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Posts by MathMate

Total # Posts: 11,748

Counting and Probability
These are very interesting problems. If you show some efforts in solving them, there would be likely to be more chances of response.


Algebra 2

Hint: the ratio is 2:3, so from A to B, it is 2/(2+3)=2/5. The coordinates of M are: M(xa+(xb-xa)*2/5, ya+(yb-ya)*2/5)

Algebra 2
x-intercept is obtained by solving for x after setting y=0. For example: f(x)=x^2+2x+1 set y=f(x)=0, then x^2+2x+1=0 (x+1)²=0 x=-1 (x-intercept) y-intercept is obtained by solving for y after setting x= 0. For example : f(x)=x^2+2x+1 Set x=0, then f(x)=y=0^2+2(0)+1=1 y=1 ...

Numerical Analysis MATLAB

Math - ratios
Let N=number of papers graded in 1.5 hours (90 minutes). Use ratio (assuming the grading rate is constant) 5 papers: 45 minutes = N papers : 90 minutes. Cross multiply: N=(5/45)*90=10 papers.

There are two ways to solve this problem. A. The intuitive (and fast) approximation is by prorating the ratio, assuming that the ratio is constant. Let N=total population, then N/30=20/4 => N=150 B. The more accurate (and elaborate) way is to use the hypergeometric ...

Let x=cost of pizza. then 3x/8+4=5x/8+1.5 solve for x.

math-legs and heads, again
See response at

math-legs and heads
You can choose to do the sum mentally as follows: If all the animals were ducks, there would be 2*22=44 legs. Since there are (60-44)=16 more legs, there must be (16/2)=8 dogs, the rest (22-6)=14 ducks. If you prefer to solve the sum mathematically, you would set up an ...

Since the area is bounded by two parallel lines y=5 and y=-3, the area is a trapezoid, with a height of (5-(-3))=8. We need to find the intersection of the line y=2x-5 with each of the parallel lines. Setting 5=2x-5 => x=5 Setting -3=2x-5 => x=1 So the upper width is (8-...

(2+x)(-sinx) is an expression, and cannot be solved. To solve an equation, the expression must be equated to a value, such as x²+2x+1=0

This is an elastic impact problem. Impact problems have one available equation, namely conservation of momentum. m1u1+m2u2=m1v1+m2v2. u, v represent initial and final velocities respectively, and m1, m2 are masses of bodies involved. Note that velocities have signs, e.g. ...

To Physics nerd
When expression exponents, please precede the exponent by the ^ sign. For example, 10² should be written as 10^2. 102 means one hundred and two, (write 10^2) 103 means one hundred and three, (write 10^3) Confusions will arise if the numbers are not expressed correctly.

Hint: un repas

Discrete Mathematics. Need Help
For R to be an equivalence relation, it must satisfy all the following conditions: 1) Reflexivity, i.e. (a,b)R(a,b) ∀(a,b). 2) Symmetry, i.e. (a,b)R(c,d) => (c,d)R(a,b) 3) Transistivity, i.e. (a,b)R(c,d) and (c,d)R(e,f) => (a,b)R(e,f). Use the definition of R to ...

Cht Ningi
T(9)=29.............9th term T(22)=55............22nd term If the AP is T(n)=T(n-1)+d, then d=(T(22)-T(9))/(22-9)=26/13=2 T(1)=T(9)-(9-1)d = 13 and therefore T(n)=11+2n T(1)=13 T(60)=11+120=131 To find the sum of the 1st to the 60th term, we use Little Gauss's method: T(1...

This we need to make two assumptions: 1. The car is on a perfectly horizontal plane/road 2. The car is in neutral AND friction is negligible. Use Newton's second law: F=ma F=400N m=(200 + 50n ) kg n=number of bags. a=1 m/s^2 (acceleration is measured in m/s^2) Set up ...

Ap physics
Use continuity equation, namely the volume of sand coming out per second equals the diameter * speed of sand. Volume = 75 L/min = 1.25 L/s Total area of jets (d=diam in dm) =2π(d²)/4 Speed of sand = 45 m/s = 450 dm/s Equate volumes of sand 450*2π(d²)/4=1.25 d=...

Let the number be x. then x+1/x=29/10 Solve for x. The answers are rational fractions.

First we have to decide how many slices we cut the pizza! It could be 8, but inspiring from the mushroom of 4/16 slices, I assume it is a large pizza cut into 16 slices. Then we add up the fractions to get toppings to cover 3/4+5/8+4/16=26/16 of the pizza. Evidently, if we ...

Mechanical engineering
With a point load in the middle, draw the bending moment diagram, which is a triangle with zero at both ends, and linearly increasing to the middle at R1*L/2. In fact, the standard formula for the maximum bending moment for a centrally placed point load is PL/4. Review your ...

Physics 101
Increase in length = Length (m) * ΔT (° C) * coefficient of expansion (°-1)

0 HP if there is no friction, pulling at a steady speed on a level road does not do work. If there is kinetic friction μk, then F=force = μk * mg v=velocity = 10 m/s Power = F.v j/s = F.v watts

In the long run, it would be equivalent to 120 plays with 120*0.60=72 as revenue and the following payouts: 97 green at 0.95 22 yellow at 0.40 1 red at 11.00 Subtract payouts from revenue and divide by 120 plays to get gain on individual play.


This is a free fall situation. The horizontal velocity has no effect on the time to reach ground. Vertical distance, X=0+(1/2)at^2 =0+(1/2)(-9.81)*3^2 =44 m approximately.

The "jerk" depends on the difference between static friction (the stickiness) and kinetic friction. The former is always greater than (perhaps or equal to) the kinetic friction. You need to estimate the mass m of the drawer, the force F required to overcome the ...

Resolve the initial velocities into the horizontal component, vx =v0 cos(θ) and the vertical component, vy= v0 sin(θ) where θ=-20 degrees (below horiz.) The horizontal component is subjected to only air resistance which in general is neglected, so travels at ...

basic chemistry(projectile)
Use sum of potential and kinetic energies = constant when air resistance is neglibible. Potential energy = mgh at a height h from datum kinetic energy = (1/2)mv^2 when moving at a speed of v.

Physics - Inverted pendulum
* d²y/dt²

Physics - Inverted pendulum
Interesting problem. The vertical motion exerts an acceleration of d²y/dy² on the mass. Intuition tells me the mass will move on each side on successive vertical strokes, hence frequency = ω/2. Next time ask him to drill his calculus and give the bambin a mug ...

In the absence of air resistance we can split the movement of the bullet into the vertical and horizontal components. The former is a free-fall. Using the kinematics equation below, we can solve for the time it takes to free-fall through 2.4 cm: S=(v0)t+(1/2)at^2 with v0=...

We have a right triangle ABC, CA lies on the equator, where C is the destination (where plane intercepts the equator). B is the initial position of the plane, and is immediately south of A. So AB=150 km, ∠ABC=30°. We need length of BC. Using definition of cosine, AB/BC...

The faster automobile is basically playing a catch-up game, with a distance (gap) of 146 m. at a catch-up speed of 72.5-55.5=17 km/h. Converting this speed to m/s: 17 km/h = 17*1000 m/3600 s = 4.72 m/s How long will it take to catch up a distance of 146m at a speed of 4.72 m/s...

ignoring air resistance, we can apply the kinematics equation v1^2-v0^2=2aS S=distance travelled = 3 m v0=initial velocity (to be found) v1=final velocity =0 m/s at highest point a=acceleration due to gravity = -9.81 m/s^2 Solve for v0 and show that it is approximately 7.7 m/s...

1. draw a free-body diagram. 2. Let T be the tension in each of the wires, which makes an angle of 27° with the vertical. 3. Sum forces on the sign in the y-direction (vertical) to get 2Tcos(27°)=23kg * 9.81 Solve for T.

I am not sure if I understand what you're supposed t find. But here's what I have found. I have mod(23*17,26)=1 (and not 9), so 23 cannot be the multiplier. I found it by trial and error, that mod(25*17,26)=9, (encrypting) mod(25*9,26)=17, (decrypting). So 25 is the ...

P(A and B) represents the probability that both events A and B occurring. Physically, it means that a person has both private and government insurance, which is unlikely. The probability of having any insurance is the sum of the two probabilities, i.e. P(A or B) = P(A) + P(B...

If we assume uniform acceleration, we can use: ΔX=(v0)t+(1/2)at^2 v0=initial velocity = 0 m/s t=time=8.6 s ΔX=displacement=0.1994 m Solve for a (in m/s^2)

It is decelerating over the three seconds, with v0=initial velocity=+58 m/s acceleration due to gravity, a = -9.81 m/s^2 time, t=3 s Use kinematics equation: Displacement=(v0)t+(1/2)at^2 Substitute above values to get displacement.

Use v1^2-v0^2 = 2aS v1=final velocity v0=initial velocity a=acceleration S=distance Use an appropriate frame of reference such as positive = upwards.

Use v1^2-v0^2 = 2aS v1=final velocity v0=initial velocity a=acceleration S=distance Use an appropriate frame of reference such as positive = upwards.

Z table
Draw a sketch of what you want, similar to this: THen look up the standard normal distribution table (left tail) the number of standard deviations that correspond to 92%. (it should be between 1.4 and 1.5). Since each standard deviation corresponds to...

This is an expression derived from Bernoulli's equation, so use all the values and substitute in the given equation, making sure that the dimensions are compatible. Check dimensions (C is dimensionless) F=(1/2)CAρv^2 =m^2*kg/m^3*(m/s)^2 =m-kg/s^2 = same unit as Newton...

Please start with a free-body diagram, then resolve forces parallel and normal to the slope. See Assuming the skier (the round object) is moving up the slope, then the friction force is towards downslope. The towbar force is therefore, equating forces...

Like this? But we need the height of the building, H.

Use v1^2-v0^2=2aS v1=final velocity v0=initial velocity (0 for a free-fall) a=acceleration due to gravity (=-9.81 m/s^2) S=-38.5m solve for v1.

v0=15.5 v1=0 v1=v0+at Solve for t=(0-15.5)/(-9.81)=1.580 sec. So it will return to the same elevation as it left off in 2*1.580=3.16 s. Instead, it took 3.3-3.16=0.14 sec. more Using the free-fall equation for H, H=(1/2)gt^2, we have H1=(1/2)g(1.580)^2 H2=(1/2)g(1.720)^2 ...

Use v1^2-v0^2=2(a)(Δx) or Δx = (v1^2-v0^2)/(2a) a=acceleration, v0=initial velocity v1=final velocity Do not forget to convert km/h to m/s to get your answer in metres.

First find from the book or Internet the Young's modulus (E) for aluminium. I use E=69 GPa for aluminium. Using stress = force (mg) / cross sectional area ε=Strain = extension/unit length = stress/E stretching = extension =ε * length =stress*length/E you ...

Average velocity = (change in position)/time Assume initial position = (0,0) First determine the displacement of the train at the end of the trip: movements(N): 1. 43 km/h for 20 min = 43/3 km due east 2. 43 km/h for 25 min at N54E = 43*25/60 km at CCW 36° from due east 3...

It is a question which requires an unreasonable assumption, namely ignore air-resistance. Without air-resistance, time it takes to reach ground is t=sqrt(2H/g) =sqrt(2*10000/32.2) =24.9 s The horizontal velocity of the plane does not change the time required. If the dimensions...

a) correct. b) use t=sqrt(2h/g) Time to go up: h=5.1m Time fall back to the ground: h=7.1m Add the two times to get your answer.

Have you done Baye's theorem, total probability and conditional probability? If not, you need to review these topics before you can tackle this problem. Here the assumption is not clear, but I will assume that it is equally probable to 1. pick one of the 4 baskets 2. pick ...

Time to free-fall 35.56m = sqrt(2*S/g) = sqrt(2*35.56/9.81) = 2.6925 s Horizontal velocity does not change during free fall, so v= Dist/time = 10.36 m/2.6925s = 3.81 m/s

Horizontal velocity does not change in a free-fall, so time = distance/velocity = 146.8/29.33 = 5.0051 s. (keeping 5th significant fig.) Initial vertical velocity = 0 for free fall, so H=(1/2)at^2 =(1/2)*(-9.81)(5.0051^2) =-122.9 m Ans. the ground is 122.9m below the cliff.

Assuming zero friction, the additional force is the equilibrant. We have a force of +480 N and -920 N. The equilibrant is the negative of the vector sum, namely -(480-920)=440 N, i.e. 440 N in the same direction as the 480N force. If friction is present, some additional steps ...

finite math
*correction I get a little less than 2500.

finite math
If you make N=27 annual payments of A=$175 with annual interest of i=0.053, the future value is FV=A(1+R+R^2+...+RN-1) =A(RN-1)/(R-1) =A(RN-1)/i where R=1+i The present value is then PV=FV/(RN) =A(RN-1)/(i*RN) I get a little over 10000.

Use equality of proportions object:shadow x:12 = 5 m : 6 m which means x/12=5/6 Cross multiply: 6x=5*12 Solve for x x=60/6=10 So the tree is 10 m tall

Hmm...It would be nice if you start working on the problem, show some thoughts and work of your own, identify the difficulties, so that we can help you.

Hint and example: distributive property means the equivalence of the following expressions: a(b+c) = ab + ac Example: 5(x+4) = 5x + 5(4) = 5x + 20

A typical line in slope intercept form is y = mx + b where m is the slope and a is the y-intercept. Two lines are parallel whenever their slopes (m1, m2) are identical. Try to spot two lines with identical slopes and find the corresponding choice of answer.

Solve for x from the equation: 5x-4 = 2(2x+10) 5x-4 = 4x + 20 5x-4x = 20+4 x=24 so angle ABC = 5(24)-4 = 120-4=116 degrees. What kind of angle is angle ABC?

French SraJMcGin
To Rose: If you mean : "if you make up the sentences in English and translate it to French, how to make sure it will be translated to the subjunctive" then SraJMcGin has already given you all the conditions that the sentence should be subjunctive in French. The ...

Please refrain from starting a new thread when information refers to a previous thread.

"last one is $300" So you would write a table as follows Date description amount Balance -......bal.brought fwd - 2000 Jan 2...deposit 500 2500 Jan 10..Alex co. 600 1900 Jan. 16 Angels co. 300 --?-- So you can calculate the final balance on the last line.

It is an optimization problem. Here are some steps to solve the problem: 1. define variables (values that are to be found). 2. Reread the question, and translate each constraint into an inequality. 3. Graph the constraints and select the feasible region, using the variables as...

math (incomplete)
There are critical characters that are not legible in the post. Please amend the post, or repost.

For every child ticket, 2.25 adult tickets were sold. This is the same as For every 4 child tickets sold, 9 adult tickets were sold, for a total of 4*2+9*9=$89. Number of sets of sets (4+9) sold = 520/13=40 Total amount = 40*$89=$3560 Alternatively, using algebra, A=number of ...

surface area = 4πr^2 Volume = 4πr^3/3 S/V ratio = 4πr^2 / (4πr^3/3) = 3/r

Base Area = triangle base * triangle height /2 Prism volume = Base Area * height You have been given triangle base: 7 ft triangle height: 4 ft prism height:8.5 ft Apply the above formulas to calculate the volume required.

Math- simple polynomials
Can you explain how you got 4 and 1/9 please. I prefer to see you post the answer, not the letters. This way you have an extra chance of checking your answer.

Hint: Reminds me of the Fibonacci numbers.

one light-year is the distance light travels in one year. Light travels at a speed of 3*10^8 m/s. In one year, there are 365*24*60*60 seconds. So one light-year = 3*10^8 * 365*24*60*60 m = 9.461*10^15 m = 9.461*10^12 km (since 1km=1000m)

the value is 7 choose 4, or choosing 4 students out of 7 (order does not count). "7 choose 4" can be evaluated as 7C4 = 7!/((7-4)!4!) = 7!/(3!4!) = 5040/(6*24) = 35

Calculus 2
hints: use the relations: x=rsinθ y=rcosθ which means the left-hand side =x²+y²=r² Also 8sin2θ = 16 sinθcosθ =16(y/r)(x/r) =16xy/r² Equating both sides, x²+y² = 16xy/r² or (x²+y²)² = 16xy =2xy/(x&...

Math (Solving Equations)
No, you do not distribute the absolute value signs. What you did is correct, i.e. keep the absolute value quantity intact, and eventually evaluate the value as either positive or negative. |x-1|=5 means x-1=5 => x=5+1=6 or -(x-1)=5 => x=1-5=-4

Discount is calculated by the formula: Discount = Maturity value * discount rate * discount period. Here I assume "face value" is what the bearer receives on maturity. So discount = 2200*0.09*140/365 = $75.95 You can read the following link for more details: http://...

Computer science
Pseudocode is almost like human language input billed_amount; amount_with_tax=billed_amount * 1.09 Total=amount_with_tax*1.15 output total

Exactly, well done! :)

In math, knowing the definition of the terms is key to solving the problem. What you have attempted to find is the mean (or average), not the median. Here the key term is "median", defined as follows: "To find the Median, place the numbers you are given in value...

Pre-Calculus (absolute values)
Knowing the definition of specific math terms helps solving the problem, most of the time. Here the term is invariant point, which is usually called fixed point, defined as follows (Wiki) "In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an ...

μs determines when skidding will begin. Maximum centripetal force provided by static friction = (μs)mg Maximum speed = v, centrifugal force = mv^2/r At equilibrium, (μs)mg = mv^2/r Solve for v v=sqrt(μs * rg) =sqrt(0.85*215*9.81) =42 m/s approximately

To Anono
Lucina has been giving you excellent and patient help. Please appreciate her time dedicated. If you want correct anwers, you need to do your part by checking the questions/answers that you post. Any typo in the post will give you a right answer to the wrong question. For ...

Plane Trigonometry
This is a very common problem for surveyors to find distances between two objects which they cannot reach. The same principle is used to find difference in heights. Surveyors can do this today because the newer generation of theodolites can measure distance without a prism ...

factors do not cancel when we add, only when we divide. For example, 2π+5.5π =(2+5.5)π =7.5π or 12πr²+23π =(12r²+23)π

Assume decimal digits, so there are 9 non-zero decimal digits [1-9]. The probability that the second digit is 8 is one choice (8) out of 9 possible digits = 1/9. Using conditional probability, Let event of getting (8) = 1/9 so assuming independence of the choice of digits, P(...

Use amount = principal * ert where principal = initial investment e=napier's constant=2.7182818284... r=annual rate of interest t=time in number of years Example: 1000$ invested for 3 years at 6% amount = 1000 * e0.06*3 = $1197.22

Fast method: Ratio of boys to girls = (69-65):(75-69) =4:6 =2:3 Number of boys = 80*2/(2+3) = 32 Standard method: Let x=number of boys (75*x + 65*(80-x))/80 = 69 Solve for x 75x-65x = 69*80-5200 = 320 10x=320 x=32 Answer: there are 32 boys.

Use Amount = principal * (1+i)^n principal=initial investment number of periods (of 3 months) = 10*4=40 i=interest per period = 3.5%/4=0.00875

Linear Functions
As an example, e=300 means she earns 300 per week flat salary. e=0.05s means she gets paid 5% of weekly sales. If she gets both a base salary and a commission of 5%, then e=300+0.05s Adapt the example to solve the given problem.

As a rough approximation, we will assume that the decrease in area is directly proportional to time. 1. Calculate the number of months between September and March = 6 2. Calculate the total decrease in area = (18-3) = 15 million square kilometers. 3. Calculate average decrease...

In math, knowing the definition of related terms can help solve a large number of problems. For example, if we know the definition of price elasticity, we can solve the above problem. Definition: The elasticity is represented in numerical form, and is defined as the percentage...

Start with the anti-symmetry of sine sin(x)=-sin(-x) so sin(-15°)=-sin(15°) Now use cos²(x)-sin²(x)=cos(2x) cos²(x)+sin²(x)=1 Subtract first equation from second: 2sin²(x)=(1-cos(2x)) sin(x)=sqrt((1-cos(2x))/2) Put x=-15° sin(15°) =-sin...

university of hartford
If velocity = v(t), then displacement s(t) = ∫v(t) Use s(0)=6 to determine the constant of integration. For example, if v(t)=3x² then s(t)=∫v(t)=x³+C Given s(1)=4, we have 1³+C=4 => C=3 So s(t)=x³+3

1. correct For the rest, think about: 2 & 3 Probability of two independent events: for two independent events A and B to both happen, the probability is P(A)*P(B) Example: The probability of throwing a 4 from a number cube AND drawing a red card from a standard deck is (1/6)*(...

sx=reflection about the x-axis (x,y)->(x,-y) so (x, 2(x+3)^2-1 ) -> (x, -(2(x+3)^2-1)) = (x, -2(x+3)^2+1) Now apply the translation of 5 units down to get the answer.

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