# Posts by MathMate

Total # Posts: 11,744

**Physics**

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

*October 15, 2015*

**Finite**

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.

*October 13, 2015*

**Math**

48+34=48+2+32=50+32=82

*October 12, 2015*

**Physics**

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.

*October 12, 2015*

**Physics**

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 ...

*October 2, 2015*

**physics**

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 ...

*October 2, 2015*

**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.

*October 2, 2015*

**Physics - Inverted pendulum**

* d²y/dt²

*October 2, 2015*

**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 ...

*October 2, 2015*

**physics**

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=...

*September 30, 2015*

**Physics**

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...

*September 30, 2015*

**Physics**

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...

*September 30, 2015*

**Physics**

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...

*September 29, 2015*

**Physics-Urgent**

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.

*September 27, 2015*

**Cryptography**

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 ...

*September 27, 2015*

**Stats**

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...

*September 27, 2015*

**Phyics**

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)

*September 26, 2015*

**Physics**

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.

*September 26, 2015*

**physics**

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.

*September 25, 2015*

**physics**

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.

*September 25, 2015*

**Z table**

Draw a sketch of what you want, similar to this: http://prntscr.com/8kitsp 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...

*September 25, 2015*

**physics**

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...

*September 25, 2015*

**Physics**

Please start with a free-body diagram, then resolve forces parallel and normal to the slope. See http://prntscr.com/8kinmn 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...

*September 25, 2015*

**physics**

Like this? http://prntscr.com/8kiqq7 But we need the height of the building, H.

*September 25, 2015*

**physics**

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.

*September 25, 2015*

**physics**

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 ...

*September 24, 2015*

**Physics**

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.

*September 24, 2015*

**Physics**

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 ...

*September 24, 2015*

**physics**

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...

*September 24, 2015*

**physics**

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...

*September 24, 2015*

**Physics**

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.

*September 23, 2015*

**probabilty**

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 ...

*September 23, 2015*

**Physics**

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

*September 23, 2015*

**Physics**

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.

*September 23, 2015*

**Physics**

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 ...

*September 5, 2015*

**finite math**

*correction I get a little less than 2500.

*September 4, 2015*

**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.

*September 4, 2015*

**Math**

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

*August 26, 2015*

**BUSINESS CONSULTING**

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.

*August 25, 2015*

**Math**

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

*August 25, 2015*

**Math**

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.

*August 10, 2015*

**math**

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?

*August 10, 2015*

**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 ...

*July 17, 2015*

**math**

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

*June 15, 2015*

**math**

"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.

*June 15, 2015*

**math**

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...

*June 8, 2015*

**math (incomplete)**

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

*June 8, 2015*

**Math/ASU**

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 ...

*May 29, 2015*

**Geometry**

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

*May 29, 2015*

**Math**

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.

*May 22, 2015*

**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.

*May 21, 2015*

**Algebra**

Hint: Reminds me of the Fibonacci numbers.

*May 17, 2015*

**Math**

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)

*May 17, 2015*

**Math**

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

*May 17, 2015*

**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&...

*May 17, 2015*

**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

*May 17, 2015*

**math**

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://...

*May 16, 2015*

**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

*May 13, 2015*

**Math**

Exactly, well done! :)

*May 12, 2015*

**Math**

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...

*May 12, 2015*

**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 ...

*May 12, 2015*

**Physics**

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

*May 12, 2015*

**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 ...

*May 12, 2015*

**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 ...

*May 11, 2015*

**geometry**

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

*May 11, 2015*

**math**

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(...

*May 10, 2015*

**math**

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

*May 10, 2015*

**Maths**

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.

*May 10, 2015*

**algebra**

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

*May 10, 2015*

**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.

*May 9, 2015*

**math**

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...

*May 9, 2015*

**Math**

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...

*May 7, 2015*

**Math**

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...

*May 6, 2015*

**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

*May 6, 2015*

**probability**

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)*(...

*May 5, 2015*

**Math**

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.

*May 5, 2015*

**mathematic**

base radius = r = 5 cm cone height = h = 12 cm Use Pythagoras theorem to find slant height slant height, L = sqrt(5²+12²) =sqrt(169)=13 cm Total surface area = π r²+πrL Substitute numerical values to get numerical answer.

*May 5, 2015*

**Calculus**

When f'(x) > 0, the function is increasing. Conversely, f'(x) <0, function is decreasing. Thus the function is increasing in the interval (-∞,-3], and decreasing on [-3,∞). This makes a maximum at x=-3. Since we do not know anything about f"(x), ...

*May 4, 2015*

**Math-Probability**

Could you please post the whole question in its original form before you make your comments, please? What is not clear is if the audit is selected/done only on those who got a refund, or a selected proportion (1.01%) of all the returns are selected at random for audit. ...

*May 3, 2015*

**Math-Conditional Probability**

Please post the exact original text of the question. We need to examine the wording, even the punctuation to interpret correctly the given information. Confirmation is needed for: - is 85.6% out of the unaudited general population? - Are 49097 and 1342674 the revised ...

*May 3, 2015*

**Trigonometry**

Very true, thanks Steve.

*May 3, 2015*

**Trigonometry**

Many math problems can be solved by understanding the definition of the key term involved. In this case, the key term is the inverse of a (trigonometric) function. From Wikipedia: "In mathematics, an inverse function is a function that "reverses" another ...

*May 3, 2015*

**Math**

When adding polynomials, group like terms (which have identical powers of variables). (8x^2 + x^2) + (- 7x - x + 2x) + (5y - 3y) notice how the x terms were grouped, preserving all the signs. The first group (8x²+x²) would give 9x² with no ambiguity. The same is...

*May 3, 2015*

**statistics**

In a normally distributed random variable, the probability of X≤μ is exactly 0.5, since the normal distribution curve is symmetrical.

*May 2, 2015*

**Math HELP! Ms.Sue**

First you need to be able to interpret the stems and leaf plot (since there are two stems). The two bars enclose the 10's digit, and the numbers to the left of the first bar represent the units digit for soil A, and the numbers to the right of the second bar stands for the...

*May 2, 2015*

**math**

The answer is correct. Don't know what you did until you posted your work.

*May 2, 2015*

**Physics Help Please --- Telescope**

b. Magnification is a pure number (no units) c. When turned around, fe=17, fo=114 M=?

*May 2, 2015*

**Maths(URGENT ANSWER please )**

The series 1 + 4/3! + 6/4! + 8/5! is Σ2k/(k+1)! for k=1,∞ =2Σk/(k+1)! k=1,∞ =2Σ(k-1)/k! k=2,∞ =2Σk/k!-1/k! k=2,∞ =2Σ1/(k-1)! k=2,∞ - 2Σ1/k! k=2,∞ =2Σ1/k! k=1,∞ - 2(Σ1/k!-2) k=0,∞ =2...

*May 2, 2015*

**engineering mechanics**

We don't get to know because we do not have the chance of looking at the numerical values in the diagram that you have in front of you.

*May 2, 2015*

**algebra**

If √N=a√3 then N=a²*3 = 3a² Substitute 3 integer values of a to find 3 possible values of N.

*May 1, 2015*

**conditional probability**

Many basic math problems can be solved by understanding the definition of terms. Conditional probability P(E|F)=conditional probability that event E will occur given that event F has already occurred = P(E∩F)/P(F) Therefore P(F|E)=P(F∩E)/P(E) =P(E∩F)/P(E) since the...

*April 30, 2015*

**probability**

First make a 6x8 table of the possible outcomes (sample space, 48 points). For random throws, each of the 48 points has equal probability (p(i,j)=1/48). a. Expected value of sum of two dice: E[X]=Σ p(i,j)(i+j) i=1,8, j=1,6 Where p(i,j)=1/48, and i+j can be taken from the...

*April 30, 2015*

**maths**

Knowing that one mango costs $2.40, we can set it up as 2A+2(2.40)=5A+2.40 and solve for A.

*April 28, 2015*

**Math 222**

A perfect square has the form (y+a)²=y²+2ay+a² If you compare with y²-18y+a² you can find a by equating the second term and solving for a: 2ay=-18y

*April 27, 2015*

**Chemistry**

* molar mass

*April 27, 2015*

**Chemistry**

The N:O ratio can be obtained by dividing the % mass by the respective atomic masses, namely N:O = 30.4/14 : 69.6/16 = 2.17:4.35=1:2 Use the 5.25g sample and the ideal gas law to find the molecular mass and hence the composition.

*April 27, 2015*

**Chemistry**

Convert the volume to V at 1 atm. At 25°C, the molar volume is 24.465 L. Use proportion to find the molar mass, M 0.642/V = M/24.465

*April 27, 2015*

**statistics**

The sample space has 36 equiprobable outcomes. You can enumerate the successful outcomes and divide by 36. Here's another approach: Success of at least one odd number means that a failure is when both are even. Probability of a failure is (1/2)*(1/2)=1/4, we gather that ...

*April 26, 2015*

**Physics**

From the given information, we deduce that It takes 4.184 J/g * 1000 g = 4184 J to raise the temperature of 1 L of water by 1°C. Assuming that all 1000J of heat are absorbed by the 1 L of water, then by proportion, the temperature increase equals 0.239°C. 1°C * (...

*April 26, 2015*

**STATISTICS**

See earlier Q & A.

*April 25, 2015*