Sunday

February 7, 2016
Total # Posts: 11,444

**Precalculus**

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 ...
*May 4, 2014*

**Geometry**

π is equivalent to 180° So 7π/4=7*180/4=315°
*May 4, 2014*

**Trignometry**

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.
*May 4, 2014*

**Trignometry**

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 ...
*May 4, 2014*

**Math**

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,∞)
*May 4, 2014*

**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.
*December 14, 2013*

**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 .....(...
*December 14, 2013*

**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)
*December 14, 2013*

**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 ...
*December 14, 2013*

**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)...
*December 7, 2013*

**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 ...
*November 29, 2013*

**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...
*November 27, 2013*

**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...
*November 27, 2013*

**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.
*November 27, 2013*

**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
*November 27, 2013*

**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...
*November 26, 2013*

**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.
*November 18, 2013*

**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.
*November 17, 2013*

**algebra**

There are two equations with one unknown, and the two possible solutions are inconsistent.
*November 17, 2013*

**math check**

69 is correct!
*November 17, 2013*

**math - Wish you luck!**

:)
*November 17, 2013*

**chemistry**

M*V=2.01*711/1000
*November 17, 2013*

**Calculus - Optimization**

Good catch, Steve. Thank you.
*November 16, 2013*

**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 ...
*November 16, 2013*

**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.
*November 10, 2013*

**Math**

7×6=42 7×7=49 so there are 6 and (48-42)=6/7 apples, or 6 6/7 apples.
*October 15, 2013*

**Homework Help Calculus**

Problem of units conversion. 0.4071504079 m³ =0.4071504079×10^6 cm³ =407150 cm³ approximately.
*October 15, 2013*

**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)
*October 15, 2013*

**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
*October 15, 2013*

**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
*September 23, 2013*

**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 ...
*September 23, 2013*

**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...
*September 21, 2013*

**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...
*September 21, 2013*

**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
*September 20, 2013*

**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
*September 20, 2013*

**chemistry**

When heated: 1. acetic acid phase change 2. sodium bicarbonate decomposition into sodium carbonate, carbon dioxide and water. 3. arsenic trioxide phase change
*September 7, 2013*

**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 + ...
*September 7, 2013*

**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.
*September 7, 2013*

**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.
*September 6, 2013*

**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.
*September 1, 2013*

**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.
*September 1, 2013*

**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.
*September 1, 2013*

**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.
*August 24, 2013*

**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 ...
*August 24, 2013*

**project management**

It would be an interesting exercise if only we know what it is... we do not happen to have your textbook.
*August 23, 2013*

**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. ...
*August 23, 2013*

**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.
*August 23, 2013*

**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.
*August 20, 2013*

**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 ...
*August 20, 2013*

**Math**

Yes, your next step is to solve for x which represents Oliver's share.
*August 19, 2013*

**MaTh**

Correct! Good job! :)
*August 19, 2013*

**Math**

yes.
*August 19, 2013*

**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...
*August 18, 2013*

**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 ...
*August 15, 2013*

**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.
*August 15, 2013*

**math**

Mass = mass density * volume where mass density = 23.4 g/cm³ volume = 75 cm³
*August 15, 2013*

**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?
*August 8, 2013*

**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.
*August 8, 2013*

**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.
*August 6, 2013*

**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.
*August 6, 2013*

**Discrete Mathematics**

The number of edges =(sum of degrees of all vertices)/2
*August 6, 2013*

**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.
*August 6, 2013*

**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
*July 29, 2013*

**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
*July 29, 2013*

**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...
*July 29, 2013*

**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
*July 28, 2013*

**Math-probability**

8 choose 3 =8C3 =8!/((8-3)!3!) =8*7*6/(1*2*3) =56
*July 28, 2013*

**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.
*July 28, 2013*

**Elements of Structures MIT 2.02**

Please see: http://www.jiskha.com/display.cgi?id=1374949947
*July 27, 2013*

**Math**

3/(3+4)
*July 27, 2013*

**Geometry**

We have P1(6,-2), P2(1,3) Use Slope=(y2-y1)/(x2-x1) to find slope.
*July 27, 2013*

**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
*July 27, 2013*

**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%
*July 27, 2013*

**Elements of Structures MIT 2.02**

Please clarify what are the "other" questions.
*July 27, 2013*

**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 ...
*July 27, 2013*

**Elements of Structures MIT 2.02**

Good luck!
*July 27, 2013*

**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 ...
*July 27, 2013*

**Elements of Structures MIT 2.02**

Did you use Ix=Iy=πd^4/64 ?
*July 27, 2013*

**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
*July 27, 2013*

**Elements of Structures MIT 2.02**

is q(x)=q0*x or is q(x)=q0*x*L (as you had it above?)
*July 27, 2013*

**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.
*July 27, 2013*

**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?
*July 27, 2013*

**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?
*July 27, 2013*

**algebra**

Good catch! Thank you!
*July 27, 2013*

**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
*July 27, 2013*

**math **

You may have a typo with the given answers. None of them is correct.
*July 27, 2013*

**Statistic/Psychology**

That's correct! Good job!
*July 26, 2013*

**Statistic/Psychology**

A negative correlation means that the increase of one variable will be accompanied by a decrease of the other variable.
*July 26, 2013*

**Statistic/Psychology**

Exactly!
*July 26, 2013*

**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...
*July 26, 2013*

**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 ...
*July 26, 2013*

**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
*July 26, 2013*

**Discrete Mathematics :)**

You're welcome!
*July 26, 2013*

**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.
*July 26, 2013*

**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) ...
*July 26, 2013*

**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...
*July 26, 2013*

**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 ...
*July 26, 2013*

**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: ...
*July 26, 2013*

**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 ...
*July 26, 2013*

**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...
*July 26, 2013*