Monday
July 28, 2014

Posts by MathMate


Total # Posts: 10,590

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 dur...

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...

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 f...

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

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.

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 ne...

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

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.

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 sq...

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...

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 d...

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.

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

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

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...

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 ...

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

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

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, ...

algerba
No problem. Let us know any time if you need further help.

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

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

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.

physical
C°C = (C+273.15)° K 20°C = (20+273.15)=293.15°K

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.

algerba
Answered to your other post.

algerba
You're welcome!

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.

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

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

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

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(√1...

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

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.)

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

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 m...

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 pr...

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

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

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 i...

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

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

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

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

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).

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

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.

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 g...

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&l...

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&s...

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.

physics
Time, t, to reach ground = Δx/vix = 2.329 s Use kinematics equation Δy=viy*t+(1/2)g(t)² = 10.92 m. (g=-9.81 m/s²), viy=0)

math(urgent)
Interest earned was simple interest, so in two years, the future value is 1000(1+2*0.1)=1200 With compound interest of rate i, the equivalent interest would be 1000(1+i)²=1200 or (1+i)=√(1200/1000)=1.095445 or 9.54% approx.

math
I think you mean "...from A to A'". Without the accompanying figure, every answer can be correct. You can figure it out as follows: Measure the horizontal distance between A and A', see if A' is to the left by 9 units of A. Similarly, check if A' is 3...

physics
Use conservation of momentum: m1u1+m2u2=m1v1+m2v2 m1=m2=0.5 kg u1=10 m/s u2=0 m/s v1=1.5 m/s Since m1=m2=0.5 kg, the masses can be cancelled out to give u1+u2 = v1+v2 10+0 = 1.5 + v2 v2=8.5 m/s

math
Agree! Please continue if you have a question.

geomettry
The first vertex is at 0° with the x-axis. The other vertices are at respectively θ= 60, 120, 180, 240 and 300° with the x-axis. The corresponding coordinates are at: ( 8cos(θ), 8sin(θ) ) Example: At θ=0° the vertex is (8cos(0°), 8sin(0&...

NO SCHOOL
Goods and Services Tax (applies to all Canada). Some provinces combine with the provincial sales tax to call it Harmonized Sales Tax (HST). Assume $100 includes GST, then the GST portion is $100*(10/110)=$100/11. If the GST rate is 15%, then the GST portion will be $100*(15/115).

Math
Increase per year = $900 Target=$65000 current amount = 3000 Number of years to generate exactly 65000 =(65000-3000)/900 = 68.89 years So minimum number of years to equal or exceed target = 69 years (a little more than "several" years!)

Chemistry
Heat, Q =mcΔT =1200*4.184*(86-24)° =... joules Divide by 1000 to convert to kj.

maths
I think you mean: In a triangle PQR. q=8cm , r=6cm . Cos(P)=1/12. Calculate the value of p. where capital letters mean vertices, lower-case letters mean lengths of sides opposite the corresponding vertex. Use cosine rule: p²=q²+r²-2qr(cos(P)) and solve for p.

route surveying
1 mph = 5280*.3048/3600=0.44704 m/s vi=50*.44704=22.352 m/s vf=0 a=-10 m/s² use kinematics equation vf²=vi²+2aΔx to solve for Δx. Subtract Δx from 80m to get the distance from the wall.

Math
z+7+5=4 or 14, so z=2 4+2+x+1 (from carry)=1 or 11, so x=4 0+0+1 (from carry) =y so y=1 x=4, y=1, z=2 What is xyz?

french
Jenna, In French, every accent counts, as well as capitalization. For example, "Ce concert est très ennuyeux."

math/probability
With replacement: P(BY)=P(B)*P(Y)=(6/21)*(7/21)=2/21

Physics
Without friction and air resistance, we equate potential (PE) and kinetic (KE)energies. Energies at bottom of hill = energies at top of hill. 0+(1/2)m*vi²=mgh+(1/2)m*vf^sup2; cancel m and substitute g=9.8 m/s² vi=20 m/s h=15 m (1/2)(20²)=9.8*15+(1/2)vf² Sol...

Math
Amount = Pert where P=principal, present value so 225500=Pe.0865*(8+125/365) solve for P to get: 109585 (approximately)

physics
Initial volume of liquid, V = 3.5 × 10-4 m³ Change in temperature, ΔT =(78-5)=73° Spillage, ΔV =3.6 × 10-6 m³ Coefficient of volume expansion over that of the can =(ΔV/V)/ΔT =(3.6*10^(-6)/(3.5*10^(-4)))/(78-5) =1.4090*10^(-4) C...

Calculus
This sounds like a physics problem: Work done = increase in potential energy (PE) Let PE at ground = 0 After lifting, the centre of gravity of the chain is at h=10 m above ground, so potential energy =mgh =(3 kg/m * 20m)*9.8 m/s²*10m = 5880 joules Using calculus, Let &rho...

MATH 1 QUESTION PLS HELP ASAP!!!!!
The given expression is a geometric progression, which means that successive terms are obtained by a constant multiplier. If you look at the quotient between successive terms, (a) does not even give a constant ratio, so (a) is out. For (c), there is a problem with the first tw...

pre cal
Read from the following table: https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf You will see that 2.275% of data falls beyond μ+2σ and another 2.275% of data falls below μ-2σ.

algorithms
Algorithm of sorting exactly three object, a,b,c is like comparing masses of three objects on an ungraduated balance. if a>b then _if b>c then __a>b>c _else if a>c then __a>c>b __else __c>a>b else if a>c then __b>a>c _else if b>c then ___...

Physics HELP!!!!!!!!
Oops, the reduction in volume is 41.1%, so ΔV=1.933 *10^-4 m³ and work done, W=22.4*0.021/1000*0.411*101300 =19.58 j =20 j (approx.)

Physics HELP!!!!!!!!
To get work done in joules, use metres, Pa, and m³ as units. Volume at 0° and 1 atm for n=0.021 V= 22.4*0.021 L = 4.704*10^-4 Pressure 1 atm = 101.3 kPa = 101300 Pa ΔV =0.41V =1.929 *10^-4 Using Work=PΔV, =101300*1.929*10^-4 = 19.54 J = 20 J (approx.)

(2-8) Chemistry - Science (Dr. Bob222)
For B, think of the ideal gas as a compressed spring. When the compressed spring expands, it does work on the surroundings. The external pressure has to stay constant to ensure work is done. If the external pressure decreases, the system can expand without doing any work.

ALGEBRA
I suspect the equation should read P = 14.7e-0.21a in order that the pressure decreases with altitude. For P=13.29 13.29=14.70.21a e0.21a = 13.29/14.7 take log on both sides -0.21a = ln(13.29/14.7) a=-ln(13.29/14.7)/0.21 = 0.4802 miles = 2535.3 feet (approx.) = 2535 feet (appr...

Physics
m1u1+m2u2=m1v1+m2v2 12*15+36*5=12*6+36*v2 Solve for v2.

math
effective rate =(1+i/n)^n - 1 where n is the number of compounding per year. For 7% compounded semi-annually, n=2, and i=0.07 effective rate =(1+0.07/2)²-1 = 7.1225%

Chemistry help
Think of some of the energy released has been used to transform water(l) to water(g) and adjust accordingly. Watch the stoichiometric coefficient of H2O.

Calc
Oops, I got the function wrong, got an extra t on the right hand side. Go with Steve's solution.

Calc
dy/dt=-0.15y dy/y = -0.15t ln(y)=-(0.15/2)t²+C f(t)=y=Ce-0.075t^sup2; At t=0, y=3 ml. f(0)=C=3 so, let t=time for second dose, f(t)=3e-0.075t^sup2; solve for f(t)=1 ml. -0.075t²=ln(1/3) t=sqrt(-ln(1/3)/-0.075) =3.8273 (approx.) Time for third dose (after second dose)...

chemistry
Convert 811 cg to kilograms 811.0 cg = 811.0/100 g = 8.110/1000 kg =0.008110 kg Then use formula to calculate concentration in ppm. Keep the answer to 4 significant figures.

chemistry, first year university
Assuming the temperature was at STP (0°C). Consider a 1-L volume. Total pressure = 421959.129Pa = 421.96 kPa = 4.1654 atm at 0°C Partial pressure of each product = 2.08272 atm This implies PN2=PH2 =2.08272 atm Kp=PN2²PH2² = 2.0827^4 = 18.8158475075608 = 1.882...

chemistry
oops! The example reaction should read: HCl + H2O -> H3O+ + Cl-

chemistry
Ionization of an acid in water is typically the formation of hydronium ions, H3O+ and the associated spectator ion. Example: HCl + H2O -> HH3O+ + Cl- (A) Hydrobromic acid: HBr It is very similar to ionization of hydrochloric acid above. For the rest, the reactions are simil...

Science help please
Hints: Trachea is a part between the throat and the lungs. The alveoli perform the major function of the respiratory system, namely exchanges intake of fresh air (O2) with waste carbon dioxide (CO2). They are also the ultimate destination of intake of fresh air.

Physics
Note: the degree symbol is written as & d e g ; (suppress all spaces) Difference in elevation, Δh = 270m × sin(6.5°) total mass (cyclist + bicycle), m = 95 kg total weight = mg Work done (on cyclist & bicycle) =mgΔh Component of force along slope, F = mg ...

Physic
Assume diver is 8.2 m below surface (and not 8.2mm), and at the surface, P=101.3 kPa. Pressure below surface =ρgh =1000 kg/m² * 9.8 * 8.2 + 101.3 = 80.36+101.3 kPa = 181.66 kPa Assuming temperature below water and at the surface are identical, use Boyles law: P1V1=P2V...

calculus
Unless I am mistaken, the paraboloid looks like a mountain, tapering off to zero along a circle of radius 3. The cylinder has a radius of 2 and its axis is along the z-axis. So the volume of the paraboloid outside the cylinder is like you drilled a vertical hole of radius 2 th...

calculus
First find out where z(x,y) intersects the x-y plane, which turns out to be a circle given by x²+y²=9 So you would need evaluate the volume of the paraboloid above the x-y plane between the circles x²+y²=2² (cylinder, radius = 2) and x²+y²=3&...

Plz, check my answers.
#1 is not correct. Breaking down large molecules into smaller ones helps the body absorb nutrients from different kinds of food. #2 The circulatory system has the main function of collecting carbon dioxide excreted by cells in different parts of the body and exchange for oxyge...

Science
1. incorrect Food gets digested in the stomach, and nutrients absorbed in the small intestine, and finally excess water extracted in the large intestine. 2. Not sure about the "two servings", and the left and right. 3. incorrect. It is used for grinding hard food, th...

Science-3 question
#1 incorrect. Question asks which function is not one of the circulatory system. #2. incorrect. Blood has the dual function of supplying oxygen to different parts of the body and also to exchange excreted carbon dioxide with oxygen of fresh air. #3. correct.

Engineering skill
Are you able to understand the problem without the accompanied plan/sketch? If you can, kindly describe what you understand in words, or post a link to the plan. Thank you.

physics
Since the question asks for time in the air and distance from the building, we will use vi (initial velocity) as a parameter, and solve accordingly. Assume: '=feet fps=feet per second g=32.2 m/s² vi=initial velocity in fps Horizontal component of velocity, vih =vi cos...

physics
What are being asked depends on the initial velocity. Do you know the velocity, or you are expected to come up with an algebraic expression in terms of the initial velocity? Is the ball thrown at 60° above the horizontal?

Algebra 2
an=8n Substitute n=1,2,... a1=8*1=8 a2=8*2=16 ... guess you can take it from here.

physical
Write "brake", and "braking" when stopping a car. m=2500 kg vi=25 m/s vf=0 t=20 s vf=vi+aΔt 0=25+a(20) solve to get a=-25/20=-5/4=-1.25 m/s² Use Newton's second law to get force force, f = ma =2500 (-1.25) N =-3125 N Ignore the negative sign ...

Math (Calculus)
The challenging part of this problem is to find the limits of integration, which is the intersection of the two curves. As a hint, they meet at x=1.9 and 4.5 (approximately. You can use Newton's method or other iterative methods to improve the solutions. After that, the ar...

Algebra
Ratio of 80% and 30% acids is 62-30:80-62 =32:18 =16:9 To make 50 L of 62% Volume of 80% acid = 50*(16/25)=32 L Volume of 30% acid = 50*(9/25)=18 L

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