Saturday

November 22, 2014

November 22, 2014

Total # Posts: 10,750

**Maths A level**

Cross sectional area =π(40²) =1600π change in height per unit time =dh/dt =(rate change in volume/cross sectional area) =-32πh^(0.5)/1600π =-0.02h^(0.5) The sign is negative because h decreases with time.
*May 23, 2014*

**Math**

W=wind speed A=air speed Equation are set up using Speed*Time = distance, or Distance/Speed = Time 2800/(A-W)=4 2/3 ...(1) 2800/(A+W)=4 ...(2) Solve system of equations for A and W.
*May 23, 2014*

**Probability**

P(being female | the person earns over $75,000) =P(F∩O)/P(O) =(585/1200)/(1070/1200) =585/1070 P(F)=650/1200 =>P(F∩O)/P(O) ≠ P(F), i.e. P(F∩O) ≠ P(F)*P(O) therefore they are not independent.
*May 22, 2014*

**physics**

G=6.67384 × 10-11 m3 kg-1 s-2 M=4.56*10^24 kg r=7.09*10^6 m Using Newton's law of gravitation, g=Force/1 kg mass =GM/r² m/s²
*May 22, 2014*

**Math**

You're welcome!
*May 22, 2014*

**Math**

An equation is not a function, but a function can be part of an equation. For example, f(x)=0 is an equation, while f(x) is a function. A function is like a black box that churns out values when given an input value or input values.
*May 22, 2014*

**physics**

velocity, acceleration (both are vectors)
*May 22, 2014*

**math**

Difference in interest rate =3.75%-3.5% =0.25% Difference in $ = $50 Use direct proportion 0.25% : 50$ 100% : ?
*May 22, 2014*

**Algebra 2**

focus(6,0), directrix x=-3 means If the distances are equal, then the squares of the distances from directrix and focus are also equal, so (x-(-3))²=(x-6)^2+(y-0)^2 (x+3)²-(x-6)²=y² Factor by difference of two squares 18(x-1.5)=y² (x-1.5)=y²/(4*4....
*May 22, 2014*

**Math**

All of these can produce a congruent figure, depending on the parameters. Rotations and translations ALWAYS produce a congruent figure. Reflection produces a congruent figure if the object has at least one line of symmetry. Images of dilations are mostly not congruent with the...
*May 22, 2014*

**Math**

B) divides AB in the ratio 1:5, but not 5:1. look for a choice which is 5/6 from point B instead.
*May 22, 2014*

**Statistics**

What do you think?
*May 22, 2014*

**Algebra 1**

Do not forget implicit parentheses of fractions, meaning that the expression should have been written (4x²-4x)/8x which equals 4x(x-1)/8x =(x-1)/2
*May 22, 2014*

**Data Management**

Probability of getting the right answer for 1 question = 1 choice out of 5, or p=1/5. Assuming independence among the 10 questions, probability of getting all 10 right = p10 Probability of passing (getting 6 or more right out of 10) using binomial probabilities =10C6*p^6q^4 + ...
*May 22, 2014*

**chem**

When pressure is constant: P1/T1 = P2/T2 Temperature should be in °K.
*May 22, 2014*

**chemistry - which equation?**

Balance which equation?
*May 22, 2014*

**math(urgent)**

This is a different problem from the one you posted earlier. x+y = (x-y)+25 Solve for y=12.5 and x can be any number. Thus x/y can be any number (infinite number of solutions)
*May 22, 2014*

**Calculus**

Assume 2x/((x-2)(x+2)) = A/(x-2)+B(x+2) Right hand side =(A(x+2)+B(x-2))/((x-2)(x+2)) =((A+B)x+(A-B))/((x-2)(x+2)) Compare denominators on both sides and equate coefficients of powers of x to get A+B=2 A-B=0 from which A=B=1 So the decomposition into partial fractions is 1/(x+...
*May 22, 2014*

**Chemistry**

-890 kJ / 1 mole ? kJ / 6.25 moles
*May 22, 2014*

**Chemistry**

Difference in solubility = 6.8-0.33 g =6.47 g/100 ml. 10 g / ? ml. (of solution)
*May 22, 2014*

**physics**

Use the component method to break down each vector into x,y components. 8km North = <0,8> 5km at 60° = <5cos60°,5sin60°> Assuming angle is in Cartesian plane (counterclockwise from east) and not bearing (clockwise from north). Add the two vectors and ...
*May 22, 2014*

**physics - erratum**

The minimum is when they are lined up and opposite to each other, and the maximum is when they are lined up and in the same direction.
*May 22, 2014*

**physics**

The resultant of two vectors A and B can have a magnitude ranging between ||A||±||B||. The minimum is when they are lined up and opposite to each other, and the minimum is when they are lined up and in the same direction. Now you can make your choice of answers.
*May 22, 2014*

**Algebra**

The cube has 6 faces, so 6 outcomes. When two different dice are thrown, there are a total of 6*6=36 outcomes. You can make a table of the 36 outcomes and find out how many of them are the same (6 out of 36). Alternatively, you can think of the red cube is thrown first with ...
*May 21, 2014*

**math**

Draw the line x=13 (which is a vertical line). Now can you decide which side of the line is the inequality satisfied, to the right, or to the left of the line?
*May 21, 2014*

**Business Math**

Use proportions: 248.24 : 50% x : 100% x=(100/50)*248.24=?
*May 21, 2014*

**Science**

Can you first check out where pharynx is located?
*May 21, 2014*

**math**

Tax rates and rules are different for different countries, and states/provinces. In most countries, tax rates depend on income level, so adds another parameter. To answer the after-tax part, you need to specify the tax rates.
*May 21, 2014*

**math/financial planning**

Earnings=20000*7.5% 30% marginal tax bracket means he pays 30% of his investment earnings in taxes. Tax=earnings * 0.30
*May 21, 2014*

**Algebra/Permutation**

nPr=n!/(n-r)! 4Pr=4!/(4-r)!=24/(4-r)! unless you know the value of r, this is the furthest we can go.
*May 21, 2014*

**math**

Between 0° and 90° - I 90°-180° - II 180°-270° - III 270°-360° - IV
*May 21, 2014*

**Math**

You can add a table between the other two, and the third table can sit only two more.
*May 21, 2014*

**Physics**

Energy/work in joules.
*May 21, 2014*

**Physics**

Work done (energy required) = mgh m=50 kg g=9.8 m/s² h=difference in elevation in metres.
*May 21, 2014*

**physics**

Given 4 resistances, and we need to sort out which one is which. Assume that the resistances are non-zero. We know that two resistances in parallel is always smaller than any of the two. Similarly, two resistances in series is always greater than any of the two. So the two ...
*May 21, 2014*

**physics**

sec(θ) = 1/cos(θ) so the given formula gives: distance = 120/cos(θ). You can use your calculator to find the distance and make your choice accordingly.
*May 21, 2014*

**MATH**

:)
*May 21, 2014*

**math**

The equation is written in the form x=a(y-h)^2+k where a=2, h=1, k=3 so the vertex is at (k,h)=(3,1) The axis of symmetry is at y=h, or y=1.
*May 21, 2014*

**Algebra**

Circle centred at origin: x²+y²=r² where r=radius. Here radius = √((√5)²+0²)=√5
*May 21, 2014*

**Geometry - need more information**

In a 30-60-90 triangle, the shortest side is half the longest side, because sin(30°)=1/2. We do not know what a,b and c stand for, namely which one is hypotenuse.
*May 21, 2014*

**physics**

To solve this problem, you would draw a diagram of the rod. Then indicate the pivot and the first load. Find the distance d1 between the first load P1 and the pivot: this is the lever arm for the first load. To balance, then load P2 multiplied by d2 must equal P1*d1. Since d1=...
*May 21, 2014*

**chem**

almost... vapour density is relative to H2. So M~2*vapour density=78.
*May 21, 2014*

**Math**

The best way to improve is to practise. Discuss with his teacher for options.
*May 20, 2014*

**Chemistry**

As Damon said, check the units. If you divide, the units do not give joules.
*May 20, 2014*

**Chemistry**

m=200 g c=0.897 J/g°C ΔT=10°C Calculate heat required, ΔQ using ΔQ=mcΔT
*May 20, 2014*

**Chemistry**

Would you like to show your work?
*May 20, 2014*

**Chemistry**

3H2+N2--> 2NH3+2709J Molecular mass of H2=2*1.008=2.016 According to the equation: 3*2.016 g H2 => 2709 J x g H2 => 5000 J Use proportion.
*May 20, 2014*

**math**

I hope it's not a trick question. Between the two dates, there are indeed 27 Tuesdays, so there are 27*8=216 person-days needed. Since 10 does not divide 216, they may not equally divide unless the days are split into shifts.
*May 20, 2014*

**"as shown below..."**

Please proofread your question. Does your question use proper grammar, capitalization and spelling, and contain all necessary information?
*May 20, 2014*

**algebra-permutations**

nPr=n!/((n-r)!) 6P0=6!/(6-0)!=1
*May 20, 2014*

**Math**

You would plot time (months) along the x-axis, and the weight along the y-axis. Positive slope means the y-values increase with increase in x-values, and negative slope means the y-values decrease as x increases. Since losing weight means weight decreases with time, you have a...
*May 20, 2014*

**Calculus**

All limit problems are different. If only the limit is known without knowing the question, we don't know the answer. Please post the complete question in order and answer can be formulated.
*May 20, 2014*

**math**

There is a good chance you have missed out parentheses in the numerator and the denominator. All fractions have implicit (i.e. understood) parentheses in the numerator and denominator. I believe your question means (x²+6x+9)/(5x+15) even though the question does not ...
*May 20, 2014*

**Math**

Assuming you want the difference in days between dates. It's a messy counting problem. First note that the dates are written in MM/DD/YYYY format. Difference in Months: October-May=31+30+31+31+30=153 days Difference in days 28-17=11 days Difference in years 2002-1987=15 ...
*May 20, 2014*

**Proofreading required.**

Please proofread your question. Does your question use proper grammar, capitalization and spelling?
*May 20, 2014*

**Trig help**

I guess Steve's interpretation of the question is correct. There was no indication of power! Please go with Steve's solution.
*May 20, 2014*

**Trig help**

If you are looking at solving 3sin(θ)=sin-1(θ) then you would be solving f(x)=3sin(x)-asin(x)=0 in which case the trivial solution x=0 can be obtained by inspection. If you're looking for 3sin(θ)=1/sin(θ) then there are 4 solutions between 0 and 2&...
*May 20, 2014*

**math**

The best way to solve these problems is to follow the instructions, draw the figure with the coordinates of each point, and then apply the transformation (rotation). I will give you a kickstart by giving the coordinates of the figure (not a rectangle). A(0,0) B(2,0) C(4,0) D(4...
*May 19, 2014*

**math Question**

a=12 c=30/2=15 b=√(15^2-12^2)=9 For a hyperbola with horizontal axis, x²/a²-y²/b²=1 x²/12²-y²/9²=1
*May 19, 2014*

**math**

Did you read the post previous to yours? It should help you get the right answer.
*May 19, 2014*

**math**

First, find the rule for a rotation of 180°, which is R(O,180): (x,y)->(-x,-y) so (3,-5) -> (-(3),-(-5)) can you take it from here?
*May 19, 2014*

**Finite Math**

The 25% means that she pays up front $6000 so she only needs to finance $18000. Over a period of 36 months, n=36=periods of one month i, monthly interest = 0.1/12 P, principal = 18000 R=rate=1+i=1+1/120 Monthly payment, A =PRn(R-1)/(Rn-1) =18000*(1+1/120)36*(1/120)/((1+1/120)...
*May 19, 2014*

**Math Question**

Figure out the rule of the sequence in terms of n, the number of terms We have common difference =6 T(0)=-12 T(1)=-6 T(2)=0 T(3)=6 Let's try T(n)=-12+6n so T(1)=-12+6=-6 T(2)=-12+6*2=0 T(3)=-12+6*3=6,... It works. So T(50)=-12+50*6=288
*May 19, 2014*

**Algebra 2**

It's the same as calculating the distance between two points. ||A||= sqrt((-13-2)²+(9-1)²) =17
*May 19, 2014*

**Math**

P(Bull's eye)=(6/16)²=0.1406 approx.
*May 19, 2014*

**Math - need more data**

To calculate the probability, we need to know the size of the dartboard and the radius of the bull's eye. A six-inch radius bull's eye has to be bigger than the eye of any living animal on earth!
*May 19, 2014*

**physics**

90 km/hour = 90/3.6=25 m/s deceleration rate, a = 5 m/s² time= 25/5 = 5 seconds Must be a new braking system :)
*May 19, 2014*

**science**

Apply F=ma (Newton's second law) where F=force (in N) m=mass in kg a=acceleration in m/s² so F=ma=10kg * 5 m/s²=50 N If the spring balance is graduated in kilograms (mass), which is the usual case, then it will show ma/g=5 kg (approximately).
*May 19, 2014*

**Science**

Total force on 4 legs =5 N + 9*9.8 N = 93.2 N Area of contact of each leg = 2.5*10-3 m² Pressure on each leg = 93.2/(4*2.5*10-3 = 9320 N/m² = 9320 Pa (pascals)
*May 19, 2014*

**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 ...
*May 19, 2014*

**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...
*May 19, 2014*

**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 ...
*May 19, 2014*

**chemistry - typo**

Can't seem to get it right! the -4 should be in superscript.
*May 19, 2014*

**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.
*May 19, 2014*

**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 ...
*May 19, 2014*

**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
*May 19, 2014*

**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.
*May 19, 2014*

**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 ...
*May 18, 2014*

**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...
*May 18, 2014*

**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 ...
*May 18, 2014*

**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.
*May 18, 2014*

**algerba - explain please**

Not sure what the question is asking. Explanations would definitely help.
*May 18, 2014*

**Geometry - erratum**

Add (4) and (5) 2CG²=a²++b²+3(x²+y²) =5(x²+y²)+3(x²+y*sup2;) (using (1) and (2))
*May 18, 2014*

**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...
*May 18, 2014*

**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 ...
*May 18, 2014*

**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
*May 18, 2014*

**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
*May 18, 2014*

**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, ...
*May 18, 2014*

**algerba**

No problem. Let us know any time if you need further help.
*May 18, 2014*

**algerba**

You will get two roots for x. Reject the negative one, and retain the positive root which is a little under 200.
*May 18, 2014*

**algerba**

Yes, the quadratic formula is: x=(-b±√(b²-4ac))/(2a) what you need inside the square-root sign is b²-4ac
*May 18, 2014*

**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.
*May 18, 2014*

**physical**

C°C = (C+273.15)° K 20°C = (20+273.15)=293.15°K
*May 18, 2014*

**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.
*May 18, 2014*

**algerba**

Answered to your other post.
*May 18, 2014*

**algerba**

You're welcome!
*May 18, 2014*

**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.
*May 18, 2014*

**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
*May 18, 2014*

**physisc**

From glass to air means from an optically denser medium to a lighter one, the light path will refract away from the normal.
*May 18, 2014*

**algebra**

Just a lucky guess, but you were right in the first place!
*May 18, 2014*

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