Saturday
April 19, 2014

Posts by MathMate


Total # Posts: 9,948

Math
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.

math
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...

physics
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...

MATHS
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...

german
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...

math
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.

trig.
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...

Math
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.

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

math check
69 is correct!

math - Wish you luck!
:)

chemistry
M*V=2.01*711/1000

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.

Math
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

Math
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

Chemistry
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 ...

geometry
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...

Surveying
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....

math
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

statistics
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

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

Chemistry
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...

physics
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.

math
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.

geometry
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.

physics
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.

maths
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.

math
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.

GEOMETRY (Angles) PLEASE
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.

precalc
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...

math
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.

physics
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.

statistic
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...

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

MaTh
Correct! Good job! :)

Math
yes.

French
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...

math
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...

MATH
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.

math
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

Probability
5 choose 2 * 15 choose 12 =5C2*15C12 =5!/(2!3!) * 15!/(12!3!) =5*4/2! * 15*14*13/6 =10*455 =4550

Calculus-Series
I assume the expression is (n^3)* (e^(-n^4)) for n=1 to +&inf; You can use the ratio test to show that it converges, namely, show that an+1/an < 1 ∀ k≥1. The integral test will result in a definite integral from 1 to +&inf; which is not an elementary function, but...

Calc Help Please
Implicit differentiation: (d/dx)(2x^2+2x+xy=2) 4x+2+y+xy'=0 y'(x)=-(4x+2+y(x))/x y'(2)=-(4(2)+2+y(2))/2 =-(10-5)/2 =-5/2

Math-probability
8 choose 3 =8C3 =8!/((8-3)!3!) =8*7*6/(1*2*3) =56

physics
Take moments about the centre. On father's side: M=70*0.65=45.5 kg-m On children's side: M=(30+30)*x Equate moments and solve for x.

Elements of Structures MIT 2.02
Please see: http://www.jiskha.com/display.cgi?id=1374949947

Math
3/(3+4)

Geometry
We have P1(6,-2), P2(1,3) Use Slope=(y2-y1)/(x2-x1) to find slope.

Math- probability
F=fever S=sore throat P(F)=80% P(S|F)=30% But P(S|F)=P(S∩F)/P(F) P(S∩F)=P(S|F)*P(F)=30%*80%=0.24

Math (probability)
Conditional probability. P=pool G=garage Probability of a home having a pool given that it has a garage is P(P|G)=P(P∩G)/P(G) =11%/50% =22%

Elements of Structures MIT 2.02
Please clarify what are the "other" questions.

Elements of Structures MIT 2.02
I have quite different values as you have. It would help if you show your work so we can compare notes. My approach would be: Since the beam is composite, there is only one value of 1/r at each cross section x, which is given by M(x)/EI. For a cantilever beam, M(x) is evidentl...

Elements of Structures MIT 2.02
Good luck!

Elements of Structures MIT 2.02
1. I suggest you check your EI. 2. You have not confirmed q(x)=q0*x*L (as you have written). I think you mean q(x)=q0*(x/L) If that's the case, I also get δ=-0.0582 as you did. I think the large δ comes from the erroneous EI. If you use EI=8050π, you'd g...

Elements of Structures MIT 2.02
Did you use Ix=Iy=πd^4/64 ?

Elements of Structures MIT 2.02
I have for the core I0=2.5π*10^-9 and for the sheath I1=3.75π*10^-8 Multiplied by the corresponding E gives me EI0=175π (core) and EI1=7875π (sheath). Total(effective)=8050π

Elements of Structures MIT 2.02
is q(x)=q0*x or is q(x)=q0*x*L (as you had it above?)

Elements of Structures MIT 2.02
Do you get 8050π for the EI of the composite beam? I get 8050π For some reason, I get δ=-0.1164, which is exactly double your number.

Elements of Structures MIT 2.02
I guess I did not read that x=0 at the free end (A), and the fixed end (B) is x=L. Also, do you mean q(x)=q0*x*L? What did you get for EI of the composite beam?

Elements of Structures MIT 2.02
" q(x)=qxL,with q0=2.76kN/m. " Most of the time, x is measured from the fixed end (of a cantilever). Is this the case?

algebra
Good catch! Thank you!

algebra
Initially w=width w+5=length w(w+5)=original area Subsequently: w-2=width 2(w+5)=length (w-2)*2(w+5)=2*original area=w(w+5)=area Therefore 2(w-2)(w+5)=w(w+5) Solve for w: 2(w-2)=w (w cannot be equal to -5) 2w-4=w w=4

math
You may have a typo with the given answers. None of them is correct.

Statistic/Psychology
That's correct! Good job!

Statistic/Psychology
A negative correlation means that the increase of one variable will be accompanied by a decrease of the other variable.

Statistic/Psychology
Exactly!

Statistic/Psychology
Correlation coefficients range from -1 to +1 where the two extremes enable the researcher to make almost perfect "predictions". On the other hand, the closer the correlation coefficient approaches zero, the less reliable would be the indication of the regression line...

Linear Algebra
Let x=number of bracelets y=number of necklaces then x+y=120 10x+12y=1400 Solve for x and y. Quick mental calculation, no paper required: If Rosa bought only necklaces, she would have paid 12*120=$1440. Exchanging a necklace for a bracelet saves her $2, so to pay $1400, she mu...

science
Use conservation of kinetic and potential energies: mgh1+(1/2)m(v1)² = mgh2+(1/2)m(v2)² where m=mass of cyclist and cycle (cancels out) g=acceleration due to gravity (9.81 m/s^2) h1=70m h2=35m v1=38 m/s Solve for v2

Discrete Mathematics :)
You're welcome!

Discrete Mathematics
Number of comparisons for 6 numbers: 5+4+3+2+1=15 You need all 15 comparisons unless you modify the algorithm to keep track of exchanges. There are 4 exchanges in this particular example.

Discrete Mathematics
The idea is to reduce the nesting of parentheses which will then give possibilities of simplification. Remember to name the rule of simplification as justification. Start with the left-hand side: (p ^ (~ (~ p V q))) V (p ^ q) de Morgan's law: = (p ^ ( p ^ ~q)) V (p ^ q) as...

Discrete Mathematics
If I make the statement: If it rains then I stay home. I did not say what happens if it does not rain, so we don't get to know. The inverse would be: If it does not rain then I do not stay home. Here it is making a statement which is not derived from the original statement...

Discrete Mathematics
The inverse of If p then q would be If ~p then ~q (i.e. if not p then not q) We have p=(x+2)(x-3)>0, so ~p would be (x+2)(x-3)<0 and since q=x<-2 ∨ x>3 ~q would be x>-2 ∧ x<3 (de Morgan's law). If there is no typo, then we do not find the inverse i...

Discrete Mathematics
"I am not sure what this one is but I will see whether or not I get this right. If x < -2 V x < 3 then (x + 2) (x - 3) < 0 " This translates to If q then p, which is the converse of the original statement if p then q. Remember at the beginning I wrote: stat...

Discrete Mathematics
There is no algebraic manipulation to be done, just like the raining and staying home. Let p = (x+2)(x-3) > 0 q = x<-2 ∨ x>3 Then p->q, or "if p then q", would translate to the original statement of If (x+2)(x-3)>0 then x<-2 ∨ x>3. The c...

Discrete Mathematics
The example is to apply mathematical logic to the results of the solution of an algebraic inequality. There is nothing to do algebraically, but to modify the original statement to make the converse, inverse and contrapositive. If the original statement were: "If it rains,...

Discrete Mathematics
correction: p: (x+2)(x-3) >0 q: x<-2 ∨ x>3

Discrete Mathematics
Here's a summary drawn from: http://www.jimloy.com/logic/converse.htm statement: if p then q converse: if q then p inverse: if not p then not q contrapositive: if not q then not p For the given example: Statement: ∀x∈R, if(x+2)(x-3) > 0 then x<-2 or x>...

Geometry
Vertically opposite angles are equal. What is x when 4x=56?

math :)
You're welcome!

math
If the box has dimensions which are whole number of cm's, then it can fit 1200 cm³ / 1 cm³ =1200 cubes.

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