# Posts by MathMate

Total # Posts: 12,013

Chemistry - to CJ
If the tube is 1 nm in diameter, then veryify that 5 μm = 5*1000 nm = 5000 nm = how many diameters? Can you tell us what prevents you from finding the answer with the information above?

calculus
1. find derivative with respect to h: C'(h) = 1/15-15000000/h² 2. equate C'(h) to zero and solve for h. 2. 1/15-15000000/h² = 0 h²=225000000 h=15000 3. verify that it is a minimum (not maximum) by taking second derivative, and see that C"(15000)>...

torque
Torque = force × lever arm Assuming 190 foot-pounds is in gravitational units (i.e. foot-pound wt), then force = 120 pound-wt lever arm = x feet using the torque formula, 190 foot-pound wt = 120 pound-wt * x feet Solve for x (in feet).

fluids
use the conversions from 1. pressure: psig (rel) to psi (absolute) by adding 14.69595 psi. 2. temperature: °F to °K by (°F-31)*5/9+273.15 Then use the ideal gas formula: P1 V1 / T1 = P2 V2 / T2 to calculate V2

Energy, work, power
12 feet above, below or at the same elevation as the truck? Moving things at the same level is not considered work done because there is no change of potential energy, kinetic energy nor dissipative energy.

math
First you need to find the area of an equilateral triangle with side x. Base = x Height = (√3)x/2 Area = (√3)x²/4 Thus, the area as a function of side x A(x)=(√3)x²/4 A'(x) = (√3)x/2 Substitute x=12 cm in A'(x) to get rate of change of...

Chemistry
If the tube is 1 nm in diameter, then veryify that 5 μm = 5*1000 nm = 5000 nm = how many diameters?

Chemistry
* 1 μm = 1000 nm (nanometer)

Chemistry
1m = 1000 mm (millimeter) 1 mm = 1000 μm (micrometer) 1 μ = 1000 nm (nanometer) If the tube is 1 nm in diameter, then veryify that 5 μm = 5*1000 nm = 5000 nm = how many diameters?

Physics
Using energy principles, (KE=kinetic energy, PE=gravitational potential energy) KE+PE=constant, so KEi+PEi = KEf+PEf KEi=0 (both are stationary) KEf=(1/2)Iω^2+(1/2)mv^2 PEi=0 PEf=0+mgh (weight descended) Equate energies: 0 = (1/2)Iω^2+(1/2)mv^2 + 0+mgh (note that h...

Maths
2/5 of what was left after giving 1/6 to her mother means 2/5 of (1-1/6) of her salary. Working it out: 2/5 × (6/6-1/6) =2/5 × (5/6) =2/6 =1/3

Math
Sorry, messed up codes, the iterative equation should read: xn+1=3xn/(xn+1)

Math
Fixed points are values of x when the two sides of the iterated map are equal as n->∞. This means that fixed points are essentially the solution of the iterative equation. Here we have: xn+1=3xb/(xn+1) (please check my interpretation of your equation) To find fixed ...

physics
75W for 24 hours =0.075 kW for 24 hours =1.8 kW for 1 hour =1.8 kW-h How much would that cost?

physics
Gravitational energy (in joules) = mgh where m=mass (k) g=acceleration due to gravity (m/s²) h=height (m) Solve for h.

math
No. of digits > 6 : {7,8,9} i.e. 3 of them odd digits: {1,3,5,7,9}, i.e. 5 Total = 3×5 = 15 However, subtract number of plates with identical digits. Figure out which plates there are and calculate the final numbers.

Math
IF the size of the cubes is 1 cm³, then the number of cubes is equal to the volume in cm³. If the size of the cubes is bigger than 1cm³, then it is not possible to build the prism with the larger cubes because the GCF of 8,9,5 is 1.

Probabilit
4 red out of (4+5+2)=11 marbles Probability that first draw has no red =(11-4)/11 =7 No replacement, so probability for second draw = (10-4)/10 =6/10 Probability that both have no red = product of the two probabilities.

math
Hint: Use the triangular inequality, a+b>c where a,b,c represent three sides of any triangle.

statistics
Assuming the random selection is from a large pool of people, in which case the probability remains constant throughout the experiment. This experiment could then be modeled by the binomial distribution, with probability P(X=n)=C(N,x)px(1-p)N-x where p=probability of success...

Math

Math
Probability =C(52,12) Use your calculator function nCr to calculate C(52,12) where n=52, and r=12. Or calculate =52!/((52-12)!(12!)) =52!/(40!*12!) You need to get familiar with these calculations if you are to learn anything from probabilities.

Math
There are four suits in each deck, each with 3 picture cards for a total of 12 picture cards in a deck of 52 (different) cards. The probability of choosing r objects from a pool of n different objects is C(n,r) = n! / ((n-r)!r!) where n!=factorial n = n(n-1)(n-2)...3.2.1 For ...

Math
You have probably learned C(n,r)=n!/((n-r)!r!) is the number of combinations of choosing r objects out of n. So in general, if we have letters a,a,a, b,b, c,c,c,c there are C(3,1) ways to choose a letter a C(2,1) ways to choose a letter b and C(4,1) ways to choose a letter c ...

French
In general, you have done reasonable work, because you seem to catch the sense of the text. Here are some hints to help you in future exercises and to correct the present text. One good way to do these problems is to translating mentally and reading it aloud to check if it ...

Chemistry
Assuming the temperature remains constant, you can use Boyle's law, which says that PV=constant (at constant temperature) or P1*V1 = P2*V2

Chemistry
Convert 15°C to °K: 15°C = 15+273.15°K = 288°K Then use the ideal gas equation PV=nRT n=number of moles (constant in this case) R=constant Assume also that P=pressure constant, we have V1/T1 = V2/T2 Solve for T2 to get T2=V2*(T1/V1) Substitute initial ...

physics
To prevent sliding, friction must provide (i.e. equal) the centripetal force μmg=mv²/r Solve for μ, with v=25 m/s r=220 m g=9.8 m/s² m cancels

f(x) is a quadratic equation for which exact solutions may be obtained in many ways, including factoring, completing the square, and quadratic formula. Are you studying numerical methods where an approximate solution is required instead of an exact one? Yes, your answer is ...

French Grammar
The sentences are correct or as corrected. But if you are working on, or have learned the demonstrative pronouns celui/celle/ceux/celles, then you can apply them to avoid repeating the subject in the same sentence. For example, the first sentence could have been replaced by: &...

statistic
Let's work on this together. 1. How many questions does he need to guess right to pass the test? (include all possible values) 2. What kind of distribution does this problem fall into?

math
Right, there was a typo! Thought I corrected it. Thanks Steve! Should read: g*62+(75-g)*56=75*58

math
Let g=number of girls, and assuming all data given are exact (i.e. no rounding involved), then g*62+(75-g)*58=56 Solve for g.

physical science
All free-falls on earth starts at g (9.8 m/s²) if initiated near the surface. At high elevations, g is slightly reduced because of the greater distance from the centre of the earth. Subsequently, as velocity is substantial, air-resistance plays an important rôle in ...

Astronomy
Hint: Escape velocity =√(2GM/r) G=gravitational constant M=mass r=radius When mass is doubled, replace M by 2M, similarly for r. For further reading, see for example: http://en.wikipedia.org/wiki/Escape_velocity

Math
337 is her total score, and 84.25 is her current average up to the fourth test. If she ended up with a grade of 90, that means her total score (for all five tests) is 5*90=450. So what did she score in the final test?

algebra
Hints: here are the possible situations: When discriminant is negative: 2 imaginary roots When discriminant is a positive perfect square, such as 1, 4, 9, 16... and all coefficients are rational: 2 real, rational roots When discriminant is zero, and either coefficient a or b ...

Math
Use n instead of 18% in your first and second calculations. a. 500*n%=5n net receipt=500-5n = 500(1-n/100) b. 100%-n%=(100-n)% net receipt = 500(100-n)% = 500(1-n/100) Since a and b are the same, so the two calculations are equivalent for any value of n.

math
Hints: Actual Length = model length * scale Actual area = model area * scale² Actual volume = model volume * scale³

algebra II
Use the law of logarithms: log(a)+log(b)=log(ab) => log(x+2)+log(x-3)=log(x+29) log((x+2)(x-3))=log(x+29) => (x+2)(x-3)=x+29 x²-2x-35=0 (x-7)(x+5)=0 Solve for x, and reject any solution which will result in a negative argument to the log function.

computer programming
Store three arrays: String[] model={"Chevrolet",....}; double[] dailyRate={50,85,53,60,60,70}; double[] milageRate={0.27, 0.45,....0.40}; int nModel=0; int milage=0; double cost; then present a menu for user to choose from, remembering that model[0]="Chevrlet&...

Math
Yes, that's what I got, and here's how: 1125(4*.262-1)=54

Math
Yes, you're right. I misread the 80% as the copayment. Most health insurance companies that I have seen have annual deductibles, which I assumed. Here I interpreted that the \$300 was a previous payment, which exceeds the annual deductible. However, since no mention was ...

Math
He paid \$300 in copayments, so that means that the deductible no longer applies on subsequent payments. Out of the \$2300 in hospital bill, he has to pay the copayment of 80% = 2300*0.80 = \$1840 added to the previous copayment, he paid a total of 1840+300 = \$2140 Please explain...

phy
0°K------------273.15°K 0°K-------------0°C--------232°C Conversion from °C to °K °K = °C + 273.15

physics
t = time of free fall = 35 s Horizontal distance = horizontal speed × duration of free fall For the vertical component of free fall, Vyi=initial vertical velocity = 0 a=vertical acceleration = -g = -9.8 m/s² ΔY = vertical position change ΔY = Vyi(t)+(1/2...

Physics
Yes, you have figured it out. On the other hand, extraneous information is present in everyday real problems. In solving problems, it is a necessary skill to pick out relevant information.

Calc
Given a polynomial function in t where I(t) = 0.00009045t5+0.001438t4−0.06561t3+0.4598t2−.6270t+99.33 We need to find the extrema for 0≤t≤10. Steps: find first derivative I'(0), equate to zero. Solve for the zeroes which correspond to the extrema, say t1 ...

Physics
Whole circumference of a circle of radius r = 2πr. 1 km/h = 1000/3600 m/s Distance = speed × time.

physics/chemistry
Assuming the flask was filled with propane only, and propane approximately closely an ideal gas at the given temperature, you can use the ideal gas equation PV=nRT where R=8.314 J-K-1mol-1 P=pressure in pa V=volume in m³ n=number of mols (pure number) T=temperature in &...

Calculus
Try reading the following in compensation for the quick lesson. http://www.economicshelp.org/blog/7019/economics/examples-of-elasticity/ and for equations/formulas: http://study.com/academy/lesson/the-elasticity-of-demand-definition-formula-examples.html p=price=\$2 q=quantity ...

Computer science
The logic looks correct except for one minor logic error in: sum=sum+(i*rem); which should read sum=sum+i*r; You need to make sure the statements execute correctly in Matlab syntax. For example, an integer division can be written as dec=dec./2; or dec=idivide(dec,2); Also, be ...

physics
We will take velocity and distance as positive upwards, and distance = 0 at the bottom of the cliff. Use Distance = Vi*t-(1/2)gt² For the stone thrown upwards, X1(t)=9.33t-(1/2)gt^2 For the stone thrown downwards, X2(t)=5.28-9.33t-(1/2)gt^2 When they meet, X1(t)=X2(t) and...

Math
Subdivide the shape into known sub-figures. Sum the areas of all the sub-figures.

Your answer is quite close. I get 337.66. If you have been copying intermediate answers to 4 figures, that would make the difference. Try to use the calculator memory instead of copying down intermediate answers.

physics
Vi=29.2 m/s θ=31.7° Vxi=Vi cos(θ) = 24.844 m/s Vyi=Vi sin(θ) = 15.344 m/s since Vy(t)=Vyi-gt so at the maximum, Vy(t)=0, or Vyi-gt=0 => t=Vyi/g The optimal (best) horizontal distance would therefore be the horizontal distance travelled during this time...

French
Subjunctive mood should be used when any of the following is involved in the situation: - doubt, - wish - desire - emotions So that applies to 1A and 1B. The present tense of the subjunctive mood for the two verbs are: You can use the Bescherelle or Internet to look up the ...

System ?
You can set up a system of equations: let x=number of 2-point questions, then 40-x = number of 3-point questions. 2(x) + 3(40-x) = 100 Solve for x. Or you can solve mentally as follows: If all questions are worth 2-point, then the total = 2*40=80 points, or 20 points too few. ...

Math Check
The answer is basically correct, except for an error of sign in one place which I think you will spot readily. Also, when there is multiplication following division, insert parentheses to express clearly what is needed. For example, 6/4y should be interpreted as (6/4)y (left-...

math,Computer
Are you already familiar with linked lists? We assume A and B are singly linked lists, i.e. linked in the forward direction only. To attain the end of a list, the node pointer must traverse every node from head to tail. The number of operations is therefore n, where n=size of ...

math,Computer
I interpret this as: if (A==φ)A|B == B else A|B = Ha|Tab But then we're defining A|B using Tab, which is the tail of A|B. Sounds to me a circular definition. Can you please clarify the definition, or give your comments?

maths
Time to reach bottom = t s distance 44 m= (1/2)gt^2 where g=acceleration due to gravity = 9.8 m/s² => t=sqrt(2*44/g)=2.997 s Subtract this time from 3.12 seconds will be the time needed for sound to travel 44 m. Use Distance=speed × time to find speed of sound.

French
If I say "con-" is a common prefix, does that help?

math
"...students having the best score..." ? 85/100 has a range of [84.5%,85.5%] 170/200 has a range of [84.75%,85.25%] I would take the better of the worst case, namely, candidate with a least score of 84.75%. In practice, I would decide by a final interview.

statistics
P(lose once) = (15-2)/15 = 13/15 = (13/15)1 by the multiplication rule: P(lose n times) = (13/15)n

Math
Total reading time: 8/9 World news: 1/4 of 8/9 = (1/4)*(8/9)=2/9 Remaining time = 8/9 - 2/9 =(8-2)/9=6/9 Half of remaining time = (1/2) 6/9 = 3/9 =1/3 h.

Think of how many ways you can choose a chairman (10), vice-chairman (9 remaining people), secretary(8), treasurer (7). Multiply them together using the product rule, and the product is 10*9*8*7 =10*9*8*7*6*5*4*3*2*1/(6*5*4*3*2*1) =10!/(10-4)!

math
where μ represents the frequency of occurrence (success) within a given time period (week). In this case, failure is considered "success". so μ =3 "successes" / 20 weeks =3/20 By definition of the Poisson distribution, P(x;μ)=e-μμx/x! where x...

math
The outcomes are X={0,1,2,3}, with probabilities P(x)=(1/8)x!/(3!(3-x)!) The mean, or expected value E[X]=ΣxP(x) =Σ(0*(1/8)+1*(3/8)+2*(3/8)+3*(1/8)) =12/8 =3/2

French
The apostrophe would be used when some letter is dropped, and in some cases only. For example, il faut que elle... would be shortened to il faut qu'elle... because phonetically it is difficult and unpleasant to read the two vowels one after another. It is perfectly ...

French
A. Your answer is very close, except that the qu' is part of the Est-ce que...., and should be eliminated. The question reads: Boit-elle un apéritif? Note: (bois, bois, boit, buvez, buvez, boivent) However, the auxiliary verb vouloir must be maintained, so the ...

math(Discrete)
Translation into English: For all x which are integers, there exist y and z which also are integers, such that x=5y+7z. Is the above statement true? Give it a few tries: triplet means (x,y,z) (0,7,-5) is a solution (1,10,-7) is a solution (2,-1,1) is a solution (3,2,-1) is a ...

French
The French expression "venir de" is a special tense that means "just" (in temporal sense), or "a short while ago". Je viens de terminer mon travail (I just finised work). Il vient de me parler au téléphone. (He talked to me on the ...

Yes, that is correct, but try to understand why you do that by studying the unit circle.

cotangent: 1 secant: negative square root 2 cosecant: negative square root 2 *sin: square root 2 / 2 *cosine: square root 2 / 2 tan: 1 The terminal side lands in the third quadrant, where only tangent (and cotangent) is positive. So sine (cosec) and cosine (sec) are all ...

Algebra 2 (DIVIDEPOLYNOMIALS)
Here's a link for long division. http://www.purplemath.com/modules/polydiv2.htm Quite frequently we use synthetic division, with less writing to do: http://www.purplemath.com/modules/synthdiv.htm Hint: the given problem leaves no remainder.

Math
A reference angle is the positive acute angle between an angle and the horizontal axis. For the different possible cases, see: http://www.mathwarehouse.com/trigonometry/reference-angle/finding-reference-angle.php

Math
The first step is to convert one equation into the same form as the other. Most of the time, we would convert the second to the form of the first, i.e. x=-2-(2/3)y (parentheses added according to rules of BEMPAS, or PEDMAS. x+2=-(2/3)y Multiply by 3 on bothe sides 3x+6=-2y 6=-...

math
If Esi is always behind Becky, we have only 4 independent choices for each position. So for the first position, there are 4 choices, for the second, 3 choices left, then 2, then 1. The number of permutations is the product of the 4 numbers.

math
I'll solve the first one, and the second one can be solved similarly. (n-2)!/(n-3)! =(n-2)(n-3)!/(n-3!) =n-2 therefore n-2=15 => n=17 Check: (17-2)!/(17-3)!=15!/14!=15*14*...*1/(14*13*..*1) =15 checked ok.

French, foreign language
Don't know if you have read Ms Sue's and my comments, but here's the link: http://www.jiskha.com/display.cgi?id=1426621380 Is the exercise corrected by hand or a computer? With a computer, you need to do exactly what it expects. I don't understand how it/he/she...

probability
9    10   11   `1 ********       ******** There is an overlap between the two periods. Since each individual function is uniform, the resulting f(x) is a step function such that: f(x): (1/4)/2 = 1/...

Calculus AB: Area Between Curves
hints: steps: 1. find the equation of the tangent line. The slope m of the line equals f'(-1), and passes through (-1,f(-1))=(-1,4)=(x1,y1). The equation of the line is then y-y1=m(x-x1), or g(x)=m(x-x1)+y1 Draw a sketch of f(x) and g(x) for your own information. 2. Find ...

Cal state
Number of seats in first row = 26 Number of seats in last row = 26+30-1=55 We can find the sum using Gauss's method: 26+27+28+.....+54+55=x 55+54+.....+28+27+26=x Add the two rows 81+81+.....81 (30 rows) = 2x 30*81 = 2x x=1215 seats

Maths
Yes, that is correct.

Maths
Given: S:M:L = 16:23:20 Total = £1180 Actual amounts for each S:M:L = (£1180/(16+23+20)*(16:23:20) =£(320:460:400) Marvin takes out £100, and Lucy puts in £x, so new ratio (8:9:12) = (320:360:400+x) If we multiply the left-hand side by 40, we get...

Math
Cost per litre = \$x Number of litres bought = 500/x Number of litres sold, q = 500/x-5 new sale price per litre = x+2 Total revenue = q*(x+2) = 540 so (500/x -5 )*(x+2) = 540 Solve for x (cost of paint per litre) I'll get you started: Multiply both sides by x (500-5x)(x+2...

Math
Factor by grouping: 3x^2+5xy-2y^2 =3x²+6xy -(xy+2y²) =3x(x+2y)-y(x+2y) =(3x-y)(x+2y) =0 So either (3x-y)=0 or (x+2y)=0 Hence find the two possible values of x/y.

math
25% of a class of 40 means there are 0.25*40=10 girls. Let x new girls joined the class. total number of girls = 10+x total size of class = 40+x Given girls now make 40% of class, then (10+x)÷(40+x) = 0.40 Cross multiply and solve for x. Alternatively, solve by guess ...

Math
The future value FV can be calculated by summing payments and simplification using factorization: FV = S(1+(1+r)+(1+r)^2+...+(1+r)r^(n-1)) =S((1+r)^n-1)/((1+r)-1) =S((1+r)^n-1)/r FV=future value S=Semi-annual payment r=interest per period (6-months) n=number of periods (6-...

Algebra
fourth term: ar^4 7th term: ar^7 Let common ratio = r then 7th term / 4th term = ar^7/ar^4 = r³ therefore r = cube root of r³ Fifth term = fourth term * r

math
The first step in evaluating a limit would be to substitute the limiting value into the expression. If it evaluates to a valid number, that is the limit. Example: limit x->1 x²/x =1²/1 = 1 Since sinx/tanx + tanx.sinx ≡ 1/cos(x) so the limit is 1/cos(0)=1.

Math
Solve for x in 1500+0.04x=5000

The number of CD's between Q1 and Q3 should be half of the total number of CD's. From the plot, you will not know how many cost less than \$14.6, but since Q1 is 14.6, there are at most one quarter of the number of CD's cost less than \$14.60. (One quarter of 12 CD&#...

Sum and Difference
Sum and difference problems are solved as follows: Larger number = (sum+difference)/2 Smaller number = (sum-difference)/2 So 1/p = (4+3/2)/2 = 11/4 p = 1/(11/4) = 4/11 I will leave it to you to do the smaller number (1/q).

maths
We are given x²+y²=137 (x-y)=7 this means 49=(x-y)² =x²-2xy+y² =x²+y²-2xy =137-2xy From 49=137-2xy can you solve for xy? The longer way: equation 1: x-y=7 equation 2: x²+y²=137 Now solve the non-linear system in x and y.

Math
Use law of exponents (ax)^b = a^b × x^b y=kx^3 y1=k(1.5x)³=k(1.5^3)x³=3.375kx³=...

math
There is an ambiguity in the question to be clarified about the interest rate. Generally annual interest is quoted. The wording of the question casts a doubt as to 7.2% is monthly or annual interest. Considering that 86.4% annual interest is illegal in some countries, 7.2% ...

See later post

Math
You're welcome. Also note a correction is required: 0.02/5 = 0.004/1 < 0.01=1%

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