Posts by MathMate

Total # Posts: 12,017

science..physics
r=70 semi-circumference = πr = 70πm Displacement = 2r = 140m

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

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

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

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 ...

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.

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 ...

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

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 = ...

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

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, ...

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)

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 ...

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...

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 ...

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

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 (...

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

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.

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

geometry

geometry

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 ...

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 ...

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?

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

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

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?

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 = ...

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...

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...

math
3 persons.

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

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.

math
84:112 =(7*4)*3:(7*4)*4 =28*3:28*4 =3:4

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 ...

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

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?

physics - ?
and the question is...

Math
84 =(2³)4 =212 =10000000000002

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 ...

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

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.

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

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...

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.

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 ...

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

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

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

Physics I for College :)
You're welcome ! :)

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).

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.

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.

physics
Oops,wrong post.

physics
See for example: http://en.wikipedia.org/wiki/Coulomb's_law

physics
See for example: http://en.wikipedia.org/wiki/Coulomb's_law

finite math
You can use the formula for A in the previous problem.

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

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 ...

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

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

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

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)

physics
See if you can post by omitting "http://"

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.

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)?

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

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

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°))

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.

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

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

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)

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

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

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

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

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)

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?

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

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...

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=&...

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?

Physics :)
You're welcome! :)

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

Physics
Initial velocity=√(2gh) h=height reached. Spring constant=k compression = x = 0.125m Potential energy=(1/2)mv²=mgh =(1/2)kx² solve for k in (1/2)kx² = mgh k=2gh/x²

physics
Assuming no air resistance, and PE at bottom of tower to be zero, then At the maximum height, mgh=(224mg+m(80²)/2 h=224+80²/(2g) [assume g=32.2 '/s² =224'+99.38' =323.38' At bottom of tower, mv²/2 = m(80²)/2+mg(224) solve for v to get v...

venn diagram
If 10 failed in both, that means 130-10=120 passed at least one subject. Since 85 passed math, 60 passed science, there are 145 passes from 120 students. We conclude that 145-120=25 passed both. Hence (b) 120-25=95 passed (or failed) exactly one subject. For (a), 60 passed ...

Maths
Q1. HCF and LCM could be found using 1. factoring 2. Euclidean algorithm Q2. Let H(p,q) denote the HCF of positive integers p,q, and L(p,q) denote the LCM of p,q, then H(p,q)*L(p,q)=pq

Physics
26 m/s is about 10% from stalling for a Cessna 150. With a tailwind, the airspeed does not change, but it will be added to the ground speed ("actual velocity"). With a headwind, the airspeed does not change either, but it will be subtracted from the ground speed. ...

physics
Explained with the help of diagrams here: http://web.physics.ucsb.edu/~lecturedemonstrations/Composer/Pages/64.42.html

Math - correction
*1,499,999

Math
149,999 is the greatest integer that may be rounded to the nearest million.

Physics
It will gather speed because of acceleration due to gravity. The acceleration is g=9.8 m/s²

Physics-half way fin.
I get 62.5 using g=9.8

mathematics
The same as X or Z.

Physics
Kinetic energy is proportional to mass and also varies with the square of the velocity. So the new kinetic energy =(5*105 joules)*(114/50)²

ap physics
Magnitude:use Pythagoras theorem (note 90° between the teammate and the green). Angle (from point of view of teammate) = atan(120/60)+75° West of south since the golfer is at 75° west of south from the point of view of the teammate.

Physics
Assuming both sides of the canyon are at the same elevation, then use the range equation: range = vi²sin(2θ)/g 6.5=vi²sin(2*9.45°)/9.8 vi=sqrt(6.5*9.8/sin(18.9°) =14.0 m/s

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