Tuesday
September 16, 2014

Posts by MathMate


Total # Posts: 10,730

physics
Use the component method to break down each vector into x,y components. 8km North = <0,8> 5km at 60° = <5cos60°,5sin60°> Assuming angle is in Cartesian plane (counterclockwise from east) and not bearing (clockwise from north). Add the two vectors and ...
May 22, 2014

physics - erratum
The minimum is when they are lined up and opposite to each other, and the maximum is when they are lined up and in the same direction.
May 22, 2014

physics
The resultant of two vectors A and B can have a magnitude ranging between ||A||±||B||. The minimum is when they are lined up and opposite to each other, and the minimum is when they are lined up and in the same direction. Now you can make your choice of answers.
May 22, 2014

Algebra
The cube has 6 faces, so 6 outcomes. When two different dice are thrown, there are a total of 6*6=36 outcomes. You can make a table of the 36 outcomes and find out how many of them are the same (6 out of 36). Alternatively, you can think of the red cube is thrown first with ...
May 21, 2014

math
Draw the line x=13 (which is a vertical line). Now can you decide which side of the line is the inequality satisfied, to the right, or to the left of the line?
May 21, 2014

Business Math
Use proportions: 248.24 : 50% x : 100% x=(100/50)*248.24=?
May 21, 2014

Science
Can you first check out where pharynx is located?
May 21, 2014

math
Tax rates and rules are different for different countries, and states/provinces. In most countries, tax rates depend on income level, so adds another parameter. To answer the after-tax part, you need to specify the tax rates.
May 21, 2014

math/financial planning
Earnings=20000*7.5% 30% marginal tax bracket means he pays 30% of his investment earnings in taxes. Tax=earnings * 0.30
May 21, 2014

Algebra/Permutation
nPr=n!/(n-r)! 4Pr=4!/(4-r)!=24/(4-r)! unless you know the value of r, this is the furthest we can go.
May 21, 2014

math
Between 0° and 90° - I 90°-180° - II 180°-270° - III 270°-360° - IV
May 21, 2014

Math
You can add a table between the other two, and the third table can sit only two more.
May 21, 2014

Physics
Energy/work in joules.
May 21, 2014

Physics
Work done (energy required) = mgh m=50 kg g=9.8 m/s² h=difference in elevation in metres.
May 21, 2014

physics
Given 4 resistances, and we need to sort out which one is which. Assume that the resistances are non-zero. We know that two resistances in parallel is always smaller than any of the two. Similarly, two resistances in series is always greater than any of the two. So the two ...
May 21, 2014

physics
sec(θ) = 1/cos(θ) so the given formula gives: distance = 120/cos(θ). You can use your calculator to find the distance and make your choice accordingly.
May 21, 2014

MATH
:)
May 21, 2014

math
The equation is written in the form x=a(y-h)^2+k where a=2, h=1, k=3 so the vertex is at (k,h)=(3,1) The axis of symmetry is at y=h, or y=1.
May 21, 2014

Algebra
Circle centred at origin: x²+y²=r² where r=radius. Here radius = √((√5)²+0²)=√5
May 21, 2014

Geometry - need more information
In a 30-60-90 triangle, the shortest side is half the longest side, because sin(30°)=1/2. We do not know what a,b and c stand for, namely which one is hypotenuse.
May 21, 2014

physics
To solve this problem, you would draw a diagram of the rod. Then indicate the pivot and the first load. Find the distance d1 between the first load P1 and the pivot: this is the lever arm for the first load. To balance, then load P2 multiplied by d2 must equal P1*d1. Since d1=...
May 21, 2014

chem
almost... vapour density is relative to H2. So M~2*vapour density=78.
May 21, 2014

Math
The best way to improve is to practise. Discuss with his teacher for options.
May 20, 2014

Chemistry
As Damon said, check the units. If you divide, the units do not give joules.
May 20, 2014

Chemistry
m=200 g c=0.897 J/g°C ΔT=10°C Calculate heat required, ΔQ using ΔQ=mcΔT
May 20, 2014

Chemistry
Would you like to show your work?
May 20, 2014

Chemistry
3H2+N2--> 2NH3+2709J Molecular mass of H2=2*1.008=2.016 According to the equation: 3*2.016 g H2 => 2709 J x g H2 => 5000 J Use proportion.
May 20, 2014

math
I hope it's not a trick question. Between the two dates, there are indeed 27 Tuesdays, so there are 27*8=216 person-days needed. Since 10 does not divide 216, they may not equally divide unless the days are split into shifts.
May 20, 2014

"as shown below..."
Please proofread your question. Does your question use proper grammar, capitalization and spelling, and contain all necessary information?
May 20, 2014

algebra-permutations
nPr=n!/((n-r)!) 6P0=6!/(6-0)!=1
May 20, 2014

Math
You would plot time (months) along the x-axis, and the weight along the y-axis. Positive slope means the y-values increase with increase in x-values, and negative slope means the y-values decrease as x increases. Since losing weight means weight decreases with time, you have a...
May 20, 2014

Calculus
All limit problems are different. If only the limit is known without knowing the question, we don't know the answer. Please post the complete question in order and answer can be formulated.
May 20, 2014

math
There is a good chance you have missed out parentheses in the numerator and the denominator. All fractions have implicit (i.e. understood) parentheses in the numerator and denominator. I believe your question means (x²+6x+9)/(5x+15) even though the question does not ...
May 20, 2014

Math
Assuming you want the difference in days between dates. It's a messy counting problem. First note that the dates are written in MM/DD/YYYY format. Difference in Months: October-May=31+30+31+31+30=153 days Difference in days 28-17=11 days Difference in years 2002-1987=15 ...
May 20, 2014

Proofreading required.
Please proofread your question. Does your question use proper grammar, capitalization and spelling?
May 20, 2014

Trig help
I guess Steve's interpretation of the question is correct. There was no indication of power! Please go with Steve's solution.
May 20, 2014

Trig help
If you are looking at solving 3sin(θ)=sin-1(θ) then you would be solving f(x)=3sin(x)-asin(x)=0 in which case the trivial solution x=0 can be obtained by inspection. If you're looking for 3sin(θ)=1/sin(θ) then there are 4 solutions between 0 and 2&...
May 20, 2014

math
The best way to solve these problems is to follow the instructions, draw the figure with the coordinates of each point, and then apply the transformation (rotation). I will give you a kickstart by giving the coordinates of the figure (not a rectangle). A(0,0) B(2,0) C(4,0) D(4...
May 19, 2014

math Question
a=12 c=30/2=15 b=√(15^2-12^2)=9 For a hyperbola with horizontal axis, x²/a²-y²/b²=1 x²/12²-y²/9²=1
May 19, 2014

math
Did you read the post previous to yours? It should help you get the right answer.
May 19, 2014

math
First, find the rule for a rotation of 180°, which is R(O,180): (x,y)->(-x,-y) so (3,-5) -> (-(3),-(-5)) can you take it from here?
May 19, 2014

Finite Math
The 25% means that she pays up front $6000 so she only needs to finance $18000. Over a period of 36 months, n=36=periods of one month i, monthly interest = 0.1/12 P, principal = 18000 R=rate=1+i=1+1/120 Monthly payment, A =PRn(R-1)/(Rn-1) =18000*(1+1/120)36*(1/120)/((1+1/120)...
May 19, 2014

Math Question
Figure out the rule of the sequence in terms of n, the number of terms We have common difference =6 T(0)=-12 T(1)=-6 T(2)=0 T(3)=6 Let's try T(n)=-12+6n so T(1)=-12+6=-6 T(2)=-12+6*2=0 T(3)=-12+6*3=6,... It works. So T(50)=-12+50*6=288
May 19, 2014

Algebra 2
It's the same as calculating the distance between two points. ||A||= sqrt((-13-2)²+(9-1)²) =17
May 19, 2014

Math
P(Bull's eye)=(6/16)²=0.1406 approx.
May 19, 2014

Math - need more data
To calculate the probability, we need to know the size of the dartboard and the radius of the bull's eye. A six-inch radius bull's eye has to be bigger than the eye of any living animal on earth!
May 19, 2014

physics
90 km/hour = 90/3.6=25 m/s deceleration rate, a = 5 m/s² time= 25/5 = 5 seconds Must be a new braking system :)
May 19, 2014

science
Apply F=ma (Newton's second law) where F=force (in N) m=mass in kg a=acceleration in m/s² so F=ma=10kg * 5 m/s²=50 N If the spring balance is graduated in kilograms (mass), which is the usual case, then it will show ma/g=5 kg (approximately).
May 19, 2014

Science
Total force on 4 legs =5 N + 9*9.8 N = 93.2 N Area of contact of each leg = 2.5*10-3 m² Pressure on each leg = 93.2/(4*2.5*10-3 = 9320 N/m² = 9320 Pa (pascals)
May 19, 2014

Chemistry
Only volume and temperatures change, pressure remains constant, Charles's law applies. V1/T1=V2/T2 Temperatures must be converted to °K. V1=100 ml T1=27°C=300.15°K V2=80 ml. The above applies when the volume change is at constant pressure to avoid work done ...
May 19, 2014

Physics
If the string remains taut at all positions, the minimum tangential speed of the rock has to generate a centripetal force equal to the weight of the rock, or mg = mv²/r Here m=2 kg r=0.80 g=9.8 m/s² w=weight=mg=19.6 N solve for v: 2(9.8)=2v²/0.8 v=√(196/25...
May 19, 2014

Physics
Kinematics equation: Δx = vi*Δt + (1/2)aΔt² Here Δt = elapsed time, in seconds vi=initial velocity = +35 m/s a=acceleration due to gravity = -9.8 m/s² Δx=displacement = -100 m -100=35Δt + (-9.8/2)Δt² Solve by quadratic ...
May 19, 2014

chemistry - typo
Can't seem to get it right! the -4 should be in superscript.
May 19, 2014

chemistry - typo
(typo in format) Cross multiply to get 3.0*10-4(0.001-x)=x² Solve for x, reject negative root. and pH is -log10(x). It should be between 3 and 3.5.
May 19, 2014

chemistry
Denote the chemical formula for the acid to be HA, then Ka=[H+][A-]/[HA]=3.0*10-4 at a given temperature. ACE table for H+ A- HA A 0 0 0.001 C x x -x E x x 0.001-x At equilibrium, 3.0*10-4=x²/(0.001-x) Cross multiply to get 3.0*10-4(0.001-x)=x² Solve for x, reject ...
May 19, 2014

physics
Work done by force = work done by load (W) 60 N * 1.2 m = 0.2 m * W Solve for W to get W=60*1.2/0.2 N = 360 N
May 19, 2014

physics
Work done =mgh = 60 kg * 9.8 m/s² * 1.2 m = 705.6 j Power = work done / time = 705.6 j / 1.5 s. = 470 watts (approximately) The difference may be due to the assumed value of g in the question.
May 19, 2014

strength of materials
The deflection of a cantilever beam with a point load P at the end is given by δx=PL³/(3EI) P=point load L=length E=modulus of elasticity I=area moment of inertia all in compatible units. The area moment of inertia for the beam in question is equal to that of the ...
May 18, 2014

algerba - mea culpa
After reading your response, I rechecked and surely I found the culprit: me. I have the wrong sign! The correct solution should have read: This is how you could approach it: Start with: (0.052*310)/(310+g)=59.4 cross multiply to get (0.052*310)=59.4 (310+g) Expand and evaluate...
May 18, 2014

algerba
I looked over the possible answers, and 310 is among them. If you are in a chemistry or physics class, or if you have already worked on significant digits, 310 would be the correct answer to 3 significant digits, since the original data are all to that accuracy. Sorry that I ...
May 18, 2014

algerba
309.72862 is correct. This is how you could approach it: Start with: (0.052*310)/(310+g)=59.4 cross multiply to get (0.052*310)=59.4 (310+g) Expand and evaluate: 16.12=59.4g+18414 transpose 59.4g = 18414-16.12 g=(18397.88/59.4) =309.72862 as you had it.
May 18, 2014

algerba - explain please
Not sure what the question is asking. Explanations would definitely help.
May 18, 2014

Geometry - erratum
Add (4) and (5) 2CG²=a²++b²+3(x²+y²) =5(x²+y²)+3(x²+y*sup2;) (using (1) and (2))
May 18, 2014

Geometry
Nice problem involving 1. definition of sine 2. the cosine rule 3. the properties of medians, i.e. intersection of medians divides them in ratios of 2:1. First need to do a diagram in words. Given triangle ABC, with medians AX and BY meeting at G. AX and BY are orthogonal (i.e...
May 18, 2014

algebra
R(x) is the revenue as a function of the number of units sold, x, where R(x)=(100x-x²)x if p(x)=100x-x² then R(x)=0 whenever p=0. So the problem would be reduced to solve for p(x)=0, or 100x-x²=0 x(100-x)=0 which gives us x=100 would make p(x)=0 and R(x)=0. Put ...
May 18, 2014

Physics
Assume L for length of stick. Put the fulcrum at x from the 500-g mass. The centre of gravity of the stick is at the centre, L/2, where the mass is assumed to concentrate. Take moments about the fulcrum: 500*x=200*(L/2-x) Solve for x in terms of L: x=L/7
May 18, 2014

algebra
So the problem is : Pull out 2 letters out of 5 distinct letters {P, A, R, I, S} from a hat with replacement. Need P(R,vowel) P(R)=1/5 P(vowel)=2/5 With replacement, the two draws are independent, so multiplication rule applies. P(R,vowel)=(1/5)*(2/5)=2/25
May 18, 2014

algebra
Future value = 50000 period = semi-annual number of periods, n = 15*2=30 Annual interest rate, = 11% i = 0.11/2=0.055 Periodic payment (6 months) = P Let r=1+i=1.055 Future value, 50000 = P(1+r+r²+r³+...+rn-1) = P(rn-1)/(r-1) by factorizing therefore, using (r-1)=i, ...
May 18, 2014

algerba
No problem. Let us know any time if you need further help.
May 18, 2014

algerba
You will get two roots for x. Reject the negative one, and retain the positive root which is a little under 200.
May 18, 2014

algerba
Yes, the quadratic formula is: x=(-b±√(b²-4ac))/(2a) what you need inside the square-root sign is b²-4ac
May 18, 2014

college algebra
The cube root of 600 is the length of one side, s. If you use a calcultor, then you would type in: 600^(1/3) or 600 xy (1/3) depending on the type of calculator you have.
May 18, 2014

physical
C°C = (C+273.15)° K 20°C = (20+273.15)=293.15°K
May 18, 2014

physical
Use T=(m1T1+m2T2)/(m1+m2) =(50*20+50*40)/(50+50) =30°C Note: special case when the masses are equal, and the liquids are identical, the temperature is the mean of the two liquid temperatures.
May 18, 2014

algerba
Answered to your other post.
May 18, 2014

algerba
You're welcome!
May 18, 2014

algerba
Cross multiply to get: 8.44(3x²+100)=3900x+1000 Rearrange: 25.32x²-3900x-156=0 Solve for x using quadratic formula: x=-0.03999 or x=154.07 approx.
May 18, 2014

bdu applied maths
If x,y form the base, and z is the height, then Area of base = xy Lateral area = perimeter*height = 2(x+y)z Total surface area of open box =xy+2xz+2yz
May 18, 2014

physisc
From glass to air means from an optically denser medium to a lighter one, the light path will refract away from the normal.
May 18, 2014

algebra
Just a lucky guess, but you were right in the first place!
May 18, 2014

algebra
Fractions have implicit parenthese around the denominator and numerator. I have a feeling that the two log3 terms both belong to the denominator, in which case the expression should have been written, according to the BEDMAS rules, (2*log7 16)/((log3(√10+1)+log3(√...
May 18, 2014

Chemistry
When temperature remains constant, use Boyle's law: PV = constant, or P1V1=P2V2 Also, for conversion, use 1 atm = 101.325 kPa
May 18, 2014

Chemistry
Use ideal gas law: PV=nRT (T in °K) => P=nRT/V =1.3 mol *0.0821 L atm °K-1 mol-1 *(22+273.16)°K/13 L =2.423 atm =2.4 atm (approx.)
May 18, 2014

chemistry
Use c1v1=c2v2 c1=230 g/L c2=200 g/L v2=2 L Solve for v1. Water to be added equals v2 - v1=2L - v1
May 18, 2014

Physics
Use the kinematics equation: Δy = viΔt + (1/2)gΔt² Here Δy=-25' vi=0 (initial velocity) g=-32.2 ft/s² Δt=√(2Δy/g) =√(2*25/32.2) =1.246 s. (approx.) Velocity =1.246*(-32.2) fps =40.12 fps =40.12/5280*3600 mph =27.4 ...
May 17, 2014

math
In the Cartesian plane, +x-axis is to the right, -x is to the left. Similarly, +y is up, and -y is down. For example, a translation of 2 units to the left and 3 units up would be written as (x,y)->(x-2,y+3) so a point (5,3) would become (3,6). Apply the same logic to the ...
May 17, 2014

c++
If you could use further help, post what you've got so far, and we'll take it from there.
May 17, 2014

Degree symbol
The degree symbol (°) may be written (at this forum) as the following, with all spaces suppressed: & d e g ;
May 17, 2014

physics
Assuming question wants height of table, Δy. Use kinematics equation: Δy = viyΔt + (1/2)gΔt² Assuming 1.1m/s is horizontal velocity (slides off table), so viy=0 g=-9.8 m/s² Δy=0+(1/2)(-9.8)(0.35²) =-4.9(0.35²) =-0.060 m Floor ...
May 17, 2014

Math -___-
Detailed explanation on how to make a stem and leaf plot. Difficult to show without fixed format characters. http://www.purplemath.com/modules/stemleaf.htm
May 17, 2014

physics
Use Newton's second law: F=ma=100000kg * 2 m/s² = 200000 N
May 17, 2014

Science Physics
Similar to previous problem of crate. Use Newton's second law: F=ma where F is net force=applied - friction.
May 17, 2014

Science Physics
F=160 N m=20 kg Ffr=80 N Net force causing acceleration = 160-80 =80 N Use Newton's second law, F=ma a=F/m =80/20 =4 m/s²
May 17, 2014

Algebra
At vertex, x=6/10=0.6 Try f(-1)=-2 f(0)=9 f(2)=-1 So -1 and +2 could be approximate zeroes of f(x).
May 17, 2014

UOS
Pseudocode: read Capacity, MilesPerGallon MaximumRange:=Capacity*MilesPerGallon print "Maximum Range = ", MaximumRange
May 17, 2014

CHemistry
First calculate molecular masses of MH2 = (2*1.008) and MH2O = (2*1.008+15.999) Then mass of hydrogen produced =mass of water *(MH2/(2MH2O)) Note the factor 2 in the denominator comes from the stoichiometric coefficient of H2O.
May 17, 2014

Math
The answer to the question as posted is n=942!/(15), which is a large number approximately equal to: 1.45*10^2393. I suspect the factor 15n should read 15n. If that's the case, I offer the following. 942! is the product 942*941*940*....3*2*1 If n=1, then 942!/(15) should ...
May 17, 2014

Math
There are 20 yellow x green 80-x pink Total 100 P(YP)=(20/100)(80-x)/99 P(GY)=(x/100)(20/99) If P(YP)=P(GY) then 20(80-x)=20x after cancelling identical denominators Solve for x: x=1600/40=40 So there are 40 green and 40 pink mints. If P(YP)>P(GY) then 20(80-x)>20x 40x&...
May 16, 2014

Physics
1. calculate distance travelled before brakes have effect. 2. Once deceleration of 10 m/s² starts, car decelerates at that rate. Time taken to decelerate = initial velocity / 10 m/s² = 2 seconds. 3. Calculate distance travelled during those two seconds: vf²=vi&...
May 16, 2014

Algebra
I think the formula should read: h=-16t^2+vt+s Where s=initial height = 25' v=initial velocity = 96 fps t=time in seconds -16=half of acceleration due to gravity in ft/s² so the equation becomes h(t)=-16t²+96t+25 solve for t when h(t)=0.
May 16, 2014

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