# Posts by MathMate

Total # Posts: 11,748

Physics
For the velocity, equation PE and KE. PE=KE mgh = (1/2)mv² and solve for v. (both g and h are negative, y is positive upwards) For time, use y=vi*t+(1/2)at² for vi=0, equation simplifies to y=(1/2)at² (Notice that both y and g are negative)

PHYSICS
Resolve forces into x,y components. Let the x-components of forces be f1,f2 then f1+f2=332 f1-f2=122 Solving f1=(332+122)/2=227 f2=(332-122)/2=105 Assuming θ=0 (in direction of raft) so the forces are 227 and 105N

not statistics
It depends on the tax rate, hence on where the payment is done. If the tax rate is 10%, then the sales tax is 993.91*0.10=\$99.39

physics
average speed = total distance travelled / total time Total distance travelled = 30km/h * 0.5 h + 25km/h * 1 2/3 h + 40km/h *2 h = 136.667 km Total time = 0.5+1 2/3 + 2 = 4.1667 h Average speed = 136.667/4.1667 = 32.8 km/h

physics
Given: θ=arctan(3/4)=36.87° approx. m=0.5 kg μ=0.25 weight of block can be resolved into force down plane, F = mg sin(θ) and normal force, N = mg cos(θ) Let P be applied force parallel to plane (upwards) to maintain equilibrium, then Consider ...

Physics
Don't know how much work "I" do during this motion because I don't have the equations to calculations human work done during physical activities. However, work done on the 10N block is zero, the way you calculated it. When you lift the block, you are doing ...

computer system organization
Have you reviewed the three given sites as suggested? What are your thoughts about the quality of information supplied?

Physics
Nice question! Use energy. KE=PE+W Let x=distance up the slope (1/2)mv²=mg(sin(&theta))+μmg(cos(&theta))x Solving for x: x=(v²/((2g(sin(θ)+μcos(&theta))

Statistics
Use binomial distribution. P(r)=nCr*(p^r)(q^(n-r)) n=7 p=1/6 q=1-1/6=5/6 we need to calculate P(5)+P(6)+P(7) P(5)=7C5*(1/6)^5*(5/6)^2 =0.001875 P(6)=1.25*10^-4 P(7)=3.57*10^-6

Algebra
If you plot the graph, it will be a parabola concave up, with a zero at x=0, or x=4. Therefore f(x)≤0 when x∈[0,4). The correct answer would be S={x|x∈(-∞,0]∪[4,+∞)}

mathematics
Assuming garden has uniform width w. 2*60*50=(50+w)(60+w) => w²+110w-3000=0 w=22.62 or -132.62 (rejected) So wall is 22.62 m from the house.

physics
In the case of uniform acceleration, distance = average speed * time distance = 0.04m average velocity = (350+210)/2 m/s = 280 m/s Time = distance / average speed = 0.04/280 s = 1.43*10-.4 s

math
Out of 100 questions, 48 correct answers 11 blank 41 wrong answers total 100 We don't get to see the scheme. Assume the scheme says: 1 point for each correct answer, -1 point for each incorrect answer, 0 for leaving it blank. So total points =48-41-0 =7

physics
Acceleration = (vf-vi)/t = -2.24/2.55 = -0.8784 m/s Δx = vi*t + (1/2)at² =2.24(2.55)+(1/2)(-0.8784)(2.55²) = 2.85 m

Geometry
Have you read the Wiki article on cyclic quadrilaterals? It gives a lot of information on the subject. If it still does not answer your question, you could post your question and we could all learn something. http://en.wikipedia.org/wiki/Cyclic_quadrilateral

physics
For maximum height, equate PE and KE mgh=(1/2)mv² h=(1/2)37.1²/9.8=70.2 m at 50m, KE is reduced by mgh => (1/2)mv²=(1/2)m(37.1)²-mg(50) v=sqrt((37.1²-2(g)(50)) =19.9 m/s

physics
Conversion factor: 1 m/s = 3.6 km/h Δv=(vf-vi)=vi+aΔt 163 km/h = 163/3.6 = 45.28 m/s 45.28=vi+5.79*3.6 vi = 24.4 m/s = 88.0 km/h

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.

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%

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.

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

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....

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

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

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 + ...

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

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-...

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*...

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

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 ...

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.

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

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

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?

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