing the overall density of the body. Read more about it, for example: http://www.slate.com/articles/news_and_politics/explainer/2005/09/...

*January 6, 2016*

**Math**

A dart board has sectors numebered from 1 to 20. We require combinations, so order does not count. Here's how we could proceed: 1. to avoid repetitions, we assume the smallest number is thrown first, then the next smallest, and the largest numeber. 2. There are no limit to...

*January 5, 2016*

**Counting and Probability**

Let k=number of 4's to add then E(x)=Σx*P(x) =(8*2+(2+k)*4)/(8+2+k) If E(x)≥3.5 then (8*2+(2+k)*4)/(8+2+k)≥3.5 solve by cross multiplication 16+8+4k≥35+3.5k 0.5k≥11 k≥22

*January 5, 2016*

**partial fraction**

step 1: decompose denominator into factors (x³_x²-x-1) =x²(x+1)-1(x+1) =(x²-1)(x+1) =(x+1)²(x-1) Now decompose expression into partial fractions: (Ax+B)/(x+1)² + C/(x-1) = (2x²+7x-1)/(x+1)²(x-1) .....(1) Now match coefficients of powers ...

*January 5, 2016*

**math**

What's left is is 100-80=20% So the original amount A can be found by proportions: P100/20%=X/100% solve for X: P100*100%/20%=P500

*January 5, 2016*

**french(le passe compose)**

To help you better, I suggest you propose your translation and we will be glad to help you make necessary corrections. For example, (for a male speaker) "I went to school yesterday" would be Je suis allé à l'école hier. Recall that in French...

*January 5, 2016*

**Physics**

Hint: read up about Newton's first law, for example, at the following link: http://www.physicsclassroom.com/class/newtlaws/Lesson-1/Newton-s-First-Law

*January 4, 2016*

**physics**

Inelastic collision means the two objects do not rebound and move at a common velocity. Yes, choice a is correct.

*January 4, 2016*

**math**

*...is related to sign of...

*January 3, 2016*

**math**

monotonicity of ln(x) is equal to sign of (ln(x))'=1/x, and domain of ln(x) is D=(0,+∞) Since 1/x is strictly positive for x∈D, so ln(x) is strictly monotonically increasing.

*January 3, 2016*

**physics...perhaps horizontal plane**

I assume that the block of mass m=80 kg slides horizontally, and that the force F=400N pushes downwards at an angle of θ=37° below the horizontal. Initial horizontal velocity is u=20 m/s, and we look for velocity v at time t=6 seconds. Further assumption: friction &...

*January 3, 2016*

**Math - typo?**

The question as is would provide 3 equations for two unknowns. It would be a good idea to check the question before/after posting.

*January 1, 2016*

**MATHS HELP URGENT(TIME AND WORK)**

Fraction of work accomplished W at the end of day t will be denoted W(t). W(0)=0 W(10)=5/6 W(12)=5/6-2/3=1/6 W(22)=1/6+5/6=1 work completed.

*January 1, 2016*

**math**

Hint: adjacent angles of parallelgrams are supplementary, i.e. they add up to 180°. For the given problem, if one angle is x, then the adjacent angle is 2x. Since they are supplementary, we have x+2x=180°. Solve for x and hence the angles of the parallelogram.

*January 1, 2016*

**dynamics**

Let time t=0 when mass is 3500 and speed is 1220 m/s. then F(t)=500 kN m(t)=3500-80t a(t)=(500*1000/m(t))=acceleration => (i) v(10)=v(0)+∫(500000/(3500-80t))dt for t=0 to 10. =1220-500000[ln(3500-80t)]/80 =1220+1621.945 =2841.945 m/s (ii) using initial mass v(10)=v(0)+(...

*December 29, 2015*

**Math**

In four years, the total of the ages will be 46+4+4=54 years. The ratio in four years will be 7:2 So age of daughter in four years = 54*(2/(7+2))=12 age of mother in four years = 54*(7/(7+2))=42 Continue to find their present ages.

*December 28, 2015*

**chem question?answer_to=1210023143**

(115 psi)/(14.7 psi/atm) = 7.82 atm assuming the air in the tire has room temperature.

*December 28, 2015*

**physics**

Assuming the 10N force is along the positive x-axis. Then the three forces in (magnitude, angle °) are P(10,0), Q(30,120), R(50,240) or in component form: P<10,0> Q<30cos(120),30sin(120)>=<-15, 25.9808> R<50cos(240),50cos(240)>=<-25, -43.301> ...

*December 28, 2015*

**mathematics**

Assuming parentheses around the denominator have been omitted, the expression is x²+x+4/[(1-x)(x²+1)] partial fractions for the third term is required, namely 4/[(1-x)(x²+1)] =-4/[(x-1)(x²+1)] =A/(x-1)+(Bx+C)/(x²+1) By adding the right-hand side, we ...

*December 28, 2015*

**Algebra**

Constraints: A. x≥0 B. y≥0 C. y-x≤100 D. x+2y≤1400 (please check this constraint) Draw the graph of the constraint equation to have a visual understanding. Solve for all possible corners of the feasible polygon. Note that all inequalities are inclusive, i.e. all ...

*December 27, 2015*

**Math**

We know that 5*7=35, so the three digit number probably starts with a 3, and the two digit number starts with a 7. We also know that we should put small digit after 7, and large digits after 3, so the numbers are 384/71 Check: 5 < 384/71=5.408 < 6 There may be other ...

*December 26, 2015*

**stats**

Good catch Reiny! I read too fast! To "Help", please go along with Reiny's answer.

*December 23, 2015*

**stats**

Yes, that would be correct, because 10+20+30+40=100 so the the probability that she selected French hens would be 10/100.

*December 23, 2015*

**stats**

There are 10 French hens. Try to enumerate the number of each kind of pet and then add up the numbers to get the total number of pets. 40 is the number of American chickens.

*December 23, 2015*

**stats**

Let success be choosing a French hen out of all possible choices (Ω) and we need to assume the probability of choosing any pet is equal. Probability of success (choosing a French hen) =Number of French hens ÷ Total number of possible choices (&Omega). Here you see...

*December 23, 2015*

**Physics**

Assuming uniform deceleration and constant friction (independent of speed). Equate energies: (1/2)mu²=μmgX X=distance u=30 m/s g=9.81 m/s² Solve for X=61.1621 m Acceleration v²-u²=2aX solve for a=(0²-30²)/(2*61.1621) =-7.3575 m/s²

*December 22, 2015*

**statistics**

The requirements for an experiment's to be considered binomial are: 1. probability of success remains constant throughout the experiment 2. all trials are independent and random 3. the number of trial is constant and known. This problem satisfies the requirements for the ...

*December 21, 2015*

**Calculus**

Distinguish between relative maximum and absolute maximum. Statement (a) is true for absolute maximum since x0 is where f(x) has the highest value over the domain of f. Relative maximum at x0 only guarantees that f(x0)>f(x0-) and f(x0)>f(x0+), i.e. a local maximum.

*December 21, 2015*

**Physics**

Work to transformed water to steam = 4*10^8 J Work to overcome safety valve=2*10^8 J. Both work are added to the internal energy.

*December 21, 2015*

**To Paige -- French**

Also a version with the accents.

*December 21, 2015*

**French**

Here a version with the accents filled in. Good luck! Vous avez besoin de: -1 c. à s. de l’huile -200 g du riz -2 oeufs -3 tranches de fromage -300 g de haricots noirs -2 tomates -1 oignon -1 c. à s. des épices mexicains -2 gousses d’ail -(...

*December 20, 2015*

**physics**

M1. The direction of the initial velocity of 3.5 m/s is not mentioned. Use S=ut+(1/2)at^2 to solve for time t. S=-100m (distance) a=acceleration due to gravity = -9.81 m/s^2 u=initial velocity u=0 if 3.5 m is horizontal u=-3.5 if he dove into the ocean at that velocity.

*December 20, 2015*

**Counting and Probability**

These are very interesting problems. If you show some efforts in solving them, there would be likely to be more chances of response.

*December 16, 2015*

**gss**

A'BC+AB'C'+A'BC+ABC+AB'C =(A'BC+ABC)+(AB'C'+AB'C)+A'BC =(BC)+(AB')+A'BC =(BC+A'BC)+AB' =BC+AB'

*December 16, 2015*

**Algebra 2**

see http://www.jiskha.com/display.cgi?id=1450209752

*December 15, 2015*

**algebra?**

Hint: the ratio is 2:3, so from A to B, it is 2/(2+3)=2/5. The coordinates of M are: M(xa+(xb-xa)*2/5, ya+(yb-ya)*2/5)

*December 15, 2015*

**Algebra 2**

x-intercept is obtained by solving for x after setting y=0. For example: f(x)=x^2+2x+1 set y=f(x)=0, then x^2+2x+1=0 (x+1)²=0 x=-1 (x-intercept) y-intercept is obtained by solving for y after setting x= 0. For example : f(x)=x^2+2x+1 Set x=0, then f(x)=y=0^2+2(0)+1=1 y=1 ...

*December 15, 2015*

**Numerical Analysis MATLAB**

Hint: http://www.mathworks.com/help/matlab/ref/fplot.html

*December 15, 2015*

**Math - ratios**

Let N=number of papers graded in 1.5 hours (90 minutes). Use ratio (assuming the grading rate is constant) 5 papers: 45 minutes = N papers : 90 minutes. Cross multiply: N=(5/45)*90=10 papers.

*December 14, 2015*

**math**

There are two ways to solve this problem. A. The intuitive (and fast) approximation is by prorating the ratio, assuming that the ratio is constant. Let N=total population, then N/30=20/4 => N=150 B. The more accurate (and elaborate) way is to use the hypergeometric ...

*December 14, 2015*

**Math**

Let x=cost of pizza. then 3x/8+4=5x/8+1.5 solve for x.

*December 14, 2015*

**math-legs and heads, again**

See response at http://www.jiskha.com/display.cgi?id=1450138210

*December 14, 2015*

**math-legs and heads**

You can choose to do the sum mentally as follows: If all the animals were ducks, there would be 2*22=44 legs. Since there are (60-44)=16 more legs, there must be (16/2)=8 dogs, the rest (22-6)=14 ducks. If you prefer to solve the sum mathematically, you would set up an ...

*December 14, 2015*

**Math**

Since the area is bounded by two parallel lines y=5 and y=-3, the area is a trapezoid, with a height of (5-(-3))=8. We need to find the intersection of the line y=2x-5 with each of the parallel lines. Setting 5=2x-5 => x=5 Setting -3=2x-5 => x=1 So the upper width is (8-...

*December 14, 2015*

**Mathematics**

(2+x)(-sinx) is an expression, and cannot be solved. To solve an equation, the expression must be equated to a value, such as x²+2x+1=0

*December 14, 2015*

**Physics**

This is an elastic impact problem. Impact problems have one available equation, namely conservation of momentum. m1u1+m2u2=m1v1+m2v2. u, v represent initial and final velocities respectively, and m1, m2 are masses of bodies involved. Note that velocities have signs, e.g. ...

*December 13, 2015*

**To Physics nerd**

When expression exponents, please precede the exponent by the ^ sign. For example, 10² should be written as 10^2. 102 means one hundred and two, (write 10^2) 103 means one hundred and three, (write 10^3) Confusions will arise if the numbers are not expressed correctly.

*December 13, 2015*

**French**

Hint: un repas

*December 13, 2015*

**Discrete Mathematics. Need Help**

For R to be an equivalence relation, it must satisfy all the following conditions: 1) Reflexivity, i.e. (a,b)R(a,b) ∀(a,b). 2) Symmetry, i.e. (a,b)R(c,d) => (c,d)R(a,b) 3) Transistivity, i.e. (a,b)R(c,d) and (c,d)R(e,f) => (a,b)R(e,f). Use the definition of R to ...

*December 13, 2015*

**Cht Ningi**

T(9)=29.............9th term T(22)=55............22nd term If the AP is T(n)=T(n-1)+d, then d=(T(22)-T(9))/(22-9)=26/13=2 T(1)=T(9)-(9-1)d = 13 and therefore T(n)=11+2n T(1)=13 T(60)=11+120=131 To find the sum of the 1st to the 60th term, we use Little Gauss's method: T(1...

*December 6, 2015*

**Physics**

This we need to make two assumptions: 1. The car is on a perfectly horizontal plane/road 2. The car is in neutral AND friction is negligible. Use Newton's second law: F=ma F=400N m=(200 + 50n ) kg n=number of bags. a=1 m/s^2 (acceleration is measured in m/s^2) Set up ...

*December 6, 2015*

**Ap physics**

Use continuity equation, namely the volume of sand coming out per second equals the diameter * speed of sand. Volume = 75 L/min = 1.25 L/s Total area of jets (d=diam in dm) =2π(d²)/4 Speed of sand = 45 m/s = 450 dm/s Equate volumes of sand 450*2π(d²)/4=1.25 d=...

*December 6, 2015*

**Math**

Let the number be x. then x+1/x=29/10 Solve for x. The answers are rational fractions.

*December 5, 2015*

**Math**

First we have to decide how many slices we cut the pizza! It could be 8, but inspiring from the mushroom of 4/16 slices, I assume it is a large pizza cut into 16 slices. Then we add up the fractions to get toppings to cover 3/4+5/8+4/16=26/16 of the pizza. Evidently, if we ...

*December 5, 2015*

**Mechanical engineering**

With a point load in the middle, draw the bending moment diagram, which is a triangle with zero at both ends, and linearly increasing to the middle at R1*L/2. In fact, the standard formula for the maximum bending moment for a centrally placed point load is PL/4. Review your ...

*November 26, 2015*

**Physics 101**

Increase in length = Length (m) * ΔT (° C) * coefficient of expansion (°-1)

*October 20, 2015*