# Posts by MathMate

Total # Posts: 12,094

Physics
1 HP = 745.6999 W 4 HP = 2982.7996 W 4t = 4000 kg Use mgh=PΔt h=PΔt/mg =2982.7996*10/(4000*10) =0.75m approximately

maths
Correct! Well done! :)

maths
use proportions/ratios: 1 7/8 : 2 1/2 ≡ x : 4 Simplify ratios: 15/8 : 5/2 ≡ x : 4 15 : 20 ≡ x : 4 3 : 4 ≡ x : 4 Solve for x.

math
Use ratio/proportions: 5.58 : 318.76 ≡ x% : 100 Product of means = product of extremes 318.76*x% = 5.58*100 x% = 5.58*100/318.76 = 1.75% approx.

fractions/math / Help!
With what Reiny showed, there should be sufficient information to work out 425 by yourself as an exercise. I will give you another example, 525: 525÷5=105 105÷5=21 21÷3=7 since 7 is a prime we cannot go further. so 525=5*5*3*7=3*5²*7 You're ...

collge sydney
Hints: Kinetic energy of a rotating object is given by: KE = Iω² I is moment of inertia in kg-m² and ω is angular velocity in rad/s. 1 RPM= 2πradians/60 s = π/30 rad/s.

Algebra
Correct! Well done! :)

math
one-to-one (injection): every element in the codomain is mapped by at most one element of the domain. onto (surjection): every element in the codomain is mapped by at least one element of the domain. We can see that f(x) is both one-to-one but not onto, since f(1)=4, f(2)=7, ...

Algebra
(E)--- 8x-14 ----(G)--- 4x+1 ----(F) Since EF=59, => 8x-14+4x+1 = 59 Solve for x.

(a) An equivalence relation must satisfy the following three requirements: 1. reflexivity (a,b)R(c,d) is reflexive if (a,b)R(a,b)is defined. Since a-2d=c-2b ≡ a+2b=c+2d so (a,b)R(a,b) is defined since a+2b=a+2b Therefore R is reflexive. 2. symmetry R is symmetric if (a,b...

math
In general, days of the week advance one day per year (on the same day/month). For leap years, days from first of January to the 28th of February will jump TWO days if it is a leap year. For example, January 1st 1900 was a Monday. January 1st 1901 was a Tuesday (note that 1900...

math
Break up 6^8 => 2^8*3^8 10^6 => 2^6 * 5^6 Multiply together the odd factor of each number to get the largest odd factor of the product.

math
Original square area = n*n u² New dimensions: (n+m), (n-m) New area = (n+m)(n-m)=n²-m² u² Change in area = difference of above areas.

math
Song 1: 1,2,3,4 song 2: 5,6,7,8 song 3: 9,10,11,12 ... song 9: 33,34,35,36 ... song ?: 73,74,75,76

phy
Given a=<-1,-4,2> b=<3,2,-2> c=<2,-3,1> bxc= i j k 3 2-2 2-3 1 =<-4,-7,-13> so a.(bxc) =<-1,-4,2>.<-4,-7,-13> =4+28-26 =6

Chemistry
Start with writing a balanced equation: 4Fe3O4+O2 => 6Fe2O3 Then use stoichiometric coefficients and molar masses to solve the remainder of the problem.

phy111
We assume that the wind is blowing east at x km/h, represented by the vector <x,0> The truck is moving along the vector <p,q>, where sqrt(p²+q²)=70 km/h, or <sqrt(70²-q²), q> We also know that the resultant of the two velocities equals <...

phy111
In what direction is the truck moving, due south, south-west? Answers will vary depending on the direction.

phy111
Displacement=0 velocity=displacement/time =0

Maths
The solution of this problem is based on finding numerical values of parameters a and b in the PDF f(x). Recall that the given PDF is zero over the domain R except that f(x) is non-zero over (0,1). Therefore all integration should be performed from -∞ to +∞ but for...

Math
1. Total area = 30*20 ft² Let x=width of walkway, final area = (30-2x)(20-2x)=400 Solve for x. 2. Lawn area = 60*80 m² Final lawn width = x Pool area = (60-2x)(80 2x)=(1/6)(60*80) Solve for x.

math
Solve by elimination: Eliminate y by adding equation (3) to equation 1: 4x+z=12 Similarly, add 2*(3) to equation (2): 5x+5z=30 You can continue the elimination process to find x and z. Back-substitute to find y.

math
Use the binomial distribution, p=P(chemistry)=0.4 n=12 (sample size) r=number taking chemistry P(n,r)=nCr*0.4^r*(1-0.4)^(n-r) where nCr=n!/((n-r)!r!) is binomial coefficient. For probability of getting AT MOST 4 taking chemistry, add up all possible cases, i.e. 0,1,2,3,4, or P...

college physics
360 degrees in 27.3 days. Angular speed = angle/time 360 degrees / 27.3 days = ? degrees/day? If necessary, use conversion 1 day = 86400 seconds to find degrees/s.

college physics
Assuming the mass of 5kg is suspended freely, i.e. under influence of gravity, then the force (tension) on the wire is equal to 5g, where g=acceleration due to gravity, 9.8 m/s².

Geometry
The longest side is the hypotenuse, 6a+1 So use Pythagoras: (a+1)^2+(6a)^2=(6a+1)^2 and solve for a, reject all values of a≤0.

statistics
Number of children = 3 Possible number of boys = {0,1,2,3} X=number of boys - number of girls ={-3,-1,1,3} P(X)= probability of event X. b g X P(X) 0 3 -3 1/8 1 2 -1 3/8 2 1 1 3/8 3 0 3 1/8

science (physics)
Initial velocity v0= <1,2> a(t)=<0,g> v=∫a dt = <0,gt>+C => v(t)=<1, gt+2> x(t)=∫v dt = <t,(1/2)gt²+2t>+C Assume x(t)=<0,0> at t=0, then C=0 x(t)=<t, 2t+(1/2)gt²)

PHYSICS
radius of earth = 6378.1 km Assuming g is not affected by other heavenly bodies, then Newton's law of gravitation applies: g=GMm/r^2=k/r^2 (k=a constant) => g'r'^2=gr^2 r'^2=r^2(g/g') r'=r sqrt(g/g') =6378.1 sqrt(9.80/0.980) = 2.02*10^4 km approx.

operating system
In simple terms, a deadlock is a situation where two or more (minimum 2) processes are stubbornly holding on to a resource while waiting for another, creating a situation where certain resources are never available, and hence no work gets done for either of the processes. ...

physics
1 kW = 1 kJ/s Work done = 22 kW * 60 s = 22*60 kJ = 1320 kJ If the efficiency changes to 75% from 100%, the work done is reduced in the same ratio.

math
Assuming you are referring to the normal distribution, and depending on the context, it could be sample value, observed value, sample limit, etc.

phy113
Degrees fahrenheit = deg.C*(9/5)+32

Geometry
First find area of base: hypotenuse = 13 one leg = 12 other leg = √(13²-12²)=5 Area of base = 5*12/2=30 unit² Volume of prism =(area of base)*height/3 =?

maths needed fastly
I'll solve one, and will let you try the others as exercise. x=(4/5)(x+10) multiply by (5/4) on both sides: 5x/4 = x+10 subtract x from each side 5x/4-x =10 x/4=10 x=40 Check: (4/5)(x+10)=(4/5)(40+10)=40=x ok.

mathe
Let the cone radius = R cone height = H Let cylinder height = h then cylinder radius, r = R(1-h/H) Volume of cylinder, V =πr²h =πR²(1-h/H)²h For maximum volume, dV/dh=0 π(1-h/H)^2R^2-(2πh(1-h/H)R^2)/H=0 which simplifies to: (H^2-4hH+3h^2)=0 which ...

physics
Initial speed = 98 km/h = 98/3.6 m/s Work done = KE(final)-KE(initial) = (1/2)1370(0²-(98/3.6)²) = -508 kJ (approx.)

physics
Work done = F.D = 1.57*0 = 0 J.

statisticss
Calculate Z=(x-μ)/σ and look up the normal distribution table for the probabilities.

physics
First 30km with a speed of 30km/h means it took 1 hour. For an average of 40km/h over 60 km, total time = 60/40 = 1.5 hours. Time left for 30 km = 1.5-1 = 0.5 h. Can you calculate the speed needed for the second half of the journey?

Physics
Both correct!

Physics

Physics
Correct for both.

Physics
Let initial velocity = vi final velocity = vf (negative if opposite in direction) Change in momentum, ΔM = m(vf)-m(vi)=m(vf-vi) a) Case A: vf=0, ΔM=-m(vi) Case B: vf=-vi, ΔM=-2m(vi) The absolute value of the change is greater in case B. b) Force = ΔM/&...

math
x=blue, y=green x/(25+x+y)=1/4 Cross multiply and simplify 4x=25+x+y => 3x-y=25 y/(25+x+y)=1/3 Cross multiply and simplify 3y=25+x+y => -x+2y=25 Solving: 5x=75 => x=15 y=3*15-25=20 z+15/(60+z)=4/13 Cross multiply 13(z+15)=4(60+z) 9z=45 z=5 5 blue beads must be added.

math
If the roots of a quadratic equation are equal, that means the discriminant equals zero, or b²-4ac=0 (for ax²+bx+c=0) So expand the expression and see if you can factorize the result to suit the conditions.

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