July 28, 2014

Posts by MathMate

Total # Posts: 10,590

For #1, y′= x(1+ y) write y'/(1+y) = x put p=y+1 p'/p = x ln(p) = x²/2 + C p=ex²/2+C y=ex²/2+C-1 =Cex²/2-1 or =Cex²/2

calculus-answer check
Oh, sorry, I had the two terms divided and not multiplied.

calculus-answer check
I do not have the same value as yours. Can you post the derivative?

Newton's second law: F=ma if F and m are both identical, the a would be the same, where a=deceleration in m/s². Using the kinematic equations for the first car, vf²=vi²+2aΔx vf=final velocity=0 vi=initial velocity Δx=stopping distance and solve f...

Not sure what your choice is, and also if the actual question should read: Y(x)=sqrt(x+4)-3 or Y(x)=sqrt(x+4-3) [as you had it] Can you check if there is a typo?

I suppose you mean Y(x)=sqrt(x+4)-3 in which case you can evaluate the function for the various given values and see which one, if any, gives Y(x)=0.

[H3O+]=10-4.67 = [BrO-] [HBrO]=0.200-10-4.67 Ka=[H3O+][BrO-]/[HBrO]=2.286×10^(-9)

Assuming the "semicircular shape" is like the loop of a roller-coaster, and we want the body to complete the circle. At the top of the loop, of diameter d (radius d/2), the velocity must be such that the centripetal force exerted by the rails ≥0, or mv²/(d/2)...

Assuming the first sentence to mean: "A 10kg box is initially at rest on top of a hill 10m above the ground level." I.e. the box is resting at the top of the hill, which is 10 m. above ground level below. Using ground level as zero potential energy, then At top of hi...

Does the missing figure show the mass of the ball? There is centripetal force of magnitude mv²/r (horizontal) and the weight (vertical) of mg to form the resultant tension of the string of 7.7N. r is the horizontal radius, so must be adjusted for the angle the string make...

Economics & Statistics
20 represents the slope. Slope is defined as the increase in y-value divided by the increase in x-value, that is: slope = Δy / Δx

math probability
1/11 is correct. We can do it in two different ways, easy and difficult. Easy way: Pick 2 of the 5-marbles and any of the remainder. 2/12*1/11=2/132=1/66. The two 5-marbles can be arranged in 4P2 = 4!/(2!2!)= 6 ways, so probability = 6* (1/66) = 1/11 The difficult way: We subt...

Correction to equation (a) W=kx^2 ÷2 (watch units) (b) use same equation, with W=50 ft-lbs = 600 ft-in. solve for x.

(a) W=kx^2 (watch units) (b) use same equation, with W=50 ft-lbs = 600 ft-in. solve for x.

Chemistry - Science (Dr. Bob222)
Some of the heat generated would have been diverted to convert 2H2O(l) to 2H2O(g), so heat generated would be reduced by 2*40.7=81.4 kJ/mol. Can you take it from here?

Use: cot(θ)=cos(θ)/sin(θ) sin²(θ)+cos²(θ)=1

C1V1=C2V2 (a) 1.0 mol/L * 0.2L = C2 * 1.0 L Solve for C2 (b) C2 (from a) * 25 cm³ = (1.6 mol/L)*V2 Solve for V2.

Calculat the distance d (metres) it hits the ground when there is no wall. Use reflection to calculate the bounce off the wall. Then case 1: if d>10 m. Ball hits ground at (d-10) before the wall. case 2: if d<10 m. Ball hits ground at d m. from the girl.

This is different from public, or private. Sometimes it is call package or default access. Read up at:

use mv²/r = mg solve for v.

Data Structure
Assume the boat and the boys are on the same side of the river at the start and finish. To get one villager across, the two boys must row over, leave a boy on the other side, row back alone, let a villager row over, then then boy on the other side will bring the boat back, com...

chemistry: please check work
Procedure should be correct, did not check the calculations.

If the assumption is that the population growth is constant at 4.5%, then Let x=population in 2000, 8791894=x*1.04510 Solve for x.

transpose terms to the form y=ax+b, then a is the slope and b is the y-intercept. 6x=y+1 becomes y=6x-1, compare with y=ax+b and find what a (slope) and b (y-intercept) are.

Translating in English, you have defined a universal set of integers from one to ten. Then you defined sets (presumably belong to the universal set) which combine ("unioned") to form a new set. The first, {x|x is multiple of 2} means the set of even numbers between 1...

Use: C1V1=C2V2 Measure all concentrations in mol/dm^3, and volumes in dm^3 2.0*V = 0.5*2.5 V=1.25/2=0.625 dm^3 or, approximately, 0.63 dm^3 rounded to 2 significant figures.

Do you need help with the flow-chart, algorithm, the coding or debugging? It would be best for you to tell us what you have learned, and what you have done so far.

math mrs. sue HELP!!!
Say you have a data set {4,6,8,9,10} 1. Find the mean = (4+6+8+9+10)/5=7.4 2. Sum the deviations from the mean (absolute values, no negatives) |(4-7.4)|+|(6-7.4)|+|(8-7.4)|+|(9-7.4)|+|(10-7.4)| = 9.6 3. Divide the sum by the number of data (n=5) to get 9.6/5=1.92 4. 1.92 is th...

Use comparison method: 6-x=y=x-2 means 6-x=x-2 Solve for x and substitute into the original equations to solve for y.

Your work is correct, but probably made some mistake with the calculator. Volume = πr²h*1.06 = π(51)^2(120)×1.06; =330847.2π =1039387.133 mm³ approximately.

For the experiments to verify water-cement ratio, go with Bob Pursley's idea. Water is necessary for the concrete to set, but too much water will weaken the concrete. Too little will make it unworkable, and will end up having voids. Plastisizers are usually added to improv...

Weight = total air resistance, so by Newton's first law, the skydiver free-falls at uniform (terminal) velocity.

Algebra 2
Games are random processes. All we can say is that if he wins, he gets one point, and if he loses, he loses one point. We also know (or believe) that the probability of winning or losing is each 50%. The actual outcomes depends naturally on chance. But in the long run, the num...

Algebra 2
oops The probability on the second line should read 0.5 (not negative).

Algebra 2
Find probability of numbers matching (2/4) and not matching (2/4). Construct table for A: Outcome value,x P(outcome) x.P(x) Win..... +1 ...... 0.5 ....... 0.5 Lose.....-1 ...... -0.5 .......-0.5 Sum(x.P(x))=0, so game is fair.

Let K=[HI]²/([H2][I2]) The given reaction is in equilibrium at 430°C, if K=Kc=54.3 Substitute given concentrations to get K=[HI]²/([H2][I2]) =0.5²/(1*1) =0.25 < 54.3 Therefore the reaction is not in equilibrium and will proceed in the forward direction un...

Divide each term of the numerator by 2m^3: -6m^9/(2m^3) = -3m^6 -6m^8/(2m^3) = -3m^5 -16m^6/(2m^3) = -8m^3 Choose your answer accordingly.

Yes, the square bracket means the value is included in the interval, and ( or ) means excluded. There are other notations where ( or ) is replaced by a square bracket pointing outwards, for example, [0,2π) is the same as [0,2π[ To solve the above problem: cos^2x=2+2sinx ...

π is equivalent to 180° So 7π/4=7*180/4=315°

Since it is a rational number, the numerator and denominator can be replaced by integers. Using (b), you can create any integer, and using (a), you can divide the two numbers, which means you can create any rational number. Hope that helps.

Assuming (c) is the equivalent of the original question: "given any positive rational number q, show that pressing some finite sequence of buttons will yield q" then we need a transformation from q -> q using the given functions. We look for mapping R to R, or equ...

The important term to consider is 60(1/3)^t, which has a domain of R (all real) and a range of (0,+∞). Therefore dom T(t) = R ran T(t) = (10,∞)

The model is an exponential function such that e^rt=(1/2) where t=14 hours. e^(14r)=1/2 14r=ln(1/2) r=ln(1/2) / 14 =-.04951 (approx). In 22 hours, factor=e^(-0.04951*22) =0.336475 approx.

Step 1: Define variables: c=number of cars t=number of trucks "a dealer has 30 cars and trucks" translates to c+t=30 which means t=30-c .....(1) "If 2 more cars are delivered, the dealer will have 3 times as many cars as trucks." translates to c+2=3t .....(...

Math - Trig
Assume the observations were made from the same building. Let the distance of the building from the tree is D in m. Then D(tan22+tan50)=150 D=(150)/(tan22+tan50)

CHIMIE - English translation of question.
90 mL of 1.5N BaSO4 is mixed with 75 mL of 0.6M Na2SO4. 1. Calculate the ionic force of the resulting salt solution. 2. Deduce the value of the activity coefficient of Na+. Thank you. Rahil: SVP vérifiez si les valeurs sont bien 1,5N et 0,6M (surtout le mélange d...

SAT Math
An example problem could be: between 1 and 1000, how many numbers are neither divisible by 2 nor by 3. So from 1 to 1000, 500 numbers are divisible by 2 (even numbers), and from 1 to 999, there are 333 numbers divisible by 3. However, between 1 and 996 (next number is 1002)the...

It depends on the speed of the plane if the frame of reference is terrestrial, namely if the object is considered stationary on firm ground. If the frame of reference is the airplane itself, which cruises at a constant speed in rectilinear motion relative to the terrestrial fr...

If you are working on number theory, look up Chinese remainder theorem. If you have a puzzle or problem to solve, you can do it as follows: If we took one apple from the box, then the number of apples must be divisible by 2, 3, 4, 5, and 6. Therefore the number of apples would...

I do not speak German, but the little I know tells me that the "other" verb is placed at the end of the sentence, such as: Ich muss dort Deutsch sprechen. There I must speak German. One of our math teachers speaks fluently German. Hope he can give you a more detailed...

Bill amount * (1-0.03) to give the discounted amount, then add 6% tax Bill amount * (1-0.03) * (1+0.06) For $26.14, the final amount comes to $26.88, after rounding.

The tree top is 100*tan(52) feet higher than the person's eyes. To get the height h, above ground, h=100tan(52)+5 feet = 133 feet, approximately

Physic: Projectile Motion
let α be the angle of the projectile with the horizontal as it leaves the muzzle. Here α=0 degree. Let vi=initial muzzle velocity, then horizontal velocity, vh=vi*cos(α). Time taken to reach the target t=Horizontal distance/vh where horizontal distance = 100m...

To find the x-intercept, let y=0 and solve for x in 3x=12, or x=4. So the ordered pair would be (4,0). Follow similar rules for the y-intercept.

math urgent
Use your calculator to find 26×56. Since they are both raised to the 6th power, if you are interested in mental calculations, you can apply the law of exponents and multiply the two bases before raising to the given power.

There are two equations with one unknown, and the two possible solutions are inconsistent.

math check
69 is correct!

math - Wish you luck!


Calculus - Optimization
Good catch, Steve. Thank you.

Calculus - Optimization
Let the size of the square (cross-section) be s. Then we need to maximize V=s²(24-2s) with respect to s. First find the derivative and equate to zero: dV/ds = 48s-6s²=0 means s=0 or s=8 s=0 corresponds to a minimum volume and s=8 corresponds to a maximum volume. So t...

Business Math
Principal, P = $10000 interest per period of 6 months, i = 0.06 number of periods, n = 5 yrs/0.5 yr = 10 Value at maturity =P(1+i)^n He will have money to pay for the Jeep, and perhaps the sales taxes as well.

7×6=42 7×7=49 so there are 6 and (48-42)=6/7 apples, or 6 6/7 apples.

Homework Help Calculus
Problem of units conversion. 0.4071504079 m³ =0.4071504079×10^6 cm³ =407150 cm³ approximately.

Algebra 2
The first equation has a y-intercept of -17. The x-intercept is -17/7=-(2+3/7) =-2.4286 approx. The second equation has a y-intercept of -2.4, and x-intercept of -2.4/(-0.3)=8. If you produce the two lines to intersection, the estimated solution would be (-2, -3)

Practice Exam Calculus
you can use the same approach as for the paint on sphere. A=4πr² dA/dr=8πr ΔA=8πr Δr =8π(20)(1/5) =32π

If you mean (4/8)y - 21 = 3 then y=48 as you got. If the question were (4/8)y-21=0 then y=42

MC12H22O11=342 MCO2=44 C12H22O11+xO2=12CO2+... Ratio of mass of C12H22O11 to CO2 =342:12*44 =342:484 Mass of C12H22O11 that produces 3.6g CO2 =3.6*(342/484) =2.544g Mass ratio NaCl:C12H22O11 =(5.5-2.544):2.544 =2.956:2.544 Calculate mass percentage and reduce to 3 significant ...

The question defined what complementary angles are, but did not say that a and b are complementary. The question has a solution if a and b are complementary, and will be assumed as follows. if a and b are complementary, then a+b=90 angle a is 21 degrees more than twice angle b...

Are you measuring the vertical angle (from the horizon) where 90 degrees is vertically up, or the zenith angle (from zenith, vertically up) where 91 degrees is just below the horizon? A vertical angle of 91 degrees requires a special eye-piece/prism, and is past the vertical....

There are 9 choices for each of the first three digits, and 25 choices for the last two digits. Use the multiplication rule to get: 93252

Use a probability tree: Next person male: 42% wash his hands: 43% female: 58% wash her hands 66% P(wash)=42%*43% + 58%*66% =0.5634

When heated: 1. acetic acid phase change 2. sodium bicarbonate decomposition into sodium carbonate, carbon dioxide and water. 3. arsenic trioxide phase change

First establish the combustion equation and have it balanced: C8H18 + O2 -> 8CO2 + 9H2O. Balances for C, but not for O. Since there are 16+9=25O on the right, we need to double the number to make the number of molecules on the left a whole number. So it becomes: 2C8H18 + 25...

Hydrostatic pressure p varies linearly with height h, i.e. p=ρgh For a height of H and width of W, total force, F = W∫ρgh dh =ρgH²W/2 Ensure that all values are in SI units.

Trade discounts are successive discounts. The net price factor is equivalent to the net price of a $1 list price. Thus $1*(1-0.25)(1-0.15)(1-0.10) =0.57375 Use this factor to calculate the net price of $800 list.

I was thinking of something along the same lines, but couldn't find a good way to put it in action. Thank you for sharing the bright idea.

Make a free body diagram of the staging. Sum forces acting on the staging, and the total should be zero. Upward (reaction) forces=660+410=1070 N Downward forces = 620 N + W Sum to zero 620+W=660+410 W=660+410-620 =450 N.

Set up a system of equations: Let W=width L=length then Perimeter = 54 = 2(L+W) ...(1) L=2W-3 ...(2) Solve W by substituting (2) in (1), and hence solve for L.

Trade discounts are calculated successively. Thus for a list price of $1000, net price = $1000(1-0.3)(1-0.35)(1-0.2) = $364 Thus the trade discount amount (for a list price of 1000) is 1000-364=$636. For the list price of $29000, follow the same procedure.

You'd have to set up equations. First, let a=angle A, b=angle B and c=angle C, all in degrees. (Note: in solving math problems, it is important to define all symbols/variables used, including the units). We are given: "angle b is 5 more than twice angle A" which ...

project management
It would be an interesting exercise if only we know what it is... we do not happen to have your textbook.

Use the compound interest formula: A=P(1+i)^n A=accumulated amount after n periods (years) P=principal i=interest per compounding period n=number of compounding periods If the smaller investment catches up to the larger one, then the accumulated amounts would be equal. Therefo...

Hint: substitute u=a^2, then a^4-7a^2+9 =u^2-7u+9 and try to factorize. However, check you question to see if there is a typo. The above expression in u does not have rational factors.

Pressure = force / area Force = mg = 2.5*9.81 N a. Area = 10cm * 5 cm =0.10*0.05 m² =0.005 m² Pressure = 2.5*9.81/0.005=4905 Pa Part b can be solved similarly.

This is a binomial distribution with parameters n=3 (number of trials in the experiment) p=1/2 (probability of boys, X) q=1-p (probability of girls) For a random variable X with a binomial distribution (n,p,q), then E(x)=μ=np σ²=npq where σ=standard deviati...

Yes, your next step is to solve for x which represents Oliver's share.

Correct! Good job! :)


Just a little elaboration: If "this" stands for a masculin noun, such as a basket (un panier), or a bag (un sac), you could say Y a-t-il des oeufs dans celui-ci? If it stands for a feminine object, such as a pocket (une poche), or a plate (asiette), then we would use...

If it has 2 AND 3 in the prime factorization, it means that the number must be divisible by 2 AND by 3, which means that it is divisible by 6. The number(s) between 50 and 59 that are divisable by 6 would be 54. The prime factorization of 54 is 54 =6*9 =2*3*3*3 =2133 You can a...

What did you get? You would be well to do the 4x4. If you have difficulties, start with a 1 by 1, then 2 by 2 and then 3 by 3 grid. You will find a pattern that you can use later. Once done, do an n × n grid and check if the answer for n × n works for n=4.

Mass = mass density * volume where mass density = 23.4 g/cm³ volume = 75 cm³

Discrete Mathematics-Elementary graph theory
A cycle graph is like a polygons with vertices along the circumference. A complete graph is one where EACH vertex is connect to EVERY OTHER vertex (except itself). Using these definitions, are you able to answer the question?

Discrete Mathematics-Elementary graph theory
No it does not matter. You can even use a wavy line. However, we usually use a straight line unless we would like to avoid certain crossing of lines.

Discrete Mathematics
By definition, a tree is a connected acyaclic graph. One of the sufficient properties of a tree is that the number of edges equals the number of vertices minus one. Note: number of edges = (sum of degrees of all vertices)/2.

Discrete Mathematics
An Eulerian path is a path which passes through ALL edges exactly once. This can happen if the graph has either 0 or 2 vertices with odd degrees. So even an incomplete graph (with degree 0 at one or more vertices) can have an Eulerian path.

Discrete Mathematics
The number of edges =(sum of degrees of all vertices)/2

Discrete Mathematics
See your next post to find out how to calculate the number of edges. Hence deduce if such a graph can exist or not.

Math- Probablility
C=Casper D=Denver Conditional probability: P(C)=0.4 P(D)=0.3 P(C∪D)=0.27 Probability of having been to Casper given she has gone to Denver =P(C|D)=P(C∪D)/P(D) =0.27/P(0.3) =0.9

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