Tuesday
October 21, 2014

Posts by MathMate


Total # Posts: 10,750

Physics
Since gravity on the moon is about 1/6th of that on earth, the mercury column would be 6 times higher for the same air pressure. However, the atmosphere on the moon is about 10^13 time rarer than that on earth, the height of the mercury column is practically nil on the moon.
June 28, 2014

math
If the shapes are similar, area increase as the square of the ratio of the lengths. In this case, the shape remains the same, so old area = d*n new area = (1.1d)(1.1n) = (1.1)² dn = (1.1)² old area Percentage increase in area = 1.1²-1 = 21%
June 28, 2014

statistics
Given: μ=0.5" σ=0.01" Rejection rate = 0.8% = 0.008 rejection criterion = z<Z X=μ+Zσ =0.5+0.01Z From normal distribution tables P(Z<-2.409)=0.008 so X=0.5-0.01*2.409 =0.4758 Ans: washers with diameters less than 0.476 are rejected.
June 28, 2014

Physics
Power = work done / time = mgh / time = 55kg * 9.8 m/s² * 11 m ÷ (25*60 s) = 4.0 J/s = 4.0 W
June 27, 2014

Physics
During the reaction time of 0.59 s, car is still moving at 11 m/s, so distance to be added is 11 m/s * 0.59 s = 6.49 m. The deceleration is a=-8 m/s² vi=11 m/s vf=0 m/s (trying to stop) vf²=vi²+2ax => x=(vf²-vi²)/2a =(0²-11²)/(2*(-8)) = 7....
June 27, 2014

physics
Archimedes principle states that the buoyant force on an immersed object equals the mass of liquid displaced by the object. 230 ml of water weighs 230g Buoyant force = mg = 0.230 kg * 9.8 m/s² = 2.25 N
June 27, 2014

Physics
First convert velocities to their resultant vector: v=sqrt(vx²+vy²) =6.03 m/s Momentum=mass*velocity = 2.73 kg * 6.03 m/s = 16.5 kg-m/s
June 27, 2014

calculus
Assuming choices are payment options, i.e. we will be paying the said amounts. Total amount of payment for each choice is $9600. Assuming we have $9600 in the bank, we calculate what would we have accumulated in interest at the end of two years. Choice 1: 3800 for 2 years + ...
June 27, 2014

Physics
See http://www.jiskha.com/display.cgi?id=1259306687 as an example. Post your answer for a check if you wish.
June 27, 2014

physics
Given v=30 m/s θ=33° h=15m g=9.8 m/s² Resolve velocity into horizontal (vx) ad vertical (vy) components, vy=v*sin(θ)= 16.34 m/s vx=v*cos(θ)= 25.16 m/s Find time t to reach ground h m below: y=vy*t+(1/2)at² -15=16.34t-4.9t² => 4.9t²-...
June 27, 2014

physics
Equate KE and PE to get mgh = (m/2)vy² => vy=√(2gh) Initial velocity v=vy/sin(θ) Substitute v in range equation range=v²sin(2θ)/g = (vy²/sin²(θ))*sin(2θ)/g = (vy²*2sin(θ)cos(θ)/(g*sin²(θ) = (2gh*...
June 27, 2014

physics
given: m1 = 75.00 g c1 = ? t1 = 52.00°C m2=225.0 g c2=2.045 J/g-°C t2=07.50°C tf=9.08°C Using ΣmcΔt=0 75.00*c1*(9.08-52.00)+225.0(2.045)(9.08-7.50)=0 Solve for c1 to get c1=0.2258 J/g-°C
June 27, 2014

physics
v1=√(2gh)=√(2*9.8*0.53)=3.223 m/s v1=√(2gh)=√(2*9.8*0.53)=3.162 m/s Let ω=angular velocity r=0.363 m ω1=v1/r=8.879 rad/s ω2=v2/r=8.710 rad/s Time for one turn between t1 & t2 Δt=2π/((8.879+8.710)/2) = 0.7145s Angular ...
June 27, 2014

JEMS
t=digit in the tens place the number is then (t+2)t(t-6) If (t+2) is odd, so is t. t must be ≥ 6 or else t-6 is negative. so t could be 7 or 9 But t cannot be greater than 7 (or else t+2 will have 2 digits) therefore the three-digit number must be 571.
June 26, 2014

science..physics
r=70 semi-circumference = πr = 70πm Displacement = 2r = 140m
June 26, 2014

physics
Distance = 15+20 = 30m Displacement = final position - initial position = √(15²+20²) = 25m (magnitude) Direction =atan(20/15) =atan(4/3) =53.13 °
June 26, 2014

Physics
Actual distance = sum of length of paths Distance = sum of northings and eastings = 125cos(35°)+125sin(35°) = 102.4+71.70 m = 174.09 m Time = Displacement / velocity = 125/2.5=50s Speed = Distance / time = 174.09/50 = 3.48 m/s
June 26, 2014

physics
Acceleration = (vf-vi)/t =(0-9)/4 = -2.25 m/s²
June 26, 2014

physics
Downward component of weight (along incline) = mg(sin(θ)) Normal component of weight = mg(cos(&theta)); Upward component of horizontal force (along incline) = F(cos(θ)) Normal component of horizintal force = F(sin(θ)) Coefficient of kinetic friction = μ ...
June 25, 2014

Physics
Force on the car in the direction of the rope is F = (489/2)÷sin(θ) where θ=angle formed by the rope and the car-tree line.
June 25, 2014

math
Not clear what balance and unpaid balance are. Usually statements give unpaid balance (from last month), minus the payments, add purchases to get the new balance. Is $253 the new balance? Also, charge accounts usually charge interest by the day. How does this account work if ...
June 25, 2014

physics
Total mechanical energy = KE + PE (assume PE at ground level = 0) KE=(1/2)mv² PE=mgh h=height above ground in m v=velocity in m/s
June 25, 2014

lwtech
Interpretation of given information: The location of the theodolite (surveyor) at point A. First stake (Point B) Second stake (Point C). Points B and C are on opposite sides of the river, and distance BC represents the width of the river. For point B: distance = 562 bearing = ...
June 25, 2014

geometry
Assuming you have two triangles where ΔABC~ΔDEF, then AC/DF = AB/DE or AC=(AB/DE)*DF =(35/14)*22 =55
June 25, 2014

math
Given three non-parallel lines. We are to find the vertices of a triangle formed by the intersection of the lines. The intersections are found by solving for the three systems of two equations at a time. For example: L1: x+y+6=0 L2: x+2y-4=0 Subtract L1 from L2 gives: y-10=0, ...
June 25, 2014

Physics
Use kinematics equation: Δx = vi(t) + (1/2)at² vi=0 g=-9.8 -500=(1/2)(-9.8)t² t=√(2(-500)/(-9.8)) =10.1 s (approximately)
June 25, 2014

mathematics
It is not too clear "current" means 2014 or 2015. Will assume baseline year to be 2015 when 20 more schools are built. Number of students in 2015=1200 Number of students in 2016=1200*1.2=1440 Teacher:student ratio in 2015=1:60 Number of teachers in 2015=1200/60=20 ...
June 25, 2014

Math
Let's summarize the situation. Company: Score Total number of employees: 6 Pay period: semi-monthly. Salary break down: 2 employees at $1100 per pay 4 employees at $850 per pay Proposed employee retirement fund: $75 per pay per employee SUTA contribution (extra expense for...
June 25, 2014

Math
SUTA tax (5.4% for first $7000) =7000*0.054 =$378 Equivalent FUTA tax rates are different from state to state because of possible credit reductions. Same goes for the FUTA tax base. Assuming the FUTA tax base is $7000, and that there is no credit reduction, the effective FUTA ...
June 25, 2014

physical
Using Newton's second law: F=ma m=9.39 kg F=Fa+Fb=9.39*1.4=13.146 F=Fa-Fb=9.39*0.950=8.9205 Fa=(13.146+8.9205)/2=11.03 N Fb=(13.146-8.9205)/2=2.11 N
June 25, 2014

physics
Using Newton's second law F=ma to find the mass, then again the same law to find the frictional force. Finally use Work done = F.D Units are in kg, m/s² and J. Mass m = 7750/9.8 = 790.82 kg Frictional force = ma = 790.82 kg * 10.6 m/s² = 8382.7 N Work done (...
June 24, 2014

physics
Using the equation for spring potential energy W=(1/2)kx² so ΔW=(1/2)k(x2²-x1²) =(1/2)(30 N/m)*(0.96²-0.19²) =13.3 J
June 24, 2014

Physics
Using Distance = speed * time (a) Total time of travel =800m/6s + 800m/8s = 233.3s (b) Total distance = 800+800=1600m Average speed = total distance/total time =1600m/233.3s = 6.86 m/s Try #2 which is similar to #1.
June 24, 2014

Physics
Magnitude of displacement (vector) =290m velocity=2.0m/s (a) Walking time = distance /speed = 290m / 2.0m/s = 145s (b) Northerly distance = 290cos(25°) = 262.8m Westerly distance = 290sin(25°) = 122.6m Total distance = 385.4m Average speed = 385.4m / 145s = 2.66 m/s
June 24, 2014

geometry
Isabelle, your earlier question has been answered: http://www.jiskha.com/display.cgi?id=1403640676
June 24, 2014

geometry
Isabelle, your earlier question has been answered: http://www.jiskha.com/display.cgi?id=1403640676
June 24, 2014

Geometry
If only special parallelograms are considered (i.e. not just any parallelogram), they would be - rectangle - rhombus - square Note: one of these choices will fit more than one situation. I will leave it to you to sort out which one is which, and feel free to post your answer ...
June 24, 2014

Geometry
Since x and b are supposed to be valid for any value, take x=b=2 (or any other number) and sketch the graph. If you recognize any shape, then use the properties of the shape to do the general proof. Example: for x=b=2, the points become: (0,0),(6,2),(36,2),(30,0) A sketch ...
June 24, 2014

physics
Red is the hardest to get, since there are only 20 of them. To make sure you get some red, the worst case is you picked all the black, blue and whites (totalling 120) and still not get a red. What is the minimum you need?
June 24, 2014

MathMate Help!!!
Thank you for the brilliant and elegant proof, Steve!
June 24, 2014

pre cal
Could you tell me how far have you gone with this one? Where do you get stuck?
June 24, 2014

pre cal
I see a lot of similar questions, with no sign of effort on them, nor feed back. Do you have a problem working out these questions or you are just looking for someone to do your take-home test?
June 24, 2014

Physics
Given a position function x(t), then x'(t)=dx(t)/dt=velocity, and x"(t)=d²x(t)/dt²=acceleration. where x' and x" are the first and second derivatives with respect to time. (a) solve for x'(t0)=0 (b) evaluate position = x(t0), and displacement = ...
June 24, 2014

math
Do you mean the last "2" is a recurring decimal, like: 0.003522222222...? 0.003522222... =35.2222...÷10000 =(35+2/9)÷10000 =(317/9)÷10000 =317/90000 Note: To convert recurring decimals that start at the decimal point, divide by 999... For example...
June 24, 2014

Physics
We will assume the student was located at a point perpendicular to the direction of motion of the car. We will restrict the answer to throwing the apple in a plane perpendicular to the motion of the car, thus a two-dimentional problem. The apple has to hit somewhere on the car...
June 24, 2014

math
3 persons.
June 24, 2014

math
Let n=max. number of toppings he can afford, then 3.25*0.65n≤6.00 Solve for n.
June 24, 2014

Physics
The short answer is yes, because it all depends on the initial velocity and direction of the apple throw. Is that what the question wants? There are multiple answers unless some more constraints are imposed.
June 24, 2014

math
84:112 =(7*4)*3:(7*4)*4 =28*3:28*4 =3:4
June 24, 2014

physics
It is a question much easier to explain with a diagram. On the other hand, you probably already understand that in a simple harmonic motion (SHM), the restoring force is proportional to the angular displacement, and the direction is opposite to it (for small oscilations of a ...
June 24, 2014

statistics
If you are 85 years old, the maximum heart rate would be 220-85=135 beats per minute.
June 24, 2014

physics
The idea is that if the student did not even post the question, how much can we believe that he/she made any effort to solve the unstated problem?
June 24, 2014

physics - ?
and the question is...
June 24, 2014

Math
84 =(2³)4 =212 =10000000000002
June 24, 2014

math
I suppose the 12% is the copyright fee or an environmental surcharge. Anyway, it is some kind of a surtax. The sales taxes depend on the province in which the transaction was made. If the transaction was made in all provinces except Quebec, both GST and PST are calculated on ...
June 24, 2014

math
That would be Value * rate =110,000 *(0.025/1.00)
June 24, 2014

Geometry - ?
Do you know the area, or some other information about the triangle? With just two altitudes, an infinite number of triangles can be formed.
June 24, 2014

physics
* Δx=(vx)(t) g=acceleration due to gravity=-9.8 m/s²
June 23, 2014

physics
Quite a few assumptions have to be made as the question does not clarify them, and left them as "taken for granted". 1. The tangential speed is required at the moment the ball was caught. 2. the rotation of the ball was about an axis perpendicular to the direction of...
June 23, 2014

pre cal
Given f(x)=x²+8 Put it as y=x²+8 invert x and y: x=y²+8 Solve for y: y²=(x-8) y=√(x-8) If the question is f(x)=x³+8, you can proceed similarly.
June 23, 2014

pre cal
All even functions satisfy: f(x)=f(-x) All odd functions satisfy: f(-x)=-f(x) If a function does not satisfy either one of the above, it is neither odd nor even. Would you try to write the following expression in mathematical form? "f as a function of x is equal to 14 ...
June 23, 2014

pre cal
(fg)(x) =f(g(x)) =f(6x²) =3(6x²)+5 simplify to get final answer.
June 23, 2014

calculus
Inverse square law means that gravity is inversely proportional to the square of the distance. W2/W1 = (R1/R2)²
June 23, 2014

physics
Use mass = ρ1v1 = ρ2v2 v1/v2=ρ2/ρ1 or v1:v2 = ρ2:ρ1 v1,v2 volumes ρ1, ρ2 densities
June 23, 2014

Physics I for College :)
You're welcome ! :)
June 23, 2014

Physics I for College
If a horizontal force of 40N is needed to pull the crate, and the rope is making 30° with the horizontal, then the horizontal component is T(cos(30°) where T is the tension in the rope. So T(cos(30°))=40 N and you can then solve for T (unit is in N).
June 23, 2014

Physics
Summing up: I= 5 A V=20 V From V=IR, we have R=V/I=20/5=4 Ω So without anything in parallel with the battery, it is at the limit of tripping the fuse. Any number of resistors will reduce the main current below 5A.
June 23, 2014

physics
m=78kg v=3.5 m/s With energy conserved, PE=KE mgh=(1/2)mv² h=v²/(2g) =3.5²/(2*9.8) m Convert result to nearest centimetre.
June 23, 2014

physics
Oops,wrong post.
June 23, 2014

physics
See for example: http://en.wikipedia.org/wiki/Coulomb's_law
June 23, 2014

physics
See for example: http://en.wikipedia.org/wiki/Coulomb's_law
June 23, 2014

finite math
You can use the formula for A in the previous problem.
June 23, 2014

finite math
The right-hand side of the amortization formula should read: A(Rn-1)/(R-1) (by factoring)
June 23, 2014

finite math
Is I the annual interest or monthly interest? It will be assumed monthly interest. Present Value, P = 13000 Payment (monthly) A = 550 interest (monthly) i = 0.015 The amortization formula would equate future value with the sum of all the payments, all increased at rate of ...
June 23, 2014

finite math
You can use the amortization formula and solve for P in the next problem.
June 23, 2014

finite math
Use continuous compound formula given two problems ago, A=PeRT Here R=0.037 P=1 A=3 find T.
June 23, 2014

finhite mat
Same as previous problem, solve for R instead of T.
June 23, 2014

finite math
Continuous compound interest formula: A=PeRT to find t, take log (natural log) on both sides ln(A)=ln(P)+RT Solve for T (about 4 years) R should be written as a fraction (0.078)
June 23, 2014

physics
See if you can post by omitting "http://"
June 23, 2014

physics
Also, does N(x) represent the tensile stress at section x? Assuming the wide end is at A, then the area is given by a(x)=d²(3-2x/L) and the tensile stress is given by the weight of material below divided by the area at each section.
June 23, 2014

physics
An interesting problem. Would you kindly describe the figure so we can share how the bar was hung? Is the bar tapering downwards, i.e. thin end at the bottom, and hung at the top (ceiling)?
June 23, 2014

visual logic
input customer name input category input n if n<=50 price = 0.10*n else price = (n-50)*0.8+5.00 end if output customer name output category output n output price
June 22, 2014

finite math
I understand the formula given is to calculate interest, but does the question ask to calculate interest or amount owing?
June 22, 2014

Trig laws
Given Area of triangle ABC=7.52 m² ∠B=40° c=6 m Need to find a. We can use the trigonometric formula for area, namely Area=(1/2)ac(sin(B)) which can be solved to give a=(2*Area)/(c*sin(B)) =(2*7.52)/(6*sin(40°))
June 22, 2014

Probability
The sample space consists of 24=16 outcomes. A. more tails than heads: 1. exactly three tails: TTTH TTHT THTT HTTT 2. exactly four tails: TTTT So calculate the probability. You can try in a similar way to solve the second part.
June 22, 2014

Probability
Use the relation: P(A∪B)=P(A)+P(B)+P(A∩B) and solve P(A) Note: ∩ = & c a p ;
June 22, 2014

Probability
Choosing r unordered sets from n is given by nCr = n!/((n-r)!r!)
June 22, 2014

Compute
Missing information. You'll need three pieces of information to find the fourth in the following relation: P(A∪B)=P(A)+P(B)-P(A∩B)
June 22, 2014

Probability
7P5, where nPr=ordered set of r items chosen from n. =n!/(n-r)!
June 22, 2014

Trig laws help
Use cosine law: a²=b²+c²-2bc(cos(A))
June 22, 2014

Probability
If P(B)=p, then P(B')=1-p
June 22, 2014

Physics
Friction or not, the work done is W = F.D (scalar product) If force is applied in the same direction as the displacement, then work done is simply the product of the magnitude of the force and the distance travelled, namely W= 21N*3.3m = 69.3 J
June 22, 2014

physics
Not really. For an object which accelerates from rest, the variation of speed with time is given by: final velocity=initial velocity + acceleration * time = 0 + 10 m/s² * 2 s =20 m/s (note how the units cancel to give m/s)
June 22, 2014

Physics
Total distance = 120 km For an average of 60km/h, total time available = 120/60=2 hours Distance left = 120-30=90 km Time left = 2-1 = 1 hour What is the speed need for the remaining distance?
June 22, 2014

Algebra/Steve
Mary Ann, Hope your surgery goes well and have a speedy recovery.
June 21, 2014

math
largest 9 digit number without repeating: - must have 9 digits 999999999 - must use different digits - zero excluded (to have the largest number) - must be in reverse order starting from 9 987654321 - must be even, so invert last two digits Say 987654321 987 654 312 So what is...
June 21, 2014

physics
The fundamental frequency of a wave along a taut string is f=√(T/m)/(2L) T=tension in N m=mass of string in kg/m Since the fundamental mode of vibration consists of only half a wave, the wave velocity is f*2L, or λ=√(T/m). Here N=139 N, m=0.0036 kg/m v=&...
June 21, 2014

math
fraction of tank filled by A per minute = 1/3 fraction of tank filled by B per minute = 1/6 Fraction of tank filled in first two minutes = 1/3+1/6 = 1/2 Can you take it from here?
June 21, 2014

Physics :)
You're welcome! :)
June 21, 2014

Physics
Yes, but only in the first part. m was inadvertently omitted in the second part, my apologies. k=2mgh/x²
June 21, 2014

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