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Posts by MathMate

Total # Posts: 12,017

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.

Maths (probability)
Even though I agree that 306/600 is a closer estimate to the actual probability of heads, we have to consider another possible interpretation of "average relative frequency", which could be the literal average, namely, (50/100+252/500)/2 = 251/500. Have you tried ...

The would have to have travelled the same distance in the same lapse of time. Let time=t, then Brown roadrunner would have travelled S1=ut+(1/2)at^2 =0(t)+(1/2)2.75t^2 =1.375t^2 Black roadrunner would have travelled S2=9.25t Both distances S1 and S2 are in metres. For them to ...

If you are making a repost, or a follow-up, it always help to post the link to the original post: Part A: You will need to complete the solution in finding what S is. Parts B and C: If you are not using x,y as variables, it is ...

Were you given this density value? (1.19 g / mL) ? A published value for concentrated HCl at 1.19 g/mL has a molarity of 12.39 M. (see ref) Value of molarity obtained from density is very approximate. Ref:

See Please show your attempt for part 2. You need to draw separate FBD (free body diagrams) for the block and weight. Also, please describe the diagram in words, i.e. confirm whether the weight is free-hanging.

I understand that there should be a pulley, but is the weight free-hanging? Can you describe the diagram in words? In the following calculation for #1, I assume the weight is free-hanging from the pulley. Draw a free-body-diagram (FBD) for mass m1 (=0.52) on the table. Write ...

There should be a pulley between the weight and the cart/block. Is the weight free-hanging, or is it on an incline? If it is free-hanging, you need to calculate the acceleration a. Then equate the solve for the tension by equating the tension that will cause an acceleration of...

Just trying to find the correct size for a project
We can take advantage of the symmetry of the isosceles triangle. By cutting the isosceles triangle in two congruent triangles, each right triangle has a long leg measuring 5.25", (height, H). The short leg is half the base, K. Using trigonometry and the definition of ...

Well done! Your answer is correct.

It's correct! Would you care to explain your reasoning?

A necessary condition for a chemical change is that the material final material is different from the original material. For example, burning carbon in air gives carbon dioxide. Material before change: carbon product: carbon dioxide. Since carbon is chemically different from ...

246.25°C is close to the answer, but for the wrong reasons. E=MC(T2-T1) E=115800 J T2=unknown T1=100 °C C=386 J/(kg-°K) Solve for T2. Note: (T2-T1) should be both in °K, but since it is a difference, it is acceptable to have them both in °C.

Since no boric acid has been lost in dilution, we can use the standard equation: C1V1=C2V2 where C1=0.69, V1=1000 mL C2=0.50 Solve for V2. Note: The amount of water to be added is V2-V1.

I assume you have the two pistons linked by a hydraulic liquid, in which case the hydraulic pressures are equal in both pistons. Force/area=pressure, so F1/A1=F2/A2 Here, A1=2 m² A2=4 m² F2=20 N so F1=(F2/A2)*A1 =20/4*2 N =10 N The ratio (A2/A1) is called the ...

Maths (probability)
Multiplication rule: (10/10)*(9/10)*(8/10)=10*9/8/1000

Chemistry - to DrBob
Thank you for pointing out the oversight, and the delicate case difference!

Since no NaCl was lost, we can use C1V1=C2V2 C1=0.8 M V1=750 mL V2=(750-275)=475 mL So C2=C1V1/V2 =0.8*750/475 =1.26 mL Note: I provide an extra significant figure when the first digit is "1". Your teacher may or may not recommend this.

Part A: There are different ways to do this part, but your answer is correct. Hope you used the simplest way. Part B: Again, you answer is correct. Using integration term by term is also correct. Part C: "correct to 3 decimal places" generally means that the sum of ...

Percentage increase = (new price-old price)/old price. Here, new price is $9.68, old price is $9.57. Pull out your calculator to work it out. Post your answer for checking if you're not sure.

Math calculus - Question not clear
Donald, we do not see your original question, and we do not know what subject you're on. It is best to supply sufficient information for others to help you. Advice: Read what you are about to post, BEFORE and AFTER the post, to make sure all necessary information has been ...

Work done = increase in potential energy = mgh. Take out your calculator and find the work done mg=500 N (newton is in force units) h=1.8m Resulting work done is in joules.

This kind of question is best tackled with explorative tools such as Desmos. Go to then type in 1/(x+3) [enter] 1/(x+3)^2 [enter] You will see the effect of squaring (blue curve) on the original (red curve). Experiment with other functions and...

Review of binomial expansion: (a+b)^n =a^n+na^(n-1)b+(n(n-1)/2)a^(n-2)b²+...+nab^(n-1)+b^n =C(n,0)a^n+C(n,1)a^(n-1)b+C(n-2)a^(n-2)b^sup2;.....C(n,n)b^n For n=1 (a+b)1=a+b (a+b)2=a²+2ab+b^sup2; (a+b)3=a³+3a^sup2;b+...

Math - vectors
Velocities are vectors, so they can be added and subtracted similar to displacements in the previous problem. What is important is that to draw the triangle of velocities is to join the head of the first vector to the tail of the next vector. The resultant is the vector ...

Here's one example, along the same lines: A man walk 7km in the direction 270 degrees and then for 9km in the direction 030 degrees. Compass directions are clockwise from the north, so 270° compass = 90-270=-180 in the Cartesian plane. Similarly, 030° compass = 90-...

Step 1:Identify target unknowns. Identify them as variables. Recall that variables do not have to be X and Y. They could be initials to the target unknowns, such as C for carrots, and P for potatoes. Here we have G=number of general admissions sold S=number of student tickets ...

Scott has already given you the rule which is an=1-4n. To check the rule, put n=1, an=1-4=-3 (works) put n=2, an=1-4(2)=-7 (works) To check a8, you can either use the given rule, or you can numerate the terms (8 is not too bad!) -3, -7, -11, -15.....

is the expression to be summed really |sin(4n/π)+3|/4^n, or is it |sin(4nπ)+3|/4^n?

Total Distance = sum of distances in each direction (south, then east). Displacement = distance between end point and starting point, irrespective of path. (hint: use Pythagoras theorem, since the two legs are perpendicular to each other).

y-6≥12 Add 6 to both sides, y-6+6≥12+6 y≥18 Would be the solution. Following link would be good reading and gives more examples.

Algebra 1b
Sorry, above reply is meant to be for Anonymous, not Emma.

haha, on second thought, the 29 should be the denominator of t, as in my first post. It modifies the half-life of the radioactive material. Sorry!

DrBob222, yes, you're right. The problem should read as is, A(t)=(1/29)(1/2)^t with t in years. I got carried away!

First, if you mean A(t)=A0(1/2)^(t/29) the parentheses are mandatory because of the PEMDAS rule. After 20 years, t=20 so A(20)=(1/2)^(20/29) pull out your calculator and find the correct answer. Do not forget the parentheses this time. Post your answer for checking if you have...

Math - to Boi : please review text for completeness
The question contains non-latin or accented letters, and perhaps incomplete. Please correct and resubmit your question.

math - please review question
When posting a question, do not just copy and paste without reading the post before and after. Major reformatting could occur, and has occurred in this case. Please separate the stems and leaves from each other, For example, leaves 1: (4,6,7,9),(2,4),(1,3) stem : 1,2,3 leaves ...

18-15=3 13+4=17 6-4=2 Yes, your answer is correct.

Can you check your expression, please. I am not sure if there is a typo in the second term.

Step 1:Write the chemical equation of the oxidation: CH4+2O2=CO2+2H2O This means that 1 mole of CH4 or 2 moles of O2 will give 1 mole of CO2 Step 2: find limiting reagent CH4: 6/(12+4*1)=6/16=0.4375 mol O2: 5/(2*16)=5/32=0.15625 mol Compare with the equation in step 1, it is ...

Experimental probability is what we infer from an experiment. For example: if we toss a fair coin 100 times, head comes out 44 times. We say that head came out 44 times out of 100 (in this trial), and the experimental probability of head, P(head)=44/100=0.44. We can also say ...

visual basic
There are many steps in writing a program. You need to specify in which area you need help with, pseudocode, debugging, logic, or whatever. We are not going to post a turn-key program for you because you will not have learned anything. Learning to programme is 50% ...

physical science
A. Ethanol "dissolves" in water. In fact, it is miscible, i.e. can be mixed with water in any proportion. This property is often interpreted as "infinitely soluble". B. Iodine is only slightly soluble in water (1:3450).

college algebra
The intuitive solution is by ratio assuming the population can be extrapolated by the sample, thus population =(600*(800/10)=48000.

Algebra 2
Let x1=number of 1-point shots x2=number of 2-point shots x3=number of 3point shots "Josh scored 39 points in a game" => 3x3+2x2+x1=39.........(1) "the same number of 2-point shots as [3-point and free throws combined]" x2=x3+x1 .............(2) "...

Physics 11
The best way to clear up your question is to post the assignment question, and tell us your interpretation or your doubts.

The thickness of the lens is not given, so assume it is a thin lens. Using the thin-lens approximation of the lens-maker's formula, P=1/f=(n-1)(1/R1-1/R2) where n=refractive index of lens material in air R1, R2 are radii of curvature of lens surfaces, using the convention ...

Say each watch sells for $100. then selling 20 watches gives a revenue of $2000, out of which $400 was profit. So cost was $1600, profit was $400. Profit percentage =profit/cost =400/1600 =0.25 =25%

Google and Wiki are good friends when we need word definitions or meanings. cephalization is defined as: the concentration of sense organs, nervous control, etc., at the anterior end of the body, forming a head and brain, both during evolution and in the course of an embryo&#...

Homeostasis is maintaining balance of body functions, such as body temperature, fluid balance, electrolyte balance, etc. Can you find one of the 4 choices that does not serve the purpose of maintaining day-to-day equilibrium of body functions?

stats help
Expectation E(x) is the sum of the products of the revenue/gain multiplied by the probability of the outcome. Here we have three possible outcomes. 1. 5¤ at 10%, product=0.1*5¤=0.5¤ 2. 100¤ at 1%, product=0.01*100¤ =1¤ 3. nothing at 89...

Try to sketch the equations on paper and send us a link to the image, or graph it on and send us the link (we just need the last characters after the last slash, like kssb6j) We'll help you figure it out. But please, post the equations, either here or in twiddla.

Math (Calculus II) (Partial Fraction Decomposition
The equality should read: x/(x^4-a^4)=B/(x+a) + C/(x-a) + Dx+E/(x^2+a^2) The following step is correct. The next step is to expand the right hand side and compare coefficients, so as to set up a system of equations to solve for B,C,D and E. For example, if you assemble the ...

to xx
Don't know you're under xx or "help! pls", but this question cannot have an answer of 0.75 because it deals with experimental probability, which bases it on the outcomes of the experiment. However, the theoretical probability, which is the mathematical answer...

Experimental probability means you go with the number of success in the experiment divided by the total number of trials. Here success is defined as at least one of the coins landed on heads, i.e. includes HH, HT, TH. Count the total number of the above outcomes and divide by ...

Your answers are basically correct, but expressed using unconventional symbols. λ usually represents the wavelength (v=velocity of sound in air). So for the first harmonic, and L=length of open tube of unknown diameter, then λ=2L/1=2*1.5m=3m Frequency, f (in Hz) ...

#1 Question looks incomplete, not sure what "polygon..." stands for what. Please complete question. However, all regular polygons have rotational symmetry. #2 Translation is just one way to tessellate. There are three other ways, reflection, rotation, and glide ...

PHYSICS2, help!
Read up examples in one of which is similar to this one. After this, you can attempt the previous problem you posted, together with your previous knowledge of kinematics and energy principles.

Most supply and demand curves assume perfect competition. An increase in Q (quantity, horizontal axis) means there is a bigger demand (in a competitive market), so price goes up. On the other hand, when there is low demand for the commodity (Q goes to the left), suppliers tend...

Our body is made up of about 35 trillion cells, each of which requires maintenance, hence supply of oxygen. Since the size of cells do not generally vary from person to person, we can reasonably assume that the number of cells vary almost linearly with body weight. We can also...

Consider which of the following has a better efficiency in extracting oxygen? 1. larger/smaller surface area 2. more/less lamellae 3. thicker/thinner lamellae

To be efficient, a fish applies the counter-current principle, i.e. the most oxygen-poor blood will extract the remaining oxygen from the most "stale" part of the water stream. Does that tell you which is the direction of blood flow?

Air has a small mass & viscosity and contains 20% oxygen, while water has a much higher mass & viscosity and contains less oxygen (~5%). What do these considerations alone tell you? If you wish, further reading & discussion can be found here:

Oceans actually supply moisture to air, provided the water temperature is warm. Currents generally transport heat OR absorb heat in large quantities. Read up about El Nino and Arctic currents, for example: http://www.windows2universe....

Let x=east, y=north, then the location of the ship after two hours is (-20, -55) Since it has constant course and speed, after one hour, it is at (-10,-27.5) The course is tan-1(-10/(-27.5)) west of south, and the speed is the distance travelled, using Pythatorean theorem, s=...

Let L: y=mx+c C: (x-a)²+(y-b)²=r² And if L is tangent to C, then we can solve for the intersections of the line L with circle by substituting "y" in the circle with mx+c, thus C: (x-a)²+(mx+c-b)²=r² Expand and solve for quadratic in x to...

discrete math - To Akash
I hope you realize that 3 of the four questions that you posted have been answered before you made these reposts.

So what are your choices?

discrete math
* least

discrete math
Assuming question asks (b) The length is 8. Number of 1s is at lease 3 more than number of 0s. (c) The length is 9. Number of 1s is at lease 3 more than number of 0s. For length n, let n0=number of zero bits n1=number of one bits and n0+n1=n (b) For case n=8 situations where ...

discrete math

discrete math
I assume you have learned about the ball-and-bin problem in your calls. It may have been called the star-and-bar problem, which is easier to visualize mathematically. Try to read over your notes and post your answer for a check if you wish. If you still have difficulties, feel...

(10,6) means x=10, y=6. To check if (10,6) is a solution to y=x-4, substitute into the equation values of x and y, i.e. y=6 (left hand side) x-4=10-4=6 Since left equals right hand side, (10,6) is a solution of y=x-4. Go through each of the answer choices to choose the correct...

Mark-up percentage equals (selling price-cost price)/(cost price). For example, if I buy a case of oranges for $25 and sell it for $30, the mark-up is ($35-30)=$5 and the percentage mark-up is $5/$25=20%.

Vector Calculus
In your previous post, you have been asked what R3 stands for, and you have not clarified. We do not know yet if 3 is a superscript, a subscript, or just a number written in the wrong place. Yes, ? equals a vector < -sinφ, cosφ, 0 >. Also, are R,φ and z ...

what happen i need an answer
Another way to find out where you got stuck is to formulate your question in multiple posts. This way you can zoom in to where the problem lies. Or replace vectors <i,j,k> with (i,j,k), etc. but state that (i,j,k) is a vector.

Only the vertical component counts for the time for descent. Assuming no air resistance, we have from kinematics, S=ut+(1/2)at^2 where S=distance = 6400 ft u=initial velocity (=0 ft/s vertical in this case) a=acceleration due to gravity, g=32.2 ft/s² Substitute values, ...

Use kinematics equation: v1²-v0²=2aS v1=final velocity (0 m/s) v0=initial velocity (20 m/s) S=distance travelled (100 m) solve for a=acceleration (negative because it's a deceleration) Use Newton's second law F=ma m=mass F=average (uniform) force over the ...

First the chemical equation, combustion of a hydrocarbon yields CO2 and H2O most of the time. 2C2H2(g)+5O2(g) ? 4CO2(g) + 2H2O(g) We see that 2L of C2H2 produces 4L of CO2 and 2L of H2O. However, when cooled to STP, H2O condenses to water (l.)

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