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Posts by MathMate

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If car is accelerating uniformly, after 10 seconds, the velocity is 30/2=15 m/s. Distance travelled is time * average velocity =10 s × (0+15)/2 = 75 m Or calculate average acceleration a=30 m/s / 20 s =1.5 m/s² Distance =vi t + (1/2) a t² =0(10)+(1/2)(1.5)(10&...

Telecommunication 2.
Radio waves are electromagnetic waves and obey the relation v=fλ f=frequency (Hz) λ=wavelength (m.) v=velocity, m/s and in vacuum,equals the speed of light for electromagnetic waves c=3×108 m/s in air, v is slightly less than c. So solve for f in the above ...

"KE 1= 1/2*0.002kg*300^2m/s=30 j KE2=0 work " should result in 90 J (and not 30 J), and assuming energy dissipation is uniform, then KE=W=F*d, F=KE/d=90/.05=1800 N which is exactly the answer you got for the second part. Note: units which are proper names (pascals, ...

Correct, well-done! :)

Chemistry - Stoichiometry
From the equation, find the stoichiometric ratio of HCl and MnCl2 which equals 2. This means that 1 mol of MnCl2 will generate 2 mol of HCl. Using the fact that 1 mol of HCl occupies 22.4 L at STP, you will find how many mol of MnCl2 will be required to make 0.054 L of HCl.

maths - cosine rule
Use the cosine rule: c²=a²+b²-2ab cos(C) with a=7, b=15, and included angle C would vary from 0 to 180 degrees. Note that these limits themselves are not valid values, i.e. max>c>min. They represent the sum and difference of the two sides.

An equation of a line must include an equal sign, and your answer does not have one. You probably meant y=-4x+10 Recall some properties of a dilation includes 1. conservation of parallelism, ------------------------------ i.e. lines before and after dilation should remain ...

Almost. It's 800 cubic feet. Units are important in the answers.

(2, 2 square root 2, and 2 square root 3) means (2, 2√2, 2√3) Square each number: (4, 2²×2, 2²×3) =(4,8,12) Do these numbers make a Pythagorean triplet?

See your later post.

linear algebra check
You have u1 and u2 correct. Don't know if you're expected to rationalize the denominator, in which case, u1 would read [(√3)/3,(√3)/3,(√3)/3]...etc. u3 should be [0,....] A good way to check your answer is to verify if u1.u2=0, u1.u3=0, u2.u3=0.

Keq can be obtained by substitution of the product concentrations and reactant concentrations in the definition of Keq. If in doubt, read: or examples in...

You can solve using the compound interest formula: Fv = Pv * (1+i)^n Fv=future value, to be calculated Pv=Present value ($8000) i=interest per period (6%/2=0.03) n=number of periods (2)

chemistry ap
Assuming zinc is in excess. 18 mL of 6.00 M H2SO4 equals 0.108 mol From Zn+H2SO4 -> ZnSO4 + H2 we deduce that 1 mol of H2SO4 produces 1 mol of ZnSO4. So mass of ZnSO4 produced is 0.108 mol, multiplied by the molecular mass of ZnSO4.

Use compound interest formula: Fv=Pv(1+i)^n here Fv=7500 Pv=present value to be calculated i=8%=0.08 (assume compounding annually) n=18 transposing, Pv=Fv/(1+i)^n

math discrete
Oops, I didn't do what the question asked. Go with Reiny's solution!

math discrete
f(x)=4x³ g(x)=2x h(x)=x² h◦(g◦f) =h◦(g(x²)) =h◦(2(x²)) =h◦(2x²) =4(2x²)³-5 =4(2²x²)³;-5 =4(2^6 x^6)-5 =256x^6-5

You can read the response to the previous post and try to work out the answer.

By the law of floatation, any floating object will displace a mass of fluid equal to its own mass. So a floating object of volume 1 m³ density 400 kg/m³ will displace 400 kg of water, i.e. fraction of immersed object is 0.4, equal to its specific gravity, and ...

math - typo?
A cubic foot of water weighs 62.4 pounds. An imperial gallon of water weighs 10 pounds. You used kg all over, so it is not clear whether there is one or more typos in the question. You will need to check the question and make appropriate corrections before your answer can be ...

First possibility: 10 B = 10 B After that, we can take advantage that 3B weighs as much as 2A, so you can progressive change every 3B for 2A, for example, 7B+2A = 10B 4B+4A = 10B there is one more that I will leave you to finish.

All correct except the first: The square of the length ...

5•4•3 does not equal 40, you probably meant 5*4*2 you can add 5*8*1 If order does not count, I don't see other ways.

A vector that is orthogonal to two given vectors is the cross product, namely |i j k| |x1 y1 z1| |x2 y2 z2| which in this case is |i j k| |1 6 1| |1 -9 1| Expanding the determinant, we get the following vector: <6*1+1*9, 1*1-1*1, 1*-9-6*1> <15, 0, -15> which can be...

Some cons to think about: 1. Mandatory donation will no longer be a donation, it will be an obligation. 2. What do you think about the individual rights of citizens of Canada. 3. The need may be urgent, but will the organs of ALL Canadians be required?

A translation is defined as: T: (x,y) -> (x+p,y+q) where p and q are given constants. For example: (10,3) -> (10+p, 3+q) = (1,6) 10+p=1 => p=1-10=-9 3+q=6 => q=6-3=3 So we have established that the translation is T: (x,y) -> (x-9, y+3) (note: if p is positive, ...

Algebra 2
Expand sin2θ = 2sinθcosθ so sin2θ=-cosθ 2sinθcosθ + cosθ = 0 factoring out cosθ, cosθ(2sinθ+1)=0 cosθ(sinθ+1/2)=0 Using the zero product property, we deduce that cosθ =0 OR sin&theta=-1/2 Solve...

Exponential Equations
Direct substitution of equation: Pv=present value Fv=future value Fv=Pv*(1+i)n where i=interest rate per compounding period (assumed year here) n=number of compounding periods (assumed year here). note that 2.75% is equivalent to 0.0275 for i (interest rate). If both Pv and Fv...

The difference of 2.5 minutes per day is assumed to be due to the difference in g at the two locations. If in Cayenne it loses 2.5 minutes per day, it means the period there is longer. To find how g affects the period, we are given the relationship T=k/sqrt(g) where k is a ...

If you're not getting the correct answer, I suggest you post how you got your incorrect answer so that we will help you find what went wrong. This is the whole purpose of solving problems.

chemistry to MathMate
In case you got confused with the units, I underline that the units are the same, namely, nanometre, or nm. You have a tube of length of 5000 nm, and diameter of 1 nm. How many time is the length bigger than the diameter?

chemistry to MathMate
5000 nm is correct. How many times as big is 5000 nm (length of tube) compared to 1 nm (diameter of tube)?

to CJ
Perhaps it is easier if we go back to the question to make sure we understand information given in the question, and what the question is asking. "Nanotubes are rolled up cylinders of graphite with diameters of about 1nanometer, and lengths in micrometers." The above...

links to previous posts
For reference, these are the links to related posts on the same question.

chemistry to CJ
Also, it would be of big help to you if you would re-read the question and try to understand what is being asked. It is similar to a problem like: If I can buy a candy with one penny (1 cent), how many candies can I buy with $5.00? knowing that 1$ equals 100 cents.

chemistry to MathMate
1 metre = 100 cm 5 metres = ? cm

Algebra 2
You're welcome!

Algebra 2
use the identities tanφ=sinφ/cosφ cotφ=cosφ/sinφ sin²φ+cos²φ=1 tanφ+cotφ =sinφ/cosφ+cosφ/sinφ =(sin²φ+cos²φ)/(sinφcosφ) =1/(sinφcosφ)

Chemistry - toCJ
Recall that the original question is: (I) If a nanotube is 5 micrometers long, how many diameters does this represent?

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?

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 = 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).

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.

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...

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

* 1 μm = 1000 nm (nanometer)

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?

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...

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

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

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 ...

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?

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

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.

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.

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.

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

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...

Thank you GanonTEK! Indeed, (12/52)(11/51)(10/50) is the correct answer. My bad!

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.

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 ...

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 ...

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 ...

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

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 ...

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

Quadratic equations
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: &...

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?

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

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 ...

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:

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?

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 ...

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.

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&...

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

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 ...

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...

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

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...

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.

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 ...

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

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 &...

Try reading the following in compensation for the quick lesson. and for equations/formulas: 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 ...

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...

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

math is my answer correct
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.

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...

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-...

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 ...

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?

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