Posts by MathMate

Total # Posts: 12,095

The words are in the right places and the right form, except for #2 where the number does not agree with the definite article "le". It should be either l'assiette (sing., more probable) or les assiettes (plur.) Not knowing the instructions nor the purpose of the ...

linear algebra urgent Also, remember that u3=u3-p(u1,w3)-p(u2,w3) where p(u1,w3) is the projection of w3 on u1, etc.

linear algebra urgent
see other post

Assuming that strawberry on vanilla is considered the same flavour as vanilla on strawberry, i.e. order of the two scoops doesn't count, then there are 30C2 possible flavours, and 3 cones for a total of n=3(30C2) possible ice creams. For an order of 12 different ice-creams...

If you could post the question exactly as you were given, it would be possible for us to understand what you need. Especially in math, paraphrasing tends to lose important information.

If the GP has its third term as 9 times its first term, then the sequence is a, ar, ar² where a is the first term, ar is the second term, etc. This means that ar²/a = r²=9, or r=3. Similarly, the fifth term divided by the second term should be a^4/a^1 = a^3, or ...

The quadratic formula assume the equation to be: ax²+bx+c=0 (i.e. all terms are on the left-side of the equation). Rearrange the equation to be 3x²+4x-6=0 and try again. You do not need a graphing calculator to find the zeroes. Either by hand, or a regular calculator...

Trigonometry (identities) (last help needed)
Typically with simplification like these, you would convert all functions into sine and cosine, and simplify from there on. Use sin²x+cos²x=1 whenever appropriate.

Trigonometry (identities ?)
Trigonometric identities involve an equal sign with a different expressions on either side. So it's not clear what exactly you require in your questions. Do you need to simplify the expressions? I suggest you check for typos as well as I do not see what β has to do ...

To find W⊥, you can use the Gram-Schmidt process using the usual inner-product and the given 5 independent set of vectors. Define projection of v on u as p(u,v)=u*(u.v)/(u.u) we need to proceed and determine u1...u5 as: u1=w1 u2=w2-p(u1,w2) u3=w3-p(u1,w3)-p(u2,w3) u4=w4-...

f(x)=9x³-4x^5 F(x)=∫f(x)dx=(9/4)x^4-(4/6)x^6+C Given F(1)=0, solve for C and hence find F(4) F(1)=(9/4)1^4-(4/6)1^6+C=0 => C=(4/6)-9/4=(8-27)/12=-19/12 => F(x)=(9/4)x^4-(4/6)x^6-19/12 Find F(4)

Math (Help please)
Rows are horizontal, numbered from top to bottom, columns are vertical, numbered from left to right. For example, element at row 1 column 3 is equal to 6, element at row 2 column 4 is equal to 0.

physics - work, power
We do not support LaTeX here, but you can use / for division, and unicode symbols for special characters. Power = work / time work = Force * distance speed = distance / time force * speed = force * distance / time I believe the four equivalences are sufficient for you to get ...

READ - to Sarah
Well said! Thank you!

Mass of water that escapes per unit time = m Since the mass of water drops in height by an equivalent of h=1.14 m, we can equate change in energy = 0, or mgh-(1/2)mv^2=0 Solve for v

Power for resistors in series = V²/(R1+R2) Power for resistors in parallel = V²/(1/(1/R1+1/R2)) = V²*(1/R1+1/R2) Solve for R2.

Power = V²/r watts so resistance for the 75W bulb R1 = 120²/75 Ω = 192 Ω Similarly calculate R2 for the 25W bulb. Net resistance of two resistors in parallel R = 1/(1/R1+1/R2)

Without air resistance, time to drop to ground (irrespective of horizontal velocity) t = √(2gh) horizontal distance = horiz. velocity * t

Mechnical principles
Archimedes principle: Buoyant force on a submerged or floating object is equal to the weight of fluid displaced. Volume of metal = volume of fluid displaced = weight of fluid displaced / density of fluid = (buoyant force) / density of fluid = (500-446) g / 1000 g/L = 54 mL ...

1-4 are correct. For #5, interest = 1200*0.045*2=108 principal = 1200 Total to repay = 1200+108=1308.

Math help
Yes, B is correct, here's how: 3.36/6=(3+0.3+0.06)/6=3.00/6+0.30/6+0.06/6

4.5% compounded monthly is i=0.045/12=0.00375 per month. n=38 months Present value, Pv=125 Future value, Fv = Pv(1+i)^n

4***5***6***7***8***9***10 If your studying time is a total of 6 hours between 4 and 10 pm. Time left after 8 pm is 2 hours. Assuming random checking, probability that study time after 8 would be the time period between 8 and 10 divided by the total possible time from 4 to 10.

The four digits are distinct, so there are 4! possible permutations of the digits.

I have not checked or proved, but believe (6,8,10) is the only triplet that is consecutive even. If you would like to search for more triplets, here's a reference to the work of Brahmagupta: "Pythagorean triples[edit] In chapter twelve of his Brahmasphutasiddhanta, ...

Physics !
A. you get the idea, but results can be simplified further Since the bulbs are identical each with resistance r, then in series, R=3r, in parallel, 1/R=(1/r+1/r+1/r)=3/r, in other words, R=r/3. B. Current = i, governed by V=iR. For light bulbs in household circuit, V is ...

Let x=number of mystery books on the shelf then 3x = total number of books on the shelf we are told that x/5<10<x/4 multiply by 20, 4x<200<5x which means that 40<x<50 So the number of mystery books can be any number between 41 and 49. In other words, the ...

Energy = mgh h=difference in elevations between floors. The number of steps is irrelevant because it's the total difference in elevations that counts. If m is in kg, g in m/s², and h in metres, the result mgh is in joules.

Bread costs $2 a loaf. How much would 1 loaf cost? How much would 2 loaves cost? How much would 10 loaves cost? etc. Similarly, Babysit earns $10 an hour. How much for 2 hours? How much for 5 hours? How much for 10 hours? How much for h hours?

Physics - impressive
Your posting speed is impressive, at less than 20 second interval for 7 posts. However, your efforts in solving problems is at the other extreme. The more effort you show, the more chance that help will be given in priority. In fact, you are encouraged to post a problem, study...

(a) Total tension = tension due to mass + tension due to acceleration = mg + ma (b) tension at uniform velocity = tension due to mass only = mg

It turns out that detecting planets around other stars is by the periodic dimming of the star, caused by the "eclipse" of the star by the planet. A smaller planet will dim the star to a lesser extent, hence either the periodic dimming phenomenon is more difficult to ...

Equate the centripetal force to 6.8g, i.e. mv²r = 6.8mg solve for r. Note that mass of aeroplane cancels out.

At the bottom of the swing, the vine is subject to two forces, gravity force = mg centripetal force = mv^sup2;/r m=mass of Tarzan (kg) g=acceleration due to gravity (9.81 m/s²) v=tangential velocity (m/s) r=radius of circular motion =length of vine (m) At point of rupture...

Centripetal force is the force that maintains an object in a circular motion. This is an external force that acts on the object in the direction of the centre of the circular motion, namely tension of the string in this case. Centripetal force may be calculated using the ...

By the pigeon hole principle (where each hole houses one car), it is impossible to have 23+34=57 repairs in 50 lifts (cars). So the surplus must go to cars that need both repairs. This is the least number of cars that need both repairs. Assuming that all cars need at least one...

v²-u²=2aS v=0 u=-7.5 m/s S=-4.2 m Solve for a=acceleration in m/s² a=7.5²/(-2×4.2) =6.7 m/s²

Median is the middle number of a sorted list of data such that there are as many numbers above it as there are below. For example, median of the set of numbers {3,5,7,10,14,18} is 8.5, which is the average of the two middle numbers. The median of {1,4,9,13,16} would be 9, ...

"adorer" is a transitive verb (meaning it requires a direct object). Based on Missy literal translation can you correct the sentence? Alternatively, you can say simply J'adore ... the warm days....

French (if correct translation/grammar)
Indeed, Ms Sue is right. To clarify, could you tell us if the objective of the exercise is to write a literary essay, or is it a translation exercise? In either case, it would be much easier if you would give the original English version, seeing that the text shows evidence of...

The second parachutist must open the parachute at the moment that she catches up with the first, i.e. has fallen the same distance as the first. 1. Establish the time/distance relation of first parachutist. For the first 3 seconds, distance = 0 + 9.8*(3²) = 44.1 m total ...

1 revolution=2π radians 1 minute = 60 seconds (a) Angular acceleration = 180 rpm/8 s =22.5 rpm / s = 22.5*(2π) radians/60s /s =3π/4 rad/s² (b) No. of revolutions =average angular speed * time =(0+180)/2 rpm * (8/60) min = 12 revolutions

Power = work done / time Work done =mgh =50*9.8*250 =122500 J Time =10*60 s =600 s Power = work done /time =122500/600 J/s = 204.2 W

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.

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