Posts by MathMate

Total # Posts: 12,095

First step in evaluating limits: simplify the algebra and see what you get. If you get: (a number), then it is also the limit. (∞/(a number)), the limit is &infin. (0/(a number)), the limit is 0. (∞/∞), or (0/0), then you need other techniques/tools. Try the ...

So at 8 am, x had travelled 80*(1.25hours)=100 km. He was then 400-100=300 km away from y when the truck left y for x.

Hint: Meeting time for two travelling towards each other is the distance divided by the sum of the speeds.

Sorry, forgot the link. Will give two at different levels, just in case:

If you don't have a textbook, try the following link. After that, reread Ms.Sue's responses. The link explains how probability works, and with that knowledge, you will be able to solve other problems, without having to guess anymore, once and for all.

Chemistry, rate of reactions - help needed
Chemistry, rate of reactions - help needed

Use the formulas: Power (watts) = V^2/R V=voltage in V = 120 V R=reisistance in Ω => R=V^2/P............(1) R(30W)=120^2/30=480Ω R(90W)=120^2/90=160Ω Now using equation V=iR i=current in amps With three connected in parallel, i=4.5A R(equivalent)=V/i=120/4...

Write a 5 in the thousands place. Then fill in three more digits (0 to 9) to complete the number in a way that it is the smallest possible number.

math - aina
Aina, it would be nice to verify your earlier post before you repost. If you have objections to the response, you are free to explain your point of view.

Algebra 2 help please.
Can you explain exactly what you put in your calculator, including parentheses etc.? Can you reproduce the value? What do you get this time?

Algebra 2 help please.
Can you kindly explain the steps that led you to 6.616? It would help me understand your thinking process in order to help you solve the problem accordingly.

S=event of passing statistics M=event of passing mathematics P(S)=2/3 P(M∪S)=4/5 P(M∩S)=14/45 From the given information, we can apply the following relation, which is always valid, mutually exclusive or not. P(M∪S)=P(M)+P(S)-P(M∩S) in other words, P(M)=P(M&cup...

There isn't much we can do about it to simplify the expression, unless we are given the value of x, in which case we can evaluate it numerically. We can also transform it to (x-4)^(3/2) =(x-4)^(1+1/2) =(x-4)√(x-4) but that is not simpler. It all depends on which math...

Let original amount be A. A(1-0.1)(1-0.2)=?3600 Original amount =?3600/[(0.9)(0.8)] =?5000

Math - trigonometry
"Ferris wheel is elevated 1 metre above ground" means that the lowest point is 1 metre above ground. (Draw a sketch to show that). The highest point is 31 m. above ground, so the diameter is (31-1)=30m, and radius = 30m/2=15m. (Mark that on your sketch). The centre C...

I see π being properly displayed probably due to encoding. I also see that there is a removable discontinuity at x=π/2. Numerical integration (skipping x=π/2) gives identical results for both expressions, so hopefully no typo. Try translating limits to (-π/2, π/2).

A redox reaction would occur. Can you figure out the reaction?

A. dilation The dilation matrix is correctly done, except the original matrix (for KLM) should be in alphabetical order of the vertices, which is -2 1 -3 5 1 1 therefore you need to readjust the matrix of the dilated figure. It is normal practice to create matrices in ...

Physical science CHECK my answers
1. incorrect (review friction concepts) 2. correct 3. incorrect. (review concept of displacement) 4. correct. 5. incorrect. (Please explain justification of your choice) 6. incorrect. (review circular motion) 7. incorrect. (acceleration is not a force. review definition of a ...

hint: According to The solubility of ammonium chloride is 51.4 and 71.2 at temperatures 50°C and 90°C respectively. "Solubility" used in the above article is expressed in "grams per 100 milliliters of water...

Since you have learned about inscribed angles and intercepted arcs, it is safe to assume that you are familiar with what they are. Following is a summary of hints to help complete the proof. fact #1: the sum of the intercepted arcs of the sides of a cyclic quadrilateral (a ...


Again, see:

algebra - repost
If you are reposting within a short time, indicate repost in your subject box. It doesn't usually get faster response by reposting within a short time because tutors have to spend time answering in duplicate, thus reducing the response time of everyone. Read the following ...

fraction of income left: 1-(1/4+2/5+1/6).....[LCM=60] =1- (15/60+24/60+10/60) =1- (15+24+10)/60 =1- 49/60 =11/60 Total income/1=money left/(11/60) Cross multiply, total income=10000*60/11 =$54545.45 For faster response, enter the appropriate topic/subject in the subject box.

Assuming both are fair cubes. Any fair cube will give a "6" with theoretical probability of 1/6. (a) For case Red cube: P(6)=1/6, P(~6)=5/6 Blue cube: P(6)=1/6, P(~6)=5/6 Using the multiplication rule for the two step experiment (red, then blue), P(6R,~6B)=1/6*5/6 P...

algebra 1
Can you explain how you got 24? This permutation problem can be solved using the standard equation P(n,r)=n!/(n-r)! where n=8, (8 candidates) r=3 (three different positions out of n candidates) Use your calculator to help you find the right answer. Just in case, n!=1*2*3*4...

yes to " we can find the speed of the penny as instantaneous rate of change of height of penny when it hits ground. " Details: If you have been given the equation v²-u²=2aH then H=distance, and velocity=v (u=constant=0) If you express v as a function of H, ...

Chemistry - to Hina, Star, Rebecca,
Please use a single pen name when you post.

This is a two step experiment where each step is independent of the other. The probability of both succeed is the product of the probability of each step. [called the product rule] Step 1: P(even)=P({2,4,6} out of {1,2,3,4,5,6})=3/6 P(2)=P({2} out of {1,2,3,4,5,6})=1/6 Now use...

Algebra - to Tony
Tony, help is to give you hints or explanations to lead you to a solution. Giving answers could be help for someone who wants to understand, and detrimental for someone who does not. The help I gave above should help you eliminate two of the choices. If you need more ...

If it is a decrease, r is negative. In the proposed answers, the variable x is an exponent, so it should be written: A. f(x)=2000(0.94)^x,... and so on. Which do you think is the right answer?

"The sum of two rational numbers is always rational." - true, for example, 2+0.5=2.5 (decimals and fractions are rational) So statement is true. "The product of a nonzero rational number and an irrational number is always irrational." - true, 5*√2=5(&...

physic, please correct is am wrong
i. incorrect. The angle turned in radians? note (2π/360) is the conversion factor from degrees to radians. use 1 revolution = 2π radians For example, 5 revolutions equals (5*2π)=10π radians. ii. incorrect error inherited from (i) iii. incorrect error inherited from...

physics - to "question" and "carry on"
If you both have the above seemingly incomplete question (that finishes without a fullstop!), perhaps it is time to check with your teacher or tutor.

physics - please complete the question
It does not look like the question is complete.

Assuming the Y-shaped chords are symmetrical with respect to the vertical, and θ is angle of each chord with the vertical, then resolve forces along the y-axis (vertical), 2Fcos(θ)=mg F=tension on each chord,=force on anchor m=mass of climber Solve for F.

@ All Cheaters
Also, if you post 4-5 answers that do not make sense, one would be led to believe that they are chosen at random, and therefore do not represent your effort. However, if the answers are accompanied by your lines of thought or explanations, they will be more likely to be checked.

Algebra 2
Cos(x) is a sinusoidal function with a period of 2π and amplitude 1, i.e. it oscillates between +1 and -1. You're expected to know the basic graph of cos(x), sin(x) and tan(x). (see link below for details). Based on the basic graphs, we can graph the variants. From cos(...

"Distance" is the sum of distances travelled, irrespective of direction, just like the odometer on a car. "displacement" is the distance and angle of the final position relative to the initial position, irrespective of how and where intermediate stops are ...

Angles of elevation and depression
In geometry problems, we need to start drawing a sketch according to instructions. On the sketch, label the unknowns, and hence deduce the equations/formulas that may help to solve the problem. Start by sketching according to given information. Geometry will always be ...

Please double check your post before sending to make sure we're solving the right problem. This is what I suspect to be the correct version. Editorial changes have been indicated in italics. Also, I start a new sentence on a new line for easier reading and interpretation. ...

The monthly payment A over N=1 year(s) for a loan P=1300 at a nominal annual interest rate of i=0.10, compounded c=12 times annually is given by To simplify the formula, we write n=c*N=12*1=12=number of periods R=1+i/c=1+0.1/12=interest rate per period then monthly payment, A ...

Assuming fair coins. The "first" coin has a probability of 1/2 showing heads, and the "second" has a probability of 1/2 showing tails. Since the two events are independent, the joint probability (i.e. both are successful) is the product of the individual ...

The slope of a line Ax+By=C is given by -A/B. Therefore if A & B have different signs, the slope is positive. This will help you eliminate the third equation, since coefficients of x and y have the same sign, therefore negative slope. Now set x=0 in each of the equations and ...

The equation of a circle centred at (x0,y0) and radius r is given by (x-x0)²+(y-y0)²=r^2. The posted equation therefore represents a circle with radius=√81, centred at (-6,8). Continue with interpreting the results to complete the answer.

Physics - to adam
Congrats! What you did is valid, using strictly kinematics equations. Basically, you got H=29+14^2/(2g)=39 If you solved the energy equation above, where m (mass) cancels out on both sides of the equation, you will get H=(14^2/2+29g)/g=39 The two match exactly assuming no air ...

The air velocity is indeed still +90 m/s (due south). The velocity with reference to ground is Vg=+90+(-27)=63 m/s (due south). Think of the plane moving south for 90 m in one second, and head wind blows it back towards north by 27 m, also in one second, so the net/ground ...

Assuming the number is an integer. 45130 58269 97394 and many others, probably because question is incomplete.

Innovation - oops
It's Gay-Lussac's Law, not Charles' law (T vs V).

Charles' law, P1/T1=P2/T2, or P/T=constant, as long as volume is constant. T must be in °K. 24/(273.15+0)=P/(273.15+32) Solve for P P=24/(273.15)*(305.15) =26.8 lb/in²

Look for ordered pairs (x,y) with identical x-values. If the corresponding y-values are different, the ordered pairs do not form a function. This is the equivalent of the vertical line test (i.e. no vertical line cuts two points). However, in case where both x and y values are...

If a figure has rotational symmetry of order three, then it has either 0 or 3 lines of symmetry (one in each rotated position = 3). I would look forward to seeing a figure with rotational symmetry of order 3 and one single line of symmetry, if it exists.

Certainly, if you would post your attempt!

Math Help TIMED! -- a test?
Timed? Is it a test?

The rate i=8% is for 1 year (52 weeks). There are n=4 terms in a year. The value of the bill ($10) is not used in this problem. The effect interest rate (EAR) EAR=(1+i/n)^n - 1 =(1+0.08/4)^4 - 1 =1.08243 - 1 =0.08243 =8.24% (to hundredth %)

Exactly, we're looking for the change of sign which implies the presence of a root. It may be intuitive, but this fact is dependent on the Intermediate Value theorem, as stated above.

f(x)=x^3+5x-4 f(0)=-4 f(1)=2 Since f(x) is continuous (as are all polynomials), there exists a value c such that f(c)=0 (-4≤0≤2, and 0≤c≤1) by the Intermediate Value Theorem.

Calculus II - to Rosali
We must be careful to insert parentheses when they are needed. Expressions are evaluated according to the PEMDAS rule. For example, what you posted is mathematically equivalent 3x²+x +[9/(x²+5)]*(x-6) which is (probably...

Maths - vectors
Displacement is a vector obtained by the difference between final and initial positions, so displacement during t[1,3] =p(3)-p(1) You can leave the result in vector form <δx, δy>. Note: subtraction is done component by component, ex. <7,4>-<2,3>=&...

micro economices
First we need to understand "cardinalist", someone in favour of the cardinal utility theory, namely utility (happiness) is quantifiable, [ and can be mathematically represented by a curve, and diffentiable, most of the time. ]

trigonometry - to Jack
Drawing a diagram in geometry is a must. All we need to do is to follow instructions step by step. If you refrain from drawing diagrams, you will be handicapped in almost ALL geometry problems. This is how you could proceed: "the angle of elevation of a tower at place A ...

For scientists to predict outcome of events, they need 1. a sound and proven theory on how the events evolve according to all major parameters. 2. ability to collect all pertinent information (on parameters). Assuming such events are predictable. Unfortunately, we are in the ...

I prefer Steve's and Bosnian's method: if cos>0, right-hand quadrants. if sin>0, upper-quadrants if tan>0, 1st or 3rd quadrants. (sec same as cos, csc same as sin, cot same as tan) However, for checking, you can use the CAST method. S|A -+-- T|C They ...

You can google using keywords "genetic variation and environmental pressures" to get multiple articles on the subject, and choose the appropriate one(s) for you. One of the articles I got was:

Math - nice to use pen names
Thank you Anonymous. I wish both of you use distinct pen names to avoid confusion.

The ladder forms a right triangle with the wall, where the floor and the wall form the legs, and the ladder is the hypotenuse. Let the angle ladder makes with the floor be x. Then by definition of the ratio cosine, cosine(x)=adjacent side (floor)/hypotenuse =3.6/5.8 On the ...

Is the function y=sqrt(2x)-3xy+2 or y=sqrt(2x-3xy+2) Parentheses are very important in math.

further math
hints: 1. Circles have equal coefficients of x² and y² e.g. 2x²+2y²+3x-5y=17 2. hyperbola have different sign coefficients of x² and y² e.g. 4x²-8y²-2x+5y=24 3. Parabolas have one of the squared terms missing, e.g. x²-4x+4=0, or 2y&...

Area of wall=12*18=216 sq.ft. Area two coats will cover = 2*216 = 432 sq.ft Use proportions x gal./432 sq.ft = 1 gal./300 sq.ft Solve for x: x=(1/300)*432=1.44 gallons.

Math (Evaluating integrals)
Function h is a piece-wise continuous function, i.e. the function is defined the combination a number of segment, each of which is a different mathematical function. For example, we can consider h(t)={0 for t<0, 1 for 0≤t<0.5, -1 for 0.5≤t<1, 0 for t≥1} You ...

physics - statics
Riley & Monica, there is no need to change pen names. Most of the time students do that to hide the number of posts they make on the same subject, which is not necessary, because we know. Using the same name reduces repetition, like references, explanations of certain terms, ...

It depends on the motion of the two vehicles. We assume that both vehicles are on a horizontal surface. If both are stationary, the maximum force is μs(4M)g, the frictional force of the car reisisting motion, at the point just before motion starts. μs is the coefficient ...

In math, please do not paraphrase. Most of the time, every word in the question is important. I interpret the question as: In a class of 156 students who all took maths and physics. They all passed at leat 1 subject. Seventy-five passed both math and physics.if twice this ...

physic..plz check

physic - calorimetry
513=(T2-100) 513=T2-100 T2-100=513 T2=?

First, some properties of a rhombus: 1. a rhombus is a parallelogram with all sides equal. 2. diagonals of a rhombus intersect at right angles. If the perimeter of a rhombus is 40cm, then each side is 40cm/4=10 cm. (propert 1). Half-diagonals of a rhombus form a right triangle...

chemistry - to tom
Warning. You know what you just posted.

Please use the proper mathematical terms. We use "angle of depression" and "angle of elevation". "Depression" is for psychologists. We also need the position/location of the observer. Is the observer at a point between the buildings, or is the ...

first, factor (x³+1/x³) =(x+1/x)(x²-x*(1/x)+1/x²) =(x+1/x)(x²-1+1/x²) Further factoring gives =(x+1/x)((x+1/x)²-2(x*(1/x)-1) =(x+1/x)((x+1/x)²-3) Set k=(x+1/x), then (x³+1/x³)=k(k^2-3)=110 Solve for k and reject complex roots k...

Maths - Polar coordinates
The rotation matrix about the origin is R= | cos(t) -sin(t) | | sin(t) +cos(t) | Any rotation through angle t of a point X(x,y) is then given by RX Put t=pi/6=30° R= | 0.8660 -0.5000 | | 0.5000 +0.8660 | and X(3,2) Do the matrix multiplication: RX=(1.598,3.232) Note that a...

Mathematics question
Li=lion Le=Leopard T=tiger "the lion weighs 90 kg more than the leopard" => Li-Le=90, or Li=Le+90 ............(1) " tiger weighs 50 kg less than the lion. " => Li-T=50, or T=Li-50, subtitute (1) for Li T=(Le+90)-50 T=Le+40 .............(2) "...

It is customary to write cube as ^3, i.e. write x³y as x^3y and xy³ as xy^3. The problem is then 19x^3y-17xy^3-21+5xy^3-[8x^3y+2xy^3-18 - 12x^3y+7xy^3] Remove brackets: 19x^3y-17xy^3-21+5xy^3-8x^3y-2xy^3+18-12x^3y-7xy^3 Group like terms and add: (19-8-12)x^3y+(-17+5-...

correction: problem is f(x)=x³

Example: f(x)=x² f(x+dx) =(x+dx)³ =x³+3x²dx+3x(dx)²+(dx)³ [f(x+dx)-f(x)]/dx =[x³+3x²dx+3x(dx)²+(dx)³ - x³]/dx =[3x²dx+3x(dx)²+(dx)³]/dx =3x²+3x(dx)+(dx)² Take limit when dx->0 f'(x) =[f(x+dx...

I assume you are referring to the MBC of an anti-microbial agent. Generally it is determined by subculturing on agar plates, and much of the time, by counting colonies. MBC is the minimum concentration to kill ≥99.9% of a given bacterium. Do not confuse with MIC (minimum ...

hint: Assume the soap bubble is free-floating in the air: Pi-Po=4T/r

Hint: pressure=force/area

hints: 1. gauge pressure is zero-referenced against ambient atmospheric pressure, which (usually) cancels out at different points of the pipe if the distance is short. 2. For short distances, we might be able to justify assumption of no frictional loss. 3. Equation of ...

hints: 1. conversion from weight to mass: mass (in kg) = weight (in N) / g (in m/s²) = weight (in N) / 9.81 2. Archimedes principle The upthrust on an immersed object equals the weight of liquid displaced (i.e. weight of liquid of net volume equal to object) 3. Density of...

computer program
This can be done by writing a flow-chart, or pseudocode. The steps are exactly as you posted. Detailed design or coding depends on the coding language you are expecting to use. Some will display charts with one line of code, others might need a user-written procedure. If you ...

Finance Question - Formulas
The FVA formula gives you the effective amount at the future date. You may want to convert the amount back to present value, using the inflation rate. The formula is PV=FV/(1+i)^n where i=inflation rate n=number of years.

Economics - Formula Help
See question answered:

For information to non-North American readers, the following coins are worth: dime = 10 cents nickel = 5 cents quarter = 25 cents. 600 cents = 10 nickels and 25 dimes and quarters. Let D=number of dimes 10(5)+10(D)+25(25-D)=600 Isolate D: -15D=600-625-50=-75 => D=-75/(-15)=...

3*(-13)=-39 so 12x+6y-39=0............(1) change 4(3x=5y+26) to 4(3x-5y-26=0) => 12x-20y-104=0 ...........(2) (1)-(2) 26y+78=0 y=-3 Continue to solve for x, and check you answer by substitution.

steve reiny reiny damon probability
There are two buses after 7 and on or before 7:30. The two corresponding periods are between 7:10 and 7:15, or 7:25 and 7:30, which makes 5+5 = 10 minutes. Equivalently, we can calculate for just one bus/period, which makes P(<5)=5/15=1/3...again.

steve reiny reiny damon probability
The pdf of a uniform distribution is 1/(b-a) where a≤x≤b. Thus mean,μ=(1/2)(a+b). To wait less than (or equal to) five minutes means he has to arrive between 7:10 and 7:15, or 7:25 and 7:30, out of the 30 minute interval, which makes P(≤5)=(5+5)/30=1/3.

Assuming the question means that production cost is much reduced, and that demand does not change, then the supply curve moves to the right, resulting in a lower equilibrium price. See, for example, graph 1 of

Let's say we have drawn five-card hands A, B and C (without replacement). This means that there are no duplication of cards in each hand. The number of ways of choosing the exact 15 cards from a 52-card deck is D1=C(52,15), where C(n,r)=n!/(r!(n-r)!) The number of ways the...

Maths (probability)
You're welcome! Glad that it works out.

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